Optical Properties of (Zn, Mn) and (Cd, Mn) Chalcogenide Mixed Crystals and Superlattices

Review Article

phys. stat. sol. (b) 146, 11 (1988)

Subject classification: 78.20; 71.35; 78.55; S8.1

Sektion Physik der Hztmboldt- Universitat zu Berlin, Bereich, Halbleiteroptik’)

Optical Properties of (Zn, Mn) and (Cd, Mn) Chalcogenide Mixed Crystals and Superlattices

BY 0. GOEDE and W. HEIMBRODT

Contents

1. Introduction 2. Conventional mixed-crystal properties 3. Optical properties due to internal transitions in the Mn2f 3db ions 4. Energetic position of the Mn 3d-states 5. Mn2+ 3db spin correlation due to superexchange interaction and mean spin density in

a magnetic field

5.1 Mn chalcogenides 5.2 (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals

6. Optical and magneto-optical properties due to s,p-d exchange interactions

6.1 Magneto-optical properties of the mixed crystals 6.2 s, p-d exchange-interaction-related properties of the mixed crystals in zero

magnetic field 6.3 Mn chalcogenides

7 . Optical properties of multi-quantum-well stvucticres and superlattices

7.1 Valence and conduction band related properties 7.2 Special properties due t o Mn 3d-states

8. Concluding remarks

References

1. Introduction

(Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals a,re typical and the most extensively studied diluted magnetic (‘semimagnetic’) semiconductors. Their remarkable physical properties are characterized by the combination of a usual semiconductor mixed-crystal behaviour with the special properties caused by the half-filled 3d-shell of the Mn2+ cations. For both basic and applicative reasons in the last few years they found a continuously growing interest (see, e.g., earlier reviews [l to 51) which has been further stimulated recently by the successful preparation of multi-quantum- well structures and superlattices on the basis of these materials.

l) Invalidenstr. 110, DDR-1040 Berlin, GDR.

12 0. GOEDE and W. HEIMBRODT

The new physical properties of the semimagnetic (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals are based on the the strong S, p-d exchange interaction between electron or hole band states and the Mn2+ 3d-electron states. It leads to a giant increase of magneto-optical effects as exciton Zeeman splitting, Faraday rotation, and donor spin-flip Raman scattering, which formally can be described by a MI?+ ion-induced enhancement of the effective g-factor of these materials by up to two orders of magnitude. Furthermore, principally new interesting effects occur also in zero magnetic field as bound magnetic polaron formation. A possible application of these materials for magnetic-field tunable optoelectronic devices may be supported by the actual development of high-T, superconductivity magnets.

I n the present paper mainly the optical properties of the six broad-gap ternary mixed crystals (Zn, Mn) and (Cd, Mn) sulfide, selenide, and telluride are reviewed with emphasis on the considerable similarities between all members of this family. As many hundreds of relevant papers exist, only a restricted number could be given in the references. The (Hg, Mn) chalcogenides are not taken into consideration as their widely studied, most interesting properties appear in the small-gap (Hg-rich) region and are mainly connected with electrical conductivity phenomena (see [3]). On the other hand, the pure Mn chalcogenides are included to point out the existing inter- dependences, leading t o valuable conclusions but also to open questions.

The first section is dedicated t o those conventional optical properties of the mixed crystals which are not essentially influenced by the Mn 3d-states. Then the optical properties due t o internal transitions in the Mn2+ 3d5 cations are considered as a function of. the Mn concentration. A t present these results are only incompletely integrated in the discussion of the s, p-d exchange-interaction-induced properties of these materials. The antiferromagnetic Mn S = $spin correlation due t o superexchange interaction and the paramagnetic mean spin density in a magnetic field known from magnetic investigations are described in Section 5 as far a s necessary for the following. I n a main chapter then the specialities of the optical and magneto- optical properties are considered which are caused by the exchange interaction between the s-like conduction or p-like valence band states and the Mn 3d-states. Final- ly, the present knowledge on the optical properties of multi-quantum-well structures and superlattices prepared with (Zn, Mn) or (Cd, Mn) chalcogenides is reviewed.

2. Conventional Mixed-Crystal Properties

The (Zn, Mn) and (Cd, Mn) chalcogenides are ternary (pseudobinary) mixed crystals with randomly distributed Mn2+ ions in the cation sublattice.2) Most of the experimental results described in this review were obtained using high-quality single crystals grown by techniques well-known for the corresponding pure Zn or Cd chalcogenides. A detailed review of the (Zn, Mn) and (Cd, Mn) chalcogenide crystal preparation is given in [8]. For the tellurides and selenides and partly for (Cd, Mn)S a modified (high-pressure) Bridgman technique is successfully applied. The sulphides are mainly grown using the I,-transport method. I n some cases polycrystalline samples and recently also epitaxial layers are studied or other single-crystal growth techniques are used, for instance (Zn, Mn)S growth from a Te melt [9].

I n Fig. 1 the variation of the lattice parameter and the crystal structure determined by X-ray diffraction are given for all six mixed crystal systems. The mean cation-cation distance, d,, fulfils the Vegard law and increases for the (Zn, Mn) and decreases for the (Cd, Mn) chalcogenides with increasing Mn concentration. Obviously,

2) The random distribution of the Mn2+ ions was concluded, e.g., from high-field magnetization measurements [6,7] (see also Section 6.2).

Optical Properties of (Zn, Mn) and (Cd, Mn) Chalcogenide Mixed Crystals 13

Fig. 1. Mean cation-cation distance, d,, as a function of the Mn concentration “)I,, for the (Zn, Mn) and (Cd, Mn) chalcogenides (solid lines) after [6,10]. ZB: zincblende, W : wurtzite structure. Dashed lines: extrapolation into the miscibility gap

the bond lengths for the Mn chalcogenides are just in the middle between those for the Zn and Cd chalcogenides, respectively. In all cases a miscibility gap occurs for high XM,, values which enlarges from the tellurides t o the sulfides (see Fig. 1). Whereas (Zri, Mn)Te single-phase crystals could be grown up to zMn = 0.86 the sulfides are obtainable only for 0 5 xYn 0.45. The telluride mixed crystals show zincblende and the (a, Mn) selenides and sulfides wurtzite structure in the whole possible X M ~ region. As indicated in Fig. 1, for (Zn, Mn) selenides and sulfides, however, the crystal structure changes from zincblende to wurtzite due to the lattice expansion with increasing z h I n , but there is no detectable change in the slope of thedc(zM,,) curvesllo].

The limiting components of the mixed crystal series MnS and MnSe can be grown as larger single crystals only in the rocksalt modification by, e.g., I,-transport reaction [ll]. In the unstable zincblende or wurtzite structure these compounds can be obtained as polycrystalline powders using low-temperature growth techniques or as evaporated thin films [12]. The d, values measured for these samples are iri sufficient agreement with the extrapolated ones shown in Fig. 1. Unfortunately, MnTe exists only in NiAs structure and, therefore, the dc(zMn - 1) value for the telluride mixed crystals must be ascribed to a hypotheticaE MnTe with zincblende structure.

It is of interest for the following section to point out that the actual microscopic bond lengths in the (Cd, Mn) and (Zn, Mn) chalcogenides as in other ternary mixed crystals vary much less than given by the Vegard rule. For (Cd, Mn)Te, as an example, EXAPS measurements [13] yield nearly constant mean Mn-Te and Cd-Te bond lengths (see Fig.2). Only the weighted average of these bond lengths then leads to the d c ( x ~ , , ) variation measured by X-ray diffraction.

The conventional optical properties of the considered (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals, with the exception of (Zri, Mn)S, are mainly determined by the strong opening of the energy gap, E,, with increasing Mil content which is

14 0. GOEDE and W. HEINBRODT

2 I4

0 - 0

- 0

- Mn -Te 0 -

I I I I

shown in Fig. 3. In the case of the tellurides and selenides this variation of E , as a function of xM,, can be measured with good accuracy, as nearly in the whole miscibility region the corresponding free Wannier-type A-exciton structures can be seen in the low-temperature reflection or photoluminescence spectra. As examples the measured electroreflection and photoluminescence spectra for (Cd, Mn)Te are given for various x3fn in Fig. 4 and 5, respectively. The Eg(xM,) dependence can be obtained also from the measured bound-exciton photoluminescence spectra shown in Fig. 6 for (Zn, Mn) Se as an example or, less reliably, from the shift of the absorption edge with increasing Mn content [19, 25, 32, 671. In the considered sulfide mixed crystals exciton lines are observable only for Mn concentrations ~ $ 1 ~ 0.3 [33, 2361. Therefore, the E g ( x ~ , ) variations for these systems given in Fig. 3 are obtained with somewhat less con- fidence. I n Fig. 3, therefore, also the shift of the absorption edge [32] and the band- gap-related peaks in the excitation spectrum for photoluminescence bands caused by internal transitions in the Mn2+ 3d6 ions 1341 are taken into consideration.

ZnSe

LdS

ZnTe

GdSe

CdTe

Fig. 3. Energy gap, E,, as a function of the Mn concentration ZM,) for the (Zn, Mn) and (Cd, Mn) chalcogenides a t low temperatures (4 2 T 2 77 K) in linear approximation (solid lines) (see the text for references). Dashed lines: extrapolation into the miscibility gap

0

0

0

I I I _ I I I I . 079

x z 43

I I I 1 I I I

030

x z 43

I I I I


Fig. 4. A-exciton electroreflection spectra of (Cd, Mn)Te for various s~~ at T = = 300 K (after [14])

In the case of (Cd, Mn)Te [14 t o 21,2331 and! (Cd, Mn)Se [22 t o 261 a nearly linear EA-exc(XnIn) dependence was found which can be described by the relations

(Cd, Mn)Te (4.2 K): (Cd, Mn)Se (2 K) :

EA.~&SI, , ) = 1.595 + 1 . 5 9 ~ ~ ~ (eV) [15], EA.esc(Xnin) = 1.821 + 1.54zfi*,, (eV) [23]

in sufficient agreement with the results of other authors [16 t o 19,21, 22, 24,2331 (see also Fig. 14). Also for the broader-gap systems (Zn, Mn)Te [27 t o 291, (Zn, Mn)Se [30, 31,57,67], and (Cd, Mn)S [32,33] the measured Eg(xMD) dependences can be approximated by a linear function. A t low Mn concentrations ( ~ 1 1 ~ & 0.10) small non-linear deviations to lower energies are observed for (Cd, Mn)S and (Zn, Mn)Se being interpreted as s, p-d exchange interaction effects [30 t o 32, 57, 671 (see Sec- tion 6.2 and Fig. 33). I n the case of (Zn, Mn)S the present experimental results suggest a weak (possibly non-linear) band-gap decrease with increasing XM,, [236].

The linear extrapolation of Eg(xMn) to zhIll = 1 through the miscibility gap yields one and the same value for the tellurides, selenides, and sulfides, respectively, which must be considered as the energy gaps of the corresponding Mn chalcogenides with zincblende (or wurtzite) structure. The following mean values are obtained from Fig. 3 :

E ~ ( M I ~ T ~ z B , , ~ ~ ~ ~ ~ ~ ~ . ) = (3.2 f 0.1) eV , E,(MIISZB) = (3.7 _+ 0.1) eV.

E,(MnSeZB) = (3.3 5 0.1) eV ,


c-- € l ev) 320 300

0.490

0 221

0.4 i I \ I i I \

1 ' \ 47meV I / I 1 L I I

1.8 2.0 2.2 2.4

Fig. 5 Fig. 6

Fig. 5. 8-exciton photoluminescence spectra of (Cd, Mn)Te for various X M ~ at T = 11 K (after [14]). Dashed curve: emission band due to the 4T, + "Al internal transition in the Mn2+ 3d5 ions

Fig. 6 . Photolnminescence spectra for donor-bound excitons in (Zn, Mn)Se for various zy, at T = 6.5 I< (after [57])

The available experimentally determined E , values for MnSzB and MnSezB are not very reliable as no sharp band-gap exciton structures in the optical spectra were observed. The measured low-temperature energetic positions of the steep absorption edge with absorption constants in the order of lo6 cm-l are consistent with the given E, values [12]. Also the highest-energy band a t about 3.6 eV in the diffuse-reflection spectrum [35] and in the excitation spectrum of the photoluminescence [12] suggests a band-gap value somewhat above 3.6 eV for MnSzn. Recently a broad exciton structure was found in the reflection spectrum of MnSzB films a t about 3 .8eV

Also the results of optical measurements of the stable rocksalt structure of MnS and MnSe support the given gap values, if the E , reduction by about 0.3 eV in comparison

[331*


t o the zincblende structure is taken into account which can be concluded from the corresponding shift of the absorption edge (see Fig. 1 in [12]). Reflection and absorption measurements of MnSeEs thin films yield a band a t 3.0 t o 3.1 eV [36]. The energy of the corresponding transition in MnSRs is determined to be 3.2 and 3.3 eV from diffuse-reflection [35] and refraction-index [37] measurements, respectively. It must be pointed out, however, that in some of the earlier papers these bands were ascribed to Mn 3d-state + conduction band [37, 381 or t o p-like valence band --+ Mn 3d-state [36, 391 transitions. The p-valence band -. s-conduction band I?-point transitions in these papers were assumed to occur a t energies above about 6 eV [39,40]. Such a large E , value, however, is not consistent with the mixed-crystal results described before. The corresponding peak in the UV-reflection spectrum should be ascribed to band- band transitions in lower-symmetry critical points as in other IT-VI semiconductors.

The Mn 4s-states show the usual amalgamation-type behaviour in the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals and do not lead to additional in-gap states. Only a redistribution of the conduction band density of states occurs leading to the observed band-gap increase. Similar as in other cutionically mixed 11-VI semiconductor mixed crystals the bowing of the E g ( x ~ , , ) curves is weak and, because of the miscibility gap not reliably measured up to now. Also the observed broadening of the exciton lines with increasing xhIn (see Fig. 4 t o 6) is well-known from other amalgamation-type 11-VI semiconductor mixed crystals and can partly be attributed to local esciton-energy fluctuations due to fluctuations of the Mn concentration inside an exciton volume a t various local positions (see, e.g., [41]).

Besides the n = 1 ground state of the free A-exciton connected with the upper sub- valence band, in several papers also excited A-exciton states (n 2 2) [42] and higher- energy structures in the optical spectra due to transitions from the lower spin-orbit- split sub-valence band [17, 431 and, in the wurtzite-type systems, also from the crystal-field-split sub-valence band [22,24, 251 into the conduction band, or band-band transitions in less-symmetric points at k + 0 in the Brillouin zone 117, 92, 2331 are studied in the considered mixed crystals. For instance, in (Cd, Mn)Te optical El and (E, + A,) transitions in a A point were observed by wavelength-modulated reflection spectroscopy [ 171 for Mn concentrations up to xhfn = 0.3. The spin-orbit splitting A,, in (Cd, Mn)Te is found t o be constant [43] or t o increase weakly [17] with increasing xyn. For the wurtzite-type (Cd, Mn)Se, however, a remarkable decrease of both the crystal-field and the spin-orbit splitting parameters of the valence band is observed [22, 24,251 with increasing x~,,. The latter effect is considered as indication for an important hybridization between the anion p-states and the Mn 3d-states (see Sec- tion 4), because d-states are espected to yield a negative contribution to the total spin-orbit splitting of the valence band [24]. Excited states (n 2 2) of free A-excitons are only observed a t very low Mn concentration [42] and, therefore, do not yield information about any xnIn dependence of the exciton binding energy.

Considering the lattice vibration properties, the (Zn, Mn) and (Cd, Mn) chalcogenides also exhibit a conventional behaviour well-known for other 11-VI semiconductor mixed crystals. Especially for the optical phonons one-mode or two-mode behaviour is observed in dependence on the mass relations of the participating ions. (Cd, Mn)Te [44, 1631, (Cd, Mn)Se [45], and (Zn, Mn)Te [46 t o 481 were studied by Raman scattering [44 to 47, 1631 arid IR-absorption 1481 measurements. As shown in Fig. 7a, the optical phonons for (Cd, Mn) Te show a distinct two-mode behaviour. For small Mn concentrations a local mode due to Mn impurities appears which splits into one LO and TO mode with increasing xfiIn. In the case of (Zn, Mn)Te, however, because of the smaller mass difference of the cations a so-called mixed-mode behaviour is found (see Fig. 7 b). In ZnTe Mn impurities only yield a band mode which split- 2 physicn (b) 146/l

18

2 20

t I 200

-;' c 9 c .-

780 - G f 4

160

i Te Mn 7&

0. GEDE and W. HEIMBRODT

I n 2

Y

I I I I I I 14 0

XMn

Fig. 7. Longitudinal (LO) and transverse (TO) optical-phonon energies for a) (Cd, Mn)Te and b) (Zn, Mn)Te as function of the Mn concentration ZM,,, determined by Raman scattering measurements at 80 K. Fitted curves are based on a modified random-element isodisplacement (MREI) model (after [44, 461)

with increasing zMu. The LO, mode of ZnTe, on the other hand, directly evolves into the LO, mode of MnTe. The extrapolation Z&I,, -. 1 for both (Cd, Mn)Te and (Zri, Mn) Te yields the same optical phonon energies for the hypothetical MnTe with zincblende structure,

oLo(MnTeZB) = 216 cm-l , wTo(MnTezB) = 185 cm-l, and values for the in-gap modes of Zn and Cd impurities in MnTezB [46] (see Fig. 7). For (Cd, Mn)Se also a two-mode behaviour was observed [45]. For the remaining three mixed crystals a mixed-mode or purely one-mode behaviour can be expected as the necessary two-mode criterion,

cuTo(MnY) > WLO(XY) , X = Zn, Cd; is not fulfilled. I n a recent paper [242] the optical-phonon energies of MnSzB were shown to be nearly the same as for ZnS,

Y = S, Se, Te ,

wLO(MnSZB) = 343 cm-l , OIT~(MIISZB) = 286 cm-1.

3. Optical Properties Due to Internal Transitions in the Mn2+ 3d6 Ions

The optical properties of the (.Zn, Mn) and (Cd, Mn) chalcogenides are essentially modified by the electronic transitions within the half-filled 3d-shell of the Mn2+ ions.

The ( i0) = 252-fold degeneracy of the Mn2+ 3d5 configuration is partially removed

by the intra-ionic electron-electron and the ligand-field interactions. The electron- electron interaction, already present in free Mn2+ ions, lifts the L-degeneracy and can


r 3 Z r - I I .I I I I

Fig. 8 Fig. 9

Fig. 8. Energies of the lowest excited states of a Mn2+ 3d5 ion in a Td-symmetric ligand field as a function of the field parameter Dq for the Racah parameters B = 50 meV and C = 434 meV obtained for MnSzB (Tanabe-Sugano diagram); experimental points (Dp(MnSzs) = -57 meV )

Fig. 9. Lowest-energy excited states of Mn2+ 3d5 ions in t,etrahedrally coordinated chalcogenides (after experimental data for (Zn, Mn)S [50]) in comparison with the realizable variations of the band gap Eg(q,iu) for the (Zn, Mn) and (Cd, Mn) chdcogenides (T = 4 I<). The arrows represent the internal absorption transitions

be described by two Racah parameters, B and C . Due to covalency effects especially B is somewhat reduced in comparison with the free-ion B-value. According to Hund’s rule the ground state has the maximum total spin quantum number S = g, the possible excited quartet states are 4G, 4F, 4D, and 4P. The Td-symmetric field3) of the chalcogen ligands, on the other hand, splits a five-fold degenerate one-electron d-state into t,- and e-states providing a t$e2 configuration for the Mn2+ 3d5 ground state and tie3, tie2, and tiel configurations for the excited quartet states. Both interactions are of the same order of magnitude and can be taken into account by perturbation cal- culation after Tariabe and Sugano [49] leading to the energies of the ground and excited states of Mn3+ 3d5 ions as a function of the ligand field parameter Dq given in Fig. 8. Here the states are classified by the irreducible representations of Td, the ‘dominating’ configurations are given in parenthesis.

Optical dipole transitions between the ground state and the excited states are forbidden by spin and symmetry selection rules which, however, are softened by spin- orbit interaction and mixing with electronic states of suitable symmetry, respectively, a s discussed later. As shown in Fig. 9 the observability of these optical d-d transitions in the various mixed crystals depends decisively on the width of the band gap as a function of the Mn concentration. In the broadest-gap system (Zn, Mn)S the five d-d transition bands indicated in Fig. 9 can be observed in the whole realizable xMU region [12,34,35,50,65] (seeFig. 10a). The nearly temperature independent peak positions hardly vary with the Mn concentration as demonstrated by the photoluminescence excitation spectrum of MnSzR given in Fig. 10 b. Also in (Zn, Mn)Se

3, For the followhg the deviation of the ligand field from the Td symmetry in the case of the Cs,-symmetric lattice sites in wurtzite-type mixed crystals can be neglected. 2’


A ( n m ) -------+ t ieVl-

Fig. 10. a) Absorption spectrum of (Zn, Mn)S with z~~ = 0.10 at T = 23 K (after [51]). b) Photo- luminescence excitation spectrum of a MnSzB thin film at T = 4 K. Emission peak at 1.9 eV (after [ 121)

the three lowest-energy internal transitions can be observed already at low Mn concentration [52, 661. In the other mixed crystals, however, the distinct detection of several internal transitions within the Mn2+ 3dS ions is possible only if the band-gap window is sufficiently opened by a correspondingly high Mn concentration. In Fig. 11 a the successive observability of up to three d-d absorption bands with increasing Z M ~ is shown for (Cd, Mn)S 132,611. The same bands can be seen also in a photoluminescence excitation spectrum of (Cd, Mn)S a t sufficiently high x M n (Fig. 11 b).

A(nrn)

23 2 5 2.7 29 E ( e v ) -

Fig. 11. a) Absorption spectra of (Cd, Mn)S crystals for various Mn concentrations XM,, at T = = 114 K (after [32]). b) Photoluminescence excitation spectrum of a (Cd, Mn)S crystal with z~~ = 0.18 at T = 4 K. Emission peak at 2.1 eV (after [33])

Optical Properties of (Zn, &In) and (Cd, Mn) Chalcogenide Mixed Crystals 21

Fig. 12. Absorption spectra of (Cd, Mn)Te crystals for various Mn concentrations znfn a t T = 44 K (after [58]). Marks indicate the peak positions calculated in the ligand field model for B = 43, G = 434, and Dq = -60 meV

In the smallest-gap system (Cd, Mn)Te the effect of the d-d transitions was studied in several papers 121, 19, 581, for the highest xM,, values two d-d absorption bands are observable (see Fig. 12). A similar behaviour is found for (Cd, Mn)Se [25] and (Zn, Mn)Te (64, 198].4)

The peak positions of the five d-d absorption bands in (Zn, Mn) S can sufficiently well be fitted in the framework of the ligand-field model 1491 as shown in Fig. 8 for MnSzB as an example with the given values for Dq, B, and C . According to the simple point-ion model, Dq should vary proportional to d& and, therefore, a remarkable peak shift for the two lowest-energy bands to higher energies by about 100 meV would be expected in (Zn, Mn)S between XM,, x 0 and XM,, = 1 if dMn-s is assumed to be proportional t o the lattice constant d, of the mixed crystals. However, from the experimentally observed very weak shift & 20 meV the Mn-S bond length dMn-s can be concluded to be nearly constant in agreement with the EXAFS results given in Section 2. This conclusion is confirmed by the comparison of (Zn, Mn)S and (Cd, Mn)S for the same xMn. Also in this case the measured peak-position differences are much smaller than expected if dM,,-S - d,. Changing the anion ligands in the series S 4 Se 4 Te the Racah parameter B should decrease due to increasing covalency effects, shifting the d-d bands to lower energies and especially diminishing the energy difference between the two lowest-energy bands which, therefore, become hardly resolvable. In (Cd, Mn)Te the observed two absorption bands then can tentatively be interpreted as indicated in Fig. 12. The Dq value obtained by this fitting is nearly the same as for (Zn, Mn)S, possibly caused by a compensation of the expected decrease due to growing dl\il,-al,ion by covalency effects.

A comparison of the measured peak absorption constant a between (Zn, Mn)S a t low Mn concentration [59] and RlnSzs [12] suggests a linear relation a = CX+~XM,, .

The xDIn independence of the d-d transition probabilities should be proved in more detail. The value of &,--a, being somewhat different for the various d-d bands (see Fig. 10a), is of the same order of magnitude lo3 cm-l for all (Zn, Mn) and (Cd, Mn) chalcogenides. The remarkably high d-d transition probability in comparison with other Mn-containing compounds (e.g. MnCl,, MnBr2, KMnF,, MnCO, [ S O ] ) obviously

4, I n some papers alternative interpretations as, e.g., transitions from the valence band into unoccupied Mnz+ 3ds-states were discussed [15, 21, 28, 54 to ,561. It could be convincingly proved, however, by the absence of large Zeeman splitting and hole photocond~~ctivity and by the sign of the piezoreflect,ion [ 15, 28, 2401 and of the hydrostatic-pressure-induced shift of the absorption bands [198, 237,2381 that the explanation as intraionic d-d transitions is correct as is evident from the viewpoint of the (Zn, Mn) and (Cd, Mn) sulfides.


is caused by a strong mixing between Mn 3d-states and anion p-states being typical for the (Zn, Mn) and (Cd, Mn) chalcogenides as discussed in Section 4. The usually suggested softening of the symmetry-induced selection rules in the case of d-d transitions by electron-phonon interaction and other symmetry-reducing perturbations seems to be comparatively less important.

The d-d transition bands in the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals with Mn concentrations x M n 2 0.01 do not show any fine structure even a t lowest temperatures (see Pig. 10 to 12). Zero-phonon lines and phonon satellites are only observable in the impurity concentration region in ZnS : Mn, ZnSe: Mn, and CdS : Mn allowing a detailed and sometimes sophistical analysis of line splittings by spin-orbit interaction, Jahn-Teller effect, covalency effects, Mn2+ pair interaction, and stacking faults, which cannot be reviewed here. The vanishing of the fine structure probably must be ascribed to line broadening by inhomogeneity effects in the mixed crystals as suggested by the reappearance of zero-phonon lines for the 6Al --+ 4T1 and sAl - --+ 4A1, 4E transitions in pure MnSRs reported in 162, 631 (see also Section 6.3). The total halfwidth of the various d-d transition bands being in the region 100 t o 200 meV is caused by electron-phonon interaction and is nearly independent of xnf, in contrast t o the halfwidth of the free-exciton line. This indicates that the electron-phonon interaction characterized byaHuang-Rhysfactor X =3(6A1 - 4T1) t o l(6Al -. 4A1, 4E) does not vary essentially as afunction of xnfn and within the considered mixed crystal family.

Emission transitions occur only from the lowest excited state 4T1 t o the 6A, ground state yielding a broad, structureless luminescence band in the considered mixed

7.4 7.6 1.8 2 0 2.2 €lev)----

1 , ,; , , \J(... , ;;;..:. . . .. 4 , \

I / \

/ ... \ - 1 7 12 7L 76 78 20 L'

€ (eV) -4

Fig. 13. Photoluminescence spectra for a) (Zn, Mn)S ( 5 ~ ~ = 0.05 [SS]), b) MnSzB (--) and M ~ S R S (---) [12, 821, and C) (Cd, Mn)Te ( 5 ~ " 2 0.4, [75]) at T = 77 K; .-.-...--.. decomposition into Gaussians


crystals. Due to a Franck-Condon relaxation energy of about 250 meV the peak position is shifted to the region 2.1 t o 2.2 eV for (Zn, Mn)S 19, 12,34,50,53, 68 to 731 and (Cd, Mn)S [33, 741 and to about 2.0 eV for (Cd, Mn)Te [21, 52, 55, 69, 75 t o 79,2371. In the smaller-gap system (Cd, Mn)Te this emission band of course can be observed only after a sufficient opening of the gap by increasing the Mn concentration xMU 2 0.4 (see Fig. 5 ) . The higher-energy excited states fast relax probably radiationlessly into the 4T, state. In Fig. 13a, c the 4T, --* sAl emission band is shown for (Zn, Mn)S and (Cd, Mn)Te as examples. The peak position of this band is again nearly independent of x&In in contrast t o the strong shift of the A-exciton emission line as demonstrated in Fig. 14. The excitation spectra of the 4T, - 6Al emission band exhibit the same d-d transition peaks as the corresponding absorption spectra, and additionally, in most cases free A-exciton-related bands a t energies just below the respective band- gap value (see Fig. 11 b and [33, 34, 50, 68 to 70, 751).

The relatively low d-d transition probability causes a long lifetime of the lowest- energy excited state 4T, with respect t o the radiative transitions to the sA, ground state (for (Zn, Mn)S, e.g., 1 to 2 ms [9, 53, 70)) .which in the case of (Zn, Mn)S can be identified with the corresponding luminescence decay time measured a t lowest temperatures and a t such low xMn that the Mn2+ ions can be considered a s being isolated. With increasing xbin > 0.01 a radiationless resonance energy transfer according to a Dexter mechanism [80] occurs between sufficiently near Mn2+ ions [9, 34, 50, 53, 69, 74, 76, 771. Therefore, the excitation energy becomes mobile and can be captured with increasing rate by centres of radiationless transitions. This leads to a strong decrease of both the effective lifetime Teff of the excited state 4T1 and the luminescence quantum efficiency 71 by nearly three orders of magnitude with increasing X M ~ as shown in Fig. 15 for (Zn, Mn)S as an example. Further information about the energy transfer mechanism can be obtained by measurements of the 4T1 -+ gAl photoluminescence decay after pulse excitation for various xBr,, [9, 34, 53, 69, 74, 76, 771. A S shown in

0 0 2 04 0.6 0 8

XM"-

Fig. 14

cMn jmol X ) --+

Fig. 15

Fig. 14. Mn concentration dependence of the emission peaks due to the A-exciton annihilation (0) and the internal 4T1(4G) -+ 6A,(gS) transition in the Mn*+ 3d5 ions ( 0 ) for (Cd, Mn)Te at T = 76 K (after [21]) Fig. 15. Mn concent,ration dependence of the effective lifetime t e f f of the excited 4T, state, measured by the decay time of the 2.1 eV emission band, and quantum efficiency q for (Zn, Mh)S crystals at T = 77 I<. Excitation energy 2.48 eV (after [9]). 0 teff for MnSzs [12]


50 100 750 0 5 70 75 20 f (ps) - f ~ s J -

Fig. 16. Photoluminescence decay after 2 ns pulse excitation by a N,-laser pumped dye laser for a) the 2.1 eV emission band of (Zn, Mn)S crystals a t T = 77 K for various Mn concentrations 2~~ = 2 x (I), 0.01 (2), 0.10 (3), and 0.27 (4) (experimental points); b) the 1.9 eV emission band of a MIISZB thin film for various temperatures T = 4 (I), 77 (2), 110 (3), and 140 K (4). Excitation energy 2.48 (a) or 2.63 eV (b). Curves in Fig. 16a calculated on the basis of an energy transfer model (after [53, 121)

Fig. 16a the decay curves for (Zn, Mn)S, having a characteristic non-exponential shape for lower Mn concentrations, can well be fitted on the basis of the so-called diffusion model [81] for the energy transfer process. From the obtained xN,, dependence of the energy diffusion constant D - xg; a dipole-dipole interaction between the Mn2+ ions can be concluded a s the energy transfer mechanism [53]. At highest Mn concentrations and especially in MnS the exchange mechanism [80] may dominate.

The capture of the excitation energy by other centres for radiative transitions leads to the appearance of several lower-energy emission bands in the red and infrared regions between 1.2 and 2.0 eV as observed, e.g., in (Zn, Mn)S [9, 12,34, 50, 68 to 731, (Cd, Mn)S (741, and (Cd, Mn)Te [69] and shown in Fig. 13a, b for (Zn, Mn)S with xnIn = 0.05, M I ~ ~ z B , and MnSRs respectively. As shown in Fig. 10b for MnSZB the excitation spectra. of the red emission bands consist of the usual Mn2+ d-d transition bands confirming the excitation by energy transfer (121. Obviously, there are several different red emission centres with a nature not definitely known a t present. Prob- ably most of them are Mn2+-related and consist of Mn2+ ions in a perturbed environ- ment providing a sufficiently high Dq value.6) I n the case of MnS the infrared emission band (see Fig. 13b) is observed only for the rocksalt-structure phase and shows an excitation spectrum shifted to lower energies corresponding t o d-d transitions in octahedrally coordinated Mn2+ [82]. This suggests that also in the (Zn, Mn)S mixed crystals the infrared emission bands ([34, 50, 68, 711 and Fig. 13a) should be ascribed to sub-microscopic rocksalt-structure domains.

The temperature dependence of the energy transfer probability between the Mn2+ ions is given by the overlap integral of the emission and lowest-energy excitation

5) For instance, octahedraily coordinated Mn2+ was discussed as possible red emission centre in [9,50]. The tendency for an octahedral coordination of the Mn*+ ions in the (Zn, Mn) and (Cd, &In) chalcogenides in the case of large ZM,, is demonstrated by the hydrostatic-pressure-induced phase transition to the rocksalt structure for (Zn, Mn)Te [238] and by the optical study of the heat- treatment-induced phase transition from tetrahedrally to octahedrally coordinated RInS [82].


ri,K! --+ ,p 10 50 ID0 200 t r I 1

I I I

I ' I , i

Fig. 17. Temperature dependence of the intensities of the 2.1 eV (4Tl +6A,) (Iy) and 1.8eV (I,) emission bands for a (Zn, Mn)S crystal with XM,, = = 0.044 (experimental points). Fitted curves calculated on the basis of an energy transfer model (after [ Q ] )

I /-

\ I

bands [SO] and, therefore, increases with increasing T. This is demonstrated in Fig. 16 b by the measured decay curves of the red emission band for MnSZB after pulse excitation having the characteristic shape expected for an excitation by energy transfer. Both the delay time for getting the maximum emission intensity and the time constant of the exponential decay strongly decrease with increasing T. Prom this an effective lifetime of the 6A, - 4T1 Prenkel excitons in MnSzB of about 10 ps a t 77 K can be concluded [ 121. The typical temperature dependence of the various luminescence bands is presented in Fig. 17 for (Zn, Mn)S with xMn x 0.04. With increasing T the intensity of the red emission band increases until for T 2 150 K the thermal quenching for both emission bands dominates due to the increasing energy transfer probability to the centres of radiationless transitions. With increasing Mn concentration the intensity ratio I , / I y strongly decreases [9]. In MnSzB the yellow *T1 + 6Al Frenkel-exciton emission band a t 2.1 eV cannot be observed even at 4 K and only lower-energy emission bands occur caused by the radiative annihilation of 'bound' Frenkel excitons [ 121.

4. Energetic Position of the Mu 3d-States

The energetic position of the Mn 3d-states with respect to the valence and conduction bands is one of the most important problems in the (Zn, Mn) and (Cd, Mn) chalcogenides being discussed controversially for a long time on the basis of inadequate experimental results. The absence of an observable ionization transition from the 6Al ground state of the Mn2+ 3d5 ions into the conduction band obviously indicates the Mn 3d-states to lie below the valence band edge. First XPS measurements [83] of the kinetic-energy distribution of electrons emitted from a (Zn, Mn)S sample with ZM,, =t

x 0.03 due to X-ray (AlKJ excitation yielded an energetic position of the Mn 3d- states (3.0

In recent years ultraviolet photoemission spectroscopy (UPS) and angle-resolved UPS mostly using synchrotron radiation were successfully applied to get reliable information about the valence band density of states for (Cd, Mn)Se [84 t o 86, 1991, (Cd, Mn)Te [87 to 91, 94, 1991, (Cd, Mn)S [199] and (Zn, Mn)Se [200]. In Fig. 18 and

0.5) eV below the upper valence band edge.


I I I l / I I I I 1

--E ( O V )

Fig. 18. W photoemission spectra (UPS) for the valence band of (Cd, Mn)Te using synchrotron radiation with photon energies hw a) for various Mn concentrations xi\^,,; hw = 33 eV, b) for various hw and Z M ~ = 0.65 (after [SS]). Arrows mark Mn-induced features; . - . - a CdTe. Energy of the upper valence band edge E , = 0 eV

19 UV photoemission spectra are shown for (Cd, Mn)Te [89] and (Cd, Mn)Se [85] which in accordance lead to a Mn 3d-state-induced density- of-states feature a t about 3.4 eV below the valence band edge being in good agreement with the results of several other authors [S6, 87, 90, 199, 2001. This relatively sharp peak having a halfwidth of

i '. '.

Fig. 19. W photoemission spectrum for the valence band ( E , = 0) of (Cd, Mn)Se with z m = 0.21 (-) and CdSe (---) using synchrotron radiation with photon energy fiw = 90 eV; .-.- - difference curve (a.ft,er [SS])


about 1 eV and an xMn-independent energetic position (see Fig. 18a) increases with increasing photon energy h s relative to the contribution of the anion p-states (Fig. 18 b; see also [197]) and is assigned to the e-symmetric Mn 3d-states. The crystal- field-split, t,-symmetric Mn 3d-states, however, were assumed to hybridize signifi- cantly with the anion p-states [86, 891 and to contribute nearly uniformly t o the valence band density of states. It was pointed out in [89] that a t least in (Cd, Mn)Te the position of the upper valence band edge is not affected by increasing Mn concentration and, therefore, the observed increase of the energy gap E, with growing xN,, is mainly due to an increase of the energy of the conduction band minimum.

Although the UPS measurements of (Cd, Mn)Te and (Cd, Mn)Se led to the un- ambiguous identification of occupied Mi1 3d-states in the valence band further important questions are not yet sufficiently solved. Some controversial results between angle-resolved [SS, 941 and integrated 187, 891 UPS measurements of (Cd, Mn)Te a t different excitation energies could be explained by recent calculations [93] of the valence band density of states on the basis of a parametrized tight-binding model using CPA and taking into account the observed strong dependence of the cross-section for photoexcitation of the Mn 3d-states on the excitation energy hw. The essentially different behaviour of the e- and t,-symmetric Mn 3d-states with respect to hybridization with the t,-symmetric anion p-states, which may be expected for symmetry reasons [89, 1001, seems to be not yet convincingly proved by experiments. As the primary crystal-field splitting between the t,- and the lower-lying e-symmetric Mn 3d-states is only 10 Dq = 0.5 eV, two corresponding hypothetical peaks would be hardly resolvable by UPS. A quantitative determination of the degree of d-p hybridization and delocalization of the Mn 3d-states on the basis of UPS experiments is not very convincing up to now. In a recent paper [ 1991 first indications for an increasing p-d hybridization are obtained in the series (Cd, Mn)Te, (Cd, Mn)Se, and (Cd, Mn)S by a comparison of the corresponding UPS spectra. As only the occupied electronic (ground) state of the crystal can be studied by UPS, the energetic positions of the unoccupied Mn 3d-states and of the excited states of the Mn 3d6 configuration with respect t o the band edges must be determined from further theoretical considerations.

Band-structure calculations for the (Zn, Mn) and (Cd, Mn) chalcogenides with inclusion of the Mn Sd-states in the framework of the usual one-electron picture are properly speaking insufficient as the strong intraionic Coulomb interaction between the spatially confined electrons in the half-filled 3d5-shell of the Mil2+ ions inducing important correlation effects defies an independent-particle description and, therefore, strongly simplifying assumptions are necessary. The various spin-flip excitation energies within the Mn 3d5confignration discussed in Section 3 are simply represented in the one-electron picture by only two exchange-split 3d-levels, the lower one being completely occupied and the upper one empty (see, e.g. [loo]). This exchange-splitting energy, being a fundamental parameter of the band-structure calculations, usually is assumed to be equal to the mean energy difference between the sA, ground state and all quartet (8 = $) states of the Mn2+ 3d5 ions and is chosen to be 4 to 6 eV [89, 1001. It should be pointed out that in the considered one-electron approximation the upper unoccupied 3d-level also corresponds to the final-state energy for an electronic transition into a Mn2+3de configuration. The hybridization between both exchange and crystal- field split RiIn 3d-states and the extended anion p- (and cation s-) states is then taken into account usually in a tight-binding approximation yielding more or less broadened bonding and antibonding states.

The quantitative results of the present band-structure calculations 193 to 1051 mainly carried out for (Cd, Mn)Te and the hypothetical MnTezB, but also for MnS


[96,97], are partly controversial and depend on uncertain model parameters and, therefore, must be considered with reservation..The density of states and the width of the band gap are calculated in dependence on the magnetic ordering of the crystal, and the non-metallic behaviour of the Mn chalcogenides despite the half-filled Mn 3d-shell is explained. The unoccupied Mn 3d-states lie in the cation s-states-derived conduction band [ 100,1031 or in the band gap [95,98], but are always clearly separated from the occupied ones. For an adequate discussion of the various types of optical transitions in the framework of a one-electron picture essential relaxation corrections must be taken into account as pointed out in [loo]. The results concerning the d-d superexchange interaction between nearest and next-nearest neighbour Mn2+ ions [98, 1001 and the (s, p)-d exchange interaction [98,100] will be given in Sections 5 and 6, respectively.

6 . Mne+ 3dS Spin Correlation Due to Superexchange Interaction and Mean Spin Density in a Magnetic Field

In the present chapter the magnetic properties of the (Zn, Mn) and (Cd, Mn) chalcogenides including the pure Mn chalcogenides are reviewed only as far as necessary for an understanding of the optical and magneto-optical properties described in Section 6. The magnetic moment of the Mn2+ ions given in the free-ion limit for the 6 S 5 / 2 ground state by pc = - gpBMJ (pug = eh/2mc Bohr magneton, g = 2 Land6 factor, and M J =

external magnetic field a t higher temperatures. In dependence on the Mn concentration xM,, a t sufficiently low temperatures, however, more or less essential effects due to exchange-interaction-induced spin correlation are observed.

= , ... , $) leads to a paramagnetic behaviour of the considered systems in an

5.1 Mia chalcogenides

All Mn chalcogenides are known to become antiferromagnetic below a NQel temperature T, which depends on the crystal structure. In the paramagnetic phase (T > T?) the Mn2+ 3d5 spins and the corresponding magnetic moments are randomly distributed. I n an applied magnetic field H = (OOH) the orientation of the magnetic moment with &lJ = -f is energetically most favoured and a total magnetization M = (OOM) is observed. The temperature and magnetic-field dependence of the magnetization per mole in the paramagnetic phase is given by

M = NAp$8B5/2(5) 9 (1)

where x 2 is the effective Land6 factor, S = f, N , the Avogadro number, and (Sz)mo, = N,(S,) = -N,SB5&) the mean molar spin density with B5/2([) being the Brillouin function,

For 5 < 1 (low-field case) the magnetization is proportional t o H and from (1) the usual Curie-Weiss law for the molar magnetic susceptibility x can be derived,

The appearance of a Curie-Weiss temperature 0 > 0 in (1) to (3) is an immediate consequence of the antiferromagnetic exchange interaction between the Mn2+ ions and leads to a decrease of the magnetic susceptibility in comparison t o an ideal para-


magnetic behaviour (8 = 0 ) as both the thermal disorder (kT) and the antiferromagnetic interaction (k8) oppose the paramagnetic ordering of the spins in a magnetic field.

Some typical values for T, and 8 from measurements of, e.g., magnetic susceptibility, specific heat, thermal expansion, EPR, inelastic neutron scattering, and neutron diffraction, are given in Table 1. The mean values for T,, being nearly the same for MnS and MnSe, are about 150 and 100 K for the rocksalt and zincblende structure, respectively. The effective Land6 factor in the Mn chalcogenides is found to decrease only slightly in comparison to the free-ion value and, therefore, the maximum z-component of the magnetic moment &$us can be approximated by 5 pR.

The antiferromagnetic interaction between the Mn2+ 3d5 ions can be described phenomenologically in a good approximation by a Heisenberg Hamiltonian,

X, = - C' J(Rij) StSj = - J1 C SiSr - Jz C SiSl, (4) i ,j€ i , k i , 1

f.c.c. sublattice ( i , k = n n ) ( i , l =nnn)

taking into account only the isotropic nearest- and next-nearest-neighbour interaction SI is the total-spin operator acting on the Mn sublattice site i and Ell is the vector between the sites i and j. The corresponding exchange-interaction parameters J1 and J , can be determined experimentally using their relations) to T, and 8 and are also given in Table 1. There is a surprisingly good agreement with the theoretical J1 and J , values obtained from band-structure calculations [96, 98, 100, 1071. Due to the comparatively strong localization of the Mn 3d-stat8es the direct Mn-Mn exchange interaction is negligible in the Mn chalcogenides and the Anderson d-anion p-d superexchange mechanism [ 1131 dominates as also confirmed theoretically [98].

The negative values of J , and J, mean that the antiparallel orientation of the spins for a considered pair of both nearest- and next-nearest-neighbour Mn2+ ions is energetically favoured as follows from (4). The resulting magnetic ordering studied by neutron diffraction measurements in the case of rocksalt-structure MnS [115] and MnSe is the so-called type I1 f.c.c.. antiferromagnetic ordering which is characterized by parallel orientation of all Mn2+ spins in a (111) plane and antiparallel orientation of the spins in neighbouring (111) planes.') For MnSzB and MnSezB the somewhat more complicated type I11 f.c.c. antiferromagnetic ordering is found which is also expected for the hypothetical MnTezB. In Fig. 20 the Mil2+ spin orientations in the elementary

Fig. 20. Mn2+ spin orientations in the elementary clusters of Mn chalcogenides with a ) rocksalt, and b) zincblende structure in the case of a n f.c.c. anti-

I/ , ferromagnetic ordering of type I1 (a) and type 111 (b), respectively. o Mn?+ ions, anions; the arrows symbolize parallel and antiparallel spin orien-

,/

b tation

6, In the simplest (molecular field) approximation [114] one obtains from (4) for an f.c.c. sublattice 0 = -(W, + 125,) S(8 + 1)/3kand Tf: = -125,S(S + 1)/3kor TF* = - (8J , - 45,) x x S(S + 1)/3k for type I1 and I11 of the antiferromagnetic ordering, respectively. More exact relations were obtained on the basis of (4) using Green's function method [ 1141, magnon theory [114], or high-temperature series expansion [loel.

'1 The concrete spin orientation with respect to the crystallographic directions is det,ermined by anisotropic contributions t o the exchange Hamiltonian omitted in (4).


z z u

E d

I

I

I

h

3 0 PI

$


clusters of the rocksalt and zincblende structures are shown for both types of antiferromagnetic ordering which reduces the symmetry of a lattice site from Oh t o D3d and from T, to CBy for RS and ZB structure, respectively. In the case of type I1 the spins of six of the twelve nearest- and of all six next-nearest-neighbour Mn2+ ions are antiparallel with respect to the spin of a considered Mn2+ ion. I n type 111, however, the spins of eight nearest, but only two next-nearest Mn2r ions have the energetically favoured antiparallel orientation. The spins of the remaining Mn2+ neighbours are parallel to the spin of the considered central Mn2+ ion.

The type of antiferromagnetic ordering is determined by the ratio JJJ,. Theoreti- cally in the case of an f.c.c. lattice, type I1 and I11 are realized for J, /JI > 0.5 and 0 < J2/J1 < 0.5, respectively [lla]. For the rocksalt structure the Mn2+-anion-Mn2+ superexchange for nearest- and next-nearest-neighbouring Mn2+ ions corresponds to a 90" (pdx-pda) or 180" (pdx-pdx) coupling, respectively (see Fig. 20). Therefore, J, = J, can be expected in agreement with the experimental J-values (Table 1) and the observation of a type I1 ordering. On the other hand, for the zincblende structure only for nearest-neighbour Mn2+ ions the efficient Mn2+-anion-Mn2+ (109") superexchange is possible, whereas for next-nearest-neighbouring Mn2+ ions the inclusion of several anions is necessary, leading to a very small I J,I < 1 Jll. This is again consistent with the measured and calculated J-values and the observed type 111 antiferromagnetic ordering.*)

5.2 (Zn, M n ) and (Cd, M n ) chalcogenide mixed cvystals

In the case of the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals, often called diluted magnetic semiconductors, the decrease of the Mn concentration x M n restricts remarkable spin-ordering effects t o the lower-temperature region. As shown in Fig. 21 by the magnetic phase diagram for (Cd, Mn)Te, being typical also for the other considered systems, the paramagnetic phase widely extends to lower temperatures with decreasing XnI,,.

For sufficiently high znrn 2 0.6 below a critical temperature TN(zYn) a (disordered) antiferromagnetic phase occurs having a more or less long-range spin ordering. The corresponding phase transition is characterized by peaks at Tx(x*fn) both in t,he magnetic susceptibility and the specific heat as a function of temperature [124, 1251 similar as in the Mn chalcogenides. Due to the broad miscibility gap (see Fig. 1) this antiferromagnetic phase can he studied only in the telluride mixed crystals in a small xnfn region.

For lower Mn concentration z h l n < 0.6 below Tg(znin) a kind of spiwglass phase is observed being characterized by an antiferromagnetic short-distance ordering of the Mn2+ spins [4, 5, 2411. As revealed by neutron scattering experiments [ 126, 12'71, small antiferromagnetically ordered clusters already appear above T, and grow in size with decreasing temperature. The somewhat diffuse phase transition from the paramagnetic to the spin-glass phase leads to a peak or kink a t T,(znm) in the temperature dependence of the magnetic susceptibility as shown in Fig. 22, but to no anomaly in the specific heat [2]. In earlier papers [2, 51 the spin-glass phase was assumed to occur only above the percolation limit XY,, = 0.20 and to be induced by a lattice frustration mechanism [ 1281 caused by the short-range superexchange interaction mainly between nearest-neighbour Mn2+ ions. Recently it could be shown by low-temperature

*) Using the experimentally and theoretically suggested approximations Jp' = J:' = JfB and IJFBI > IJ:"I a.nd the equations given in footnote 6 ) one obtains the relations T ~ s / T ~ B =

"J,"'/(J?" - JtB) = and e/Tfllns,zB = 3 being well consistent wit,h the observed ratios b o 6 for MnS and MnSe (see Table 1). - -


Fig. 21

t

r m - Fig. 22

Fig. 21. Magnetic phase diagram for (Cd, &)Te showing the Mn concentration dependence of the transition temperature ( TN, Tg) between the paramagnetic (p) and the antiferromagnetic (a) or spin-glass phase (sg), respectively (after [2, 123, 1241); mg is the miscibility gap

Fig. 22. Magnetic susceptibility x as a function of temperature for (Cd, Mn)Te with various concentrations ZMn; (1) zyn = 0.20, (2) 0.30, (3) 0.40, (4) 0.50 (after [121])

susceptibility measurements [123] that the spin-glass phase persists also a t lower Mn concentrations down to a t least xMn = 0.01 with extremely low spin-freezing temperatures T, between 0.1 and 1 K. In this concentration region a comparatively long- range dipole-dipole interaction between more distant Mn2+ ions is assumed t o be the dominant spin-ordering mechanism 11231. The experimentally observed Mn concentration dependence of T , in the region 0.2 xMn 4 0.6 can well be represented by the relation In T, - xk:3 as shown in 11211 which is expected on the basis of the simplest assumption Tg(zYn) - J(R) - exp ( -y@, where - x$i3 is the mean distance between the Mn2+ ions in the mixed crystals and y the decay parameter. Below the percolation limit a linear decrease of T g ( z ~ , ) to zero with decreasing z~~ is suggested in [ 1231.

The outstanding magneto-optical properties of (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals reviewed in Section 6.1 mainly occur in the paramagnetic phase (T > > TJ. For the discussion of these properties information about the mean spin-density in an external magnetic field is needed which is provided by corresponding magnetic investigations. In the case of the mixed crystals i t was found that for T > Tg the dependence of the (molar) magnetization on magnetic field, temperature, and Mn concentration can be described by the relation

(5 ) where M is given by (l), (2), and the Curie-Weiss temperature is considered as an empirical xnf,-dependent fitting parameter e(xMn) [2, 1221. The scaling factor u ( z ~ ~ ) is obtained t o be somewhat smaller than unity with the limiting property a(zy,, - - 0) + 1 [ 1221. By this scaling factor the existence of antiferromagnetically ordered

M ( z d = a(xi\rn) z i d f 5


Mn2+-ion clusters with only small resulting magnetic moment well above T , is taken into account, which reduces the observed magnetization. As shown in [122] a(xb) is only slightly different for the various anions and nearly independent of the nature of the cation (Zn or Cd). In Fig. 23a, b the good agreement between the measured magnetization and (5) is demonstrated for the (Zn, Ma) chalcogenides as examples.

In the mixed crystals, therefore, the mean molar spin-density (Sz),,,,,~ being defined experimentally by M(sMn)/psij (c = 2) can be described by

d I

I I I 5 10 15

Fig. 23. a, b) Magnetization per unit mass, M,, measured as a function of the magnetic field a) for (Zn, Mn)Se with various Mn concentrations XM,, and b) for (Zn, Mn)S ( Z M ~ = 0.08) ( l ) , (Zn, Ivln)Se (XMn = 0.103) (2), and (zn, Mn)Te (ZMn = 0.095) (3); T = 2.2 K (after [122]). Solid curves fitted u ing ( 5 ) and M , = &f(ZMn)/m(ZMn) with m ( z M n ) = = (1 - X M ~ mzn + m n m m + nt, (a = S, S0,Te) being the average mass of a molecde and e ( X M n ) and a(zbIn) the fitting parameters. c) Steps in the high-field magnetization curve for (Zn, Mn)Se ( Z M ~ = 0.05); T = 1.8 K; experimental points; solid curve calculated on the basis of a cluster model (after [170])


The parameter O(x,,) decreases superlinearly with decreasing Xnm, and for sufficiently low Mn concentration an ideal paramagnetic behaviour is found as O(xMn -. 0) -, 0. Therefore, the measured magnetic susceptibility x a t a given temperature T > T, grows up with decreasing xRIn in spite of the concentration factor xNU in (6) as can be seen in Pig. 22. Whereas for xhfn = 0.5 typical &values between 300 and 350 K were obtained for (Cd, Mn)Te and (Cd, Mn)Se [129], 8 decreases to the range 2 to 4 K for

Recently the low-temperature measurements of the magnetization curves were extended to very high magnetic fields (H > 10 T) for (Cd, Mn)S [170], (Cd, Mn)Se [131], (Cd, Mn)Te [7], (Zn, Mn)Se [6, 1701, and (Zn, Mn)Te [171, 1721 yielding distinct steps a t H, (n = 1, 2, ...) (see Fig. 23c). These steps are caused by a magnetic-field-induced successive alignment of antiferromagnetically ordered nearest-neighbour Mn2+ pairs. The various saturation steps correspond to increasing total spin quantum number S, = 0, 1, 2, ... , 5 of the pairs. For isolated pairs and sufficiently low temperatures (kT < 21 Jll, j p B H ) , H , is simply determined by ,UGH, = -2nJ1 (n = 1, 2, ... , 5) [170 to 1721. Taking into account the influence of the more distant Mn2+ neighbours on a considered pair in a mean-field approximation a more exact relation for H, was developed [170, 1721 which is in good agreement with the experimental results (see solid curve in Fig. 23c). The J , values determined from H , are included in Table 1. From the step heights the pair concentration can be concluded which is consistent with the assumption of a random Mn2+ distribution as already mentioned in footnote2).

A theoretical explanation of the magnetic properties of the (Cd, Mn) and (Zn, Mn) chalcogenide mixed crystals in the paramagnetic phase a t higher temperatures could be developed on the basis of a Heisenberg Hamiltonian similar t o (4) but with a random distribution of the Mn2+ ions in the f.c.c. cation sublattice [130]. Many other theoretical questions in connection with the non-conventional magnetic properties a t temperatures near T, and in the spin-glass phase are still open and will not be discussed here. Especially the behaviour of antiferromagnetically ordered clusters and the decision between spin-glass and disordered antiferromagnetic phases need further theoretical insight (see also [4, 2471).

Theoretically the exchange interaction parameters JI (i = 1, 2, ...) in the Heisen- berg Hamiltonian are suggested to be nearly independent of the Mn concentration xyu and the nature of the non-magnetic cation (Zn or Cd) as the superexchange mechanism dominates which is essentially determined by the anion 1981 and because of the tendency to xM,-independent Mn-anion bond length in the mixed crystals mentioned in Section 2. This assumption is confirmed by the J-values obtained experimentally for the mixed crystals by measurements of Raman and neutron scattering, specific heat, or magnetization which, therefore, can be included in Table 1. As can be seen in Table 1 there is a slight chemical trend for the J1 values of the zincblende systems to increase in the anion series Te -+ Se -. S. After theoretical estimations [98] this trend must be ascribed mainly to the corresponding increase of the p-d hybridization which could be concluded from the magneto-optical effects described in Section 6.1. As already pointed out the zincblende systems are characterized by a strongly decreasing function J(R,,). Experimental investigations of the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals led to the estimation J1/J2 > 10 to 30 [4, 121, 1321.

x = 0.1 [122].

6. Optical and Magneto-Optical Properties Due to 8, p-d Exchange Interactions

6.1 Magneto-optical properties of the mixed crystals

The giant enhancement of the magneto-optical effects connected with electron or hole band states in the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals by more than


two orders of magnitude in comparison with conventional semiconductors is the main reason for the considerable and continuous physical and applicative interest in these materials since the first observation of a giant Zeeman splitting of free-exciton st,ates in (Cd, Mn)Te [133] in 1977. The usual Zeeman splitting of the energies of conduction and valence band states is strongly amplified by the s-d or p-d exchange interaction, respectively, with the Mn2+ 3d-electrons which a t T > T, are paramagnetically oriented in an external magnetic field. To restrict the effects of antiferromagnetic spin correlation of the Mn2+ ions, however, the Mn concentration must not be too high. There- fore, the diluted magnetic semiconductors are just an optimum between magnetic semiconductors and usual (diamagnetic) semiconductors doped with paramagnetic ions having too low mean spin densities in an applied magnetic field.

The exchange interaction of a conduction band electron with the Mn2+ 3d-electrons can be described phenomenologically by a Kondo Hamiltonian,

XeXch = - C J(r - R,) Sia , i

(7)

where S, and a are the spin operators of the Mn2+ ion on the lattice site Ri arid the conduction band electron a t T, respectively. J(r - R,) is the s-d exchange interaction energy and the summation has to be taken over all Mn2+ ions. The usual mean-field approximation leads to the lattice-periodic form

As the electron in an extended conduction band Bloch state interacts simultaneously with a sufficiently large number of Mn2+ ions, the spin operator S, can be replaced by its thermal mean value (8,) if HI1 x (molecular-field approsirnation). I n the paramagnetic phase (S,) is given by (6) as a function of temperature and magnetic-field strength and can be determined experimentally from the measured magnetization. Furthermore, in a virtual-crystal approximation J ( r - Ri) is substituted by xMnJ(r - - R) taking the summation over all cation-sublattice sites R. Assuming a parabolic E(k) dependence and taking into account the contribution of the exchange-interaction Hamiltonian (8) by perturbation theory with Kohn-Luttinger basis functions IS), I X) the energy splitting for a Conduction band electron is given by [3]

EEt = ( I + a) ~ U J , f + (g?pBH - Noziuna(Sz)) , (9) 1

where w, = eH/m:c, rn: and g: are effective mass and Land6 factor of the conduction band electron, respectively, and 1 = 0, 1, ... is the Landau quantum number. The upper and lower signs correspond to t and 4 spin states. LY = (SI J IS) is the exchange interaction parameter and No denotes the number of unit cells per em3. To collect the last two terms in (9) describing the usual Zeeman splitting for the conduction band electron and the s-d exchange-interaction-induced splitting, respectively, an effective g-factor can be defined as

geff depends on the Mn concentration xnfll and, on account of (az), also on the temperature and magnetic-field strength. In the considered broad-gap (Zn, Mn) and (Cd, Mn) chalcogenides the Landau splitting hwc = (m/mt) pBH is of the same order as the usual Zeeman splitting, because the effective mass of the conduction band electron is relatively large and g,* x 0.5 to 2. As shown by the experiments discussed in the following, usually both contributions, however, can be neglected in comparison with 3.


the dominating exchange-interaction-induced splitting (IgeEl > Is:/) and one obtains

AEc = -x~~,N,or(S , ) mi ; mI = if. (11)

In the same approximation the p-d exchange-interaction-induced energy splitting for a rs valence band hole in a magnetic field is given by

AE, = - 1 XM,N&(S,) mi ; mi = ++, i$, (12)

where ,f3 = (XIJI X ) is the corresponding p-d exchange interaction parameter. A schematic representation of the exchange-interaction-induced splitting for both the conduction and the light and heavy hole valence band states in the case of zincblende symmetry after (11) and (12) is shown in Fig. 24.

The most direct experimental verification is possible by the observation of the corresponding allowed optical A-exoiton transitions which are also indicated in Fig. 24 for the polarization of the light o'(Am, = A 1) and n(AmI = 0) , respectively. Meas- urements of this large, exchange-interaction-enhanced splitting of the A-exciton energy for the 1s ground state in magnetic fields typically up to 5 T were carried out for (Cd, Mn)Te [7, 16, 18, 133, 134, 140, 141, 1481, (Zn, Mn)Te [27, 139, 1421, (Cd, Mn)Se [143, 144, 1501, (Zn, Mn)Se [30, 122, 135, 1451, and (Cd, Mn)S [146, 1471. Only for (Zn, Mn)S such measurements are missing up to now. In most cases this exciton energy splitting, often called 'giant Zeeman splitting', is studied by low-temperature (1.6 K 5 T 5 10 K) reflection experiments [18, 27, 30, 139, 140, 142, 145 to 147, 1501, but absorption [16, 43, 144, 1471 and emission [141, 144, 1481 measurements could also successfully be used. As an example in Fig. 25 the magnetic-field-induced A-exciton energy splitting for (Cd, Mn)Te is demonstrated by the reflection curves for c+, c-, and x polarization, respectively. Taking into account the different halfwidths of the lines, a good agreement with the expected intensity ratios (see Fig. 24) can be

Fig. 24 -E (eV)

Fig. 25

Fig. 24. Schematic representation of the s - d and p-d exchange-interaotion-induced splitting for a ra conduction band electron and rs valence band hole state, respectively, in a magnetic field after (11) and (12) (a > 0 and B < 0). a+, a-, and x indicate the polarization of the corresponding allowed optical exciton transitions, the numbers give the relative transition probabilities

Fig. 25. Reflection curves of (Cd, Mn)Te ( X M ~ = 0.02) in a magnetic field B = 1.1 T at T = 1.7 K for the polarizations a+, a-, and x , respectively, showing the free A-exciton energy splitting (after [I]). The arrow indicates the zero-field position of the A-exciton


found for each pair of c+, cr-, and x lines. In Fig. 26a the magnetic-field dependence of the energies of the crf components of the A-exciton is shown for (Zn, Mn)Te with

According to (11) and (12) in particular the energy difference between the intensive

AE& = AEc(mj = $) - AE,(m, = f ) - [AE,(mi = -$) - AE,(rnf = -f)]

(13)

z M 0 = 0.15.

('outer') c+ and c- components, AE&, is expected to be

-zNnNo(B - B) ( 8 2 ) = %InNo(a - B) I (SdI . Using ( 6 ) one obtains

100

50

0 7 2 3 L 5

Pig. 26. a) Energies of the a+ and (r- components of the A-exciton for (Zn, Mn)Te with Z M ~ = = 0.15 as a function of the magnetic field obtained from reflection measurements; T= 1.6AK (after [27])). b), c) Energy splitting, 4Eexc, of the intensive (I+ and (r- components of the A-euciton for (Zn, Mn)Te as a function of the magnetic field for various Mn concentrations, b) ZM" 5 0.15, T = 1.6 K (after [27]) and c) z3fn 2 0.25, T z 4.5 K (after [139])


A s can be seen in Fig. 26b, c the exciton-energy splitting a t a given magnetic field strength strongly depends on the Mn concentration xMn (see also [18, 27, 30, 1441) and reaches a maximum near x~~ = 0.2. A t sufficiently low Mn concentrations, as far as effects of the antiferromagnetic spin-ordering of the Mn2+ ions can be neglected, a nearly linear increase of AE& is observed with increasing xMn due to the increasing mean spin density - xAfInl (8,) 1 for approximately xMn-independent (8,) (see Fig. 26 b). With further growing X M ~ , however, both the increase of e(XMn) and the decrease of a(xnrn) then lead to a strong decrease of I (8,) I as discussed in Section 5.2 and, according to (13), (14), also to a decrease of AE& forxy, 2 0.25 as shown in F i g . 2 6 ~ ~ ) A t the optimum Mn concentration typical AE& values of about 100 meV were measured a t 4 T which exceeds the conventional Zeeman splitting of exciton lines in semiconductors by two orders of magnitude.

By simultaneous magnetization measurements i t could be verified that the exciton energy splitting is really proportional t o the mean spin density in the mixed crystals as expected after (13). I n Fig. 27, as an example, AE&,, for (Zn, Mn)Se is plotted versus xMnl (S,) I for various Mn concentrations and temperatures. Here xM,,l(S,) I is obtained after (6) by fitting the measured magnetization M , yielding the parameters O(s,,) given in Fig. 27. As all experimental points can well be represented by a straight line, the value N0(a - p) obtained from the slope is shown to be constant in the investigated xhIn and T range. By evaluation of the splitting energies also for the other components, Noa and N,# can be determined independently. Representative values are collected in Table 2. The observed saturation of AE& for sufficiently high magnetic fields is appropriately described by the Brillouin function in (14). With increasing xNn this saturation starts a t higher magnetic fields due to the strong increase of (~(xnrn)) (see Fig. 26b, c)

Table 2 s-d and p-d exchange interaction parameters Noa and NOD, respectively, of the (Zn, Mn) and (Cd, Mn) cbalcogenide mixed crystals

mixed crystal N,a (eV) NOB (eV)

- (Zn, Mn)S -

(Cd, W S 0.22 [136]*) 0.20 [30] (-2.7) [146]

(Zn, Mn)Se 0.24 [1353 -1.22 [I351 0.26 [122] -1.31 [122] 0.29 [30] -1.4 [30]

(Cd, Mn)Se 0.26 [137]*) 0.23 [30] -1.26 [30] 0.24 [143] -1.2 [143]

(Zn, Mn)Te 0.20 [27] -1.1 [27] 0.19 [142] -1.14 [142]

(Cd, Mn)Te 0.22 [134] -0.88 [134] 0.16 [I331 -0.88 [I331 0.18 [138]*)

*) Determined from spin-flip Raman scattering measurements. The other values are obtained from magnetic-field induced exciton-energy splitting.

9) It should be pointed out that the measurements [139] for Fig. 26c are extended far into the spin- glass phase of (Zn, Mn)Te.


I I I I I I I Fig. 27. Energy splitting, AE& of the intensive oc

iOOU - - and o- components of the A-exciton for (Zn, Mn)Se as a function of x1\1,, I(S,)l for various Mn concentrations qfn and temperatures T (after [122]):

- -

600 - - xMn = 0.011, T =2.2 K, e = 0.20 K; 0, a, o xMn = - = 0.05, T = 2.2 K (01, 4.2 K (a), 10 K (a), e =

= 1.78 K; A xhln = 0.103, T = 2.2 K, e = 2.86 K

-

002 004 006 008 XMn I< sz >I -

The magnetic-field-induced, exchange-interaction-enhanced energy splitting was studied also for the 2s excited state of the A-exciton in the case of (Cd, Mn)Te [16] and (Zn, Mn)Te [ 1421, and practically the same splitting pattern was obtained as for the 1s ground state. Furthermore, in (Cd, Mn)Te also the magnetic-field-induced splitting for optical transitions between the lower spin-orbit split-off I?, valence band and tbe rS conduction band could be investigated by measurements of the circular dichroism [43]. As expected in the framework of the theory given before, a splitting into only one c+ and c- polarized component was found, separated by AE(I', + I?,) = x~~J"(cx -

In the wurtzite-type mixed crystals (Cd, Mn)S and (Cd, Mn)Se the exchange interaction leads to an essential mixing of the subbands A, B, and C of the crystal-field and spin-orbit split valence band as their energy differences are relatively small. The theoretical analysis [149] predicts a non-linear dependence of the energy for some evciton components on I (SJI and a significant anisotropy of the splitting patterns and selection rules for HI I c and HA- c, respectively. The experimental results for (Cd, Mn)Se [143, 1501 and (Cd, Mn)S 1146, 1471 are in quantitative agreement with the theory. Especially, the observed B-exciton energy splitting into two components was found t o be much smaller than for the A-esciton.

The exchange-interaction-enhanced effect of a magnetic field on band states could also be studied by measurements of bound-exciton emission lines, e.g. in (Cd, Mn)Te [148] and (Cd, Mn)Se [144]. Due to the thermal equilibrium between the magnetic- field-split bound-exciton states, however, in emission experiments only the lowest- energy component is observable. With increasing magnetic field a shift to lower energies is found both for the donor (D'X) and acceptor (A'X) bound-exciton lines similar as for the lowest-energy c+ component of the free A-esciton. Complications by bound magnetic polaron (BMP) effects (see Section 6.2) and the established destabilization of the bound-exciton comples a t high magnetic fields are discussed in [ 1441.

Also the giant Faraday rotation observed in the (Zn, Mil) and (Cd, Mn) chalcogenide mixed crystals [18, 133, 147, 151 to 1561 a t photon energies E just below the free A-esciton yields a direct verification of the large enhancement of the magnetic-field- induced exciton-energy splitting by S, p-d exchange interaction. The rotation angle, %,, of the plane of polarization for linearly polarized light traveling through the

- +18) I(Wl.


sample parallel to the applied magnetic field is related to the circular birefringence, @F(E) - (na'(E) - na+(E)) , (15)

where na*(E) are the refraction indices for the two circular polarizations o?. Using a single-oscillator model one obtains from (15) in a dominant-term approximation (see 11551)

where AE&(H, T, xy,) is given by (14) and EA(xJI,, T) is the zero-field position of the A-exciton. 6, is found to be proportional to the exciton energy splitting AE& discussed before.

In Fig. 28a the dispersion of the measured specific Baraday rotation for (Cd, Mn)Te is shown for various Mn concentrations in a spectral region below the (xM,-dependent) A-exciton energy. Maximum values of lo4 degree/cmT were measured which exceed the values for conventional semiconductors as CdTe or ZnTe by more than two orders of magnitude. The experimentally obtained E-dependence of @F can well be represented by (16) as shown in [155]. The obtained fitting parameters E , are in good agreement with the known A-exciton energes. The observed strong decrease of BF with increasing temperature and the saturation behaviour for high magnetic fields (see Pig. 28b) are caused by the corresponding properties of the mean spin density (8,) of the Mn2+ ions as predicted by (16) and (14).

An independent, very accurate, determination of the s-d exchange-interaction- induced energy splitting for the conduction band states is possible by measurements of the spin-flip Raman scattering for electrons bound a t shallow donors [136 to 138, 157 to 1681. Corresponding experiments were carried out successfully in the n-type materials (Cd, Mn)S [136, 159, 160, 162, 165, 1661, (Cd, Mn)Se [137, 157, 167, 1681,

f ( e V ) 8 ( T ) --------t

Fig. 28. a) Specific Faraday rotation as a function of the photon energy for (Cd, Mn)Te with various Mn concentrations 511~; T = 77 K (after [IS]). b) Magnetic field dependence of the Fara- day rotation angle, &,for (Zn, Mn)Te (znrn = 0.003) measured at 2.29 eV; T = 5 K, sample thickness 2.4 mm. Dashed curve: calculated after (16) (after [155])

Optical Properties of (Zn, &In) and (Cd, Mn) Chalcogenide Mixed Cryst,als 41

Fig. 29. Donor-electron spin-flip energy, AE,, versus the applied magnetic field for a) (Zn, Mn)Se ( 5 ~ " = 0.041) and b) (Cd, Mn)S ( 5 ~ ~ = 0.10) from

- Raman scattering measurements (after [ISO]); - T = 1.85 K. Solid curves calculated after (17) - with a) 8 = 6.2 and b) 6.1 K - - -

b -

-

- -

-

-

(Cd, Mn)Te [138, 1631, and (Zn, Mn) Se [l60]. A s the donor-bound electron states can be described in an effective-mass approximation and the corresponding Bohr radii are large enough to inlcude a sufficiently great number of Mn2+ ions, (11) can be used yielding the spin-flip energy for a, donor electron,

- AED = Z M ~ N O ~ 1 (Sz) I (17)

I I I I I I with (S,) given by (6). The shift of the a

2 4 6 8 70 72 14 observed Stokes line being equal to AE, is BIT)- plotted in Fig. 29 as a function of the

magnetic field for (Zn, Mn)Se and (Cd, Mn)S. In a first approximation the experimental data can be fitted by (17) as demonstrated by the solid lines. The obtained Noa values given in Table 2 are in good agreement with the values determined by measurements of the magnetic-field-induced exciton- energy splitting. Maximum saturation values for the donor-electron spin-flip energies of about 26 meV are found (see Big. 29b). The observed decrease of AED with increasing temperature can be represented by a Brillouin function in agreement with (17) and (6) as shown in [138]. A t higher temperatures (kT 2 A E D ) also the corresponding spin-flip anti-Stokes line appears in the Raman spectra [ 1651.

Deviations of the measured AED from (17) are found in two respects. The small deviations [160, 1661 a t very high magnetio fields ( H 2 10 T) and not too lorn Mn concentrations (zBI,, 2 0.01) are probably connected with the steps in the measured high-field magnetization curves. As discussed in Section 5.2, these steps are caused by Mn2+ pair and cluster contributions to the mean spin density which are not ade- quately describable by simple expressions like (6). Furthermore, the zero-field behaviour of A E , cannot be explained correctly on the basis of (17). In contrast to the exciton-energy splitting AE& the spin-flip energy for a donor-bound electron does not vanish for H + 0 [162, 165, 1671: AE,(H) T+; AED(0) =+ 0. As demonstrated in Fig. 30 for the case of (Cd, Mn)Se by careful low-field measurements the zero-field value AE,(O) is of the order of 1 meV. A so-called bound magnetic polaron (BMP) mechanism is suggested which is discussed in more detail in Section 6.2.

Considering the experimentally determined s, p-d exchange interaction parameters N0a and N& given in Table 2 i t can be established that in all (Zn, Mn) and (Cd, Mn) chalcogenides Noa > 0 and NOD < 0. This means that a conduction band electron is always ferromagnetically and a valence band hole is antiferromagnetically coupled to the Mn2+ ion spin. The generally found ratio 1p/a1 = 5 can be understood, as the effect of an s, p-d hybridization is much larger at the valence band edge than a t the conduction band edge for symmetry reasons (see [169]). The variation of the exchailge inter-


Fig. 30. Donor-electron spin-flip energy, AE,, determined by Raman scattering measurements in the region of low magnetic fields for (Cd, Mn)Se ( Z M ~ = 0.10) for various temperatures T = 1.9(0), 3.4 (0), 6.9 (x), 12.8 (a), 18.0 (+), and 28.3 K (0) (after [167])

action parameters within the family of the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals is surprisingly small and of the same order as the scattering of the values by different authors. The theoretically expected chemical trend for an increase from tellurides to sulfides [169] cannot be confirmed very convincingly a t present, especially as data for (Zn, Mn)S are missing and the given NoP value for (Cd, Mn)S is probably too large due to an unreliable zy,, determination.

In the framework of a strongly simplifying one-electron model the following expressions are obtained [ 1691 :

= - 2 v i d { ( & d f u e f f - E v ) - ' + (Ev - Ed)-1 } 7 (18) (19)

Here E,, E ~ , and cd + Ueffare the energies of the valence band edge and of the ground and exchange split-off state of the Mn2+ ion, respectively, treated in a Hubbard approximation (see also Section 4). TIPd is the hybridization parameter a t k = 0 and f is a constant given in [169]. If the parameters E , - E~ (x 3.4 eV [169]) and Ueff (= 7 eV [ 1691) are considered t o be nearly constant, N$ is expected t o vary proportional to J:I2 after (18), (19). Therefore, only a very slight variation of No@ is consistent with the small anion-induced change of J1 after Table 1. A possible z&I,, and cation (Cd/Zn) dependence of Noor and N$ needs further careful experimental investigations. A recently claimed strong $&In dependence of No(& - p ) 11391 cannot be esplained on the basis of the present model and may indicate the necessity for a more sophisticated theoretical treatment of the problem.

Jl = - 2 v i d { ( & d + u e f f - Ev) -2 uLflf + (Ed + ueff - E v ) - 3 } f *

6.2 s,, p-d =change-interaction-related properties of the mized crystals in zero magnetic jield

Also in the case of zero magnetic field there are remarkable s, p-d exchange-interaction-induced changes of the energies of free or bound electron and hole states in the (Cd, Mn) and (Zn, Mn) chalcogenide mixed crystals. Especially for the localized electron and hole states of neutral donors and acceptors, respectively, and for excitons bound t o these impurities an energy splitting or a distinct increase of the binding energy is observed which are attributed t o the exchange interaction between the donor electron (acceptor hole) and the Mn2+ ions inside the donor (acceptor) volume [167, 1'7Lto 1851.

A so-called bound magnetic polaron (BMP) model was developed for an explanation of the experimental results which is most simple in the case of shallow donors [167, 175,


181, 189, 1901. Due to the large donor Bohr radius aB a sufficiently great number of Mil2+ ions is included and, therefore, a Gaussian distribution can be used to describe the fluctuation of the Mn2+ ion spins inside the donor volumes. Furthermore, saturation effects need not be taken into account as the exchange interaction is not too strong. On this basis the probability distribution P(AEn) of the spin splitting energy AED for a donor electron was obtained as (see [175])

AED A E ~ , P(AED) = CAE: cosh ( 2 k T ) __ (-m)'

where C = ( 8 n ~ , k T ) - ~ / ~ exp ( - 4 2 k T ) [ l + ~ , / k T ] - l and E,, is the characteristic energy of the bound magnetic polaron

%(zxn, T ) - x1fI,/[T + O(z,,)] is the static paramagnetic susceptibility of the mixed

crystal. The average spin splitting energy (AED) = J AEDP(AED) dAE, then was calculated to be 0

co

+ ( 8 ~ , k T ) l / ~ esp - -- ( 2?T)} '

where @(z) is the error function. The first term in (22 ) describes the so-called mean- field contribution which dominates a t lower temperatures and yields (AE,) = 2ep for k T < E,. This contribution is caused by a partial alignment of the Mn2+ ion spins inside a donor volume due to the exchange interaction with the donor electron. In this donor-electron-induced magnetization field (mean field) the donor electron itself now suffers an energy splitting as in the case of a magnetization by an external magnetic field. Corresponding to (21 ) this contribution to the energy splitting is proportional to LX* and decreases with increasing temperature mainly due to the decrease of x(T) by thermal disorder. A t higher temperatures the second term in (22 ) dominates which is caused by the statistical fluctuations of the magnetization in a considered donor volume. For kT&&,, one obtains from (22 ) (AE,) = ( 2 / i G ) ( 8 ~ , k T ' ) ~ / ~ . This value is only proportional to LX and nearly temperature independent.

The theoretical results for the donor-bound magnetic polaron are in good agreement with the experimental values obtained mainly from the spin-flip Raman scattering measurements of n-type (Cd, Mn)Se 11671 and (Cd, Mn)S [160]. As already mentioned inSection6.1, in zero magnetic field a non-vanishing energy splitting AEDla=o= = 1 meV is observed (see Fig. 30), which agrees well with the theoretical value calculated for the given xMn without any additional fitting. The observed temperature independence of AEDIH=O in the region 2 to 30 K is consistent with ( 2 2 ) as the sum of both contributions is nearly constant after [175] and shows only a slight dip a t T = Ep/k. Also the halfwidth and the barid shape of the measured Raman line seem to be in satisfactory agreement with the theoretical model 1173, 1791.

In the case of neutral acceptors or excitons bound to acceptors or donors the effects of a bound-magnetic-polaron formation are much stronger but more difficult t o es- plain because hole states take part. As suggested by ( 2 1 ) , the characteristic energy of an acceptor-bound magnetic polaron should be larger by a t least one order of magnitude than for the donor case, due to the smaller acceptor Bohr radius and the increased


exchange interaction (IBI > 1 0 ~ 1 ) . For this case a theory was developed which takes into account the spatial distribution of the Mn2+ ions over the cation sublattice and in- volves magnetic saturation and fluctuation effects [182] and the valence band degeneracy [239].

Up to now, unfortunately, spin-flip Raman scattering experiments were not successful for shallow acceptors even for p-type (Zn, Mn)Te and (Cd, Mn)Te. Experi- mental results are available only from luminescence measurements of bound-exciton and donor-acceptor pair emission bands which, however, do not provide the energy splitting but only the energetically favoured component of the hole state. As an example in Fig. 31a the measured binding energy for an acceptor-bound exciton is shown for (Cd, Mn)Te. The Mn-induced enhancement of the binding energy being observed a t lower temperatures rapidly decreases with increasing temperature. Both effects can qualitatively be explained by the bound-magnetic-polaron mechanism discussed before.

Similar results were obtained for the hole binding energy of a shallow acceptor in (Cd, Mn)Te as demonstrated in Fig. 31 b. The energies were determined from an analysis of time-resolved measurements of the donor-acceptor pair emission band [ 1821. The enhancement of the hole binding energy is again caused by the exchange interaction with the Mn2+ ions inside the acceptor volume and decreases with increasing thermal disorder of the Mn2+ spin orientations.

In wurtzite-type (Cd, Mn)Se mixed crystals interesting anisotropy effects for acceptor-bound magnetic polaroils were observed [ 1841. Due to the anisotropy of the p-d exchange interaction there is a strong tendency for a bound-hole spin alignment parallel or antiparallel to the c-axis. The twofold degeneracy of this bistable BMP state can be lifted by a magnetic field HI I c, leading to a temperature-dependent circular polarization of the donor-acceptor pair luminescence being observed in the Faraday geometry by time-resolved measurements.

To demonstrate bound-magnetic-polaron effects in (Cd, Mn) and (Zn, Mn) chalcogenide mixed crystals, in recent years further experiments were reported using site-

d 4000 70 20 30 '

J ( K )

Fig. 31. Temperature dependence of the binding energy for a) the acceptor-bound exciton and b) for an acceptor in (Cd, Mn)Te for various Mn concentrations a) after [178], b) after [182]; in a) q~,, = 0.05 (0), 0.2 (o), 0.3 (A); in b) 0.1(0), 0.05 (v), 0.02 (m), 0.01 (x), 0.005 (o), 0 (0)


Fig. 32. Time dependence of the energy of the bound exciton luminescence peak for (Cd, Mn)Se (a) ZM,, = = 0.1 and b) 0.3) at T = 4.2 K for various magnetic fields (after [177])

t (ns) - selective and time-resolved spectroscopy or optical pumping [153, 174,177,191,193 to 1961. Especially, problems concerning the dynamics of bound-magnetic-polaron formation are studied, but many results are riot completely understood at present. As an example in Fig. 32 the time dependence of the peak energy shift after pulse excitation is shown for a bound-exciton emission line in (Cd, Mn)Se for two different Mn concentrations. At zero magnetic field a remarkable shift to lower energies is found which is caused by the delayed formation of bound magnetic polarons. This effect is larger for XM,, = 0.1 than for xlb = 0.3 due to increased antiferromagnetic coupling of the Mnz+ ions in the latter case. The application of a magnetic field in the case of low Mn concentrations leads t o an initial alignment of the Mnz+ ion spins and, therefore, reduces remarkably the energy shift due to BMP formation. For higher zA~,,, however, the applied magnetic field has just the opposite effect for reasons being not yet clear a t present.

A s already mentioned in Section 2, the observed bowing of the band-gap energy as a function of xafn for Z R ~ ~ < 0.2 (see Fig. 33 as an example and Fig. 11 a for xRin = 0.03)

1

1

/' L? - .

- Fig. 33. Non-linear x ~ , , dependence of the free-exciton energy for (Zn, Mn)Se determined from reflection

I measurements at T = 2.2 (1) and 77 K (2) (after [30]) 0 0 05 010 0 15

XM"-


can also be attributed to exchange interaction effects between electron and hole band states and the Mn2+ ions in zero magnetic field. Starting from the Korido Hamiltonian (4) the following expression for the s, p-d exchange-interaction-induced band-gap shift was derived in [57] by second-order perturbation theory:

AEg(xn[n, T ) - -T~(xnrn, T ) [3m,a2 + (77213” + (23) where m,, m!ll, and mLh are the electron, heavy, and light hole masses in the conduction and valence band, respectively. A s the low-temperature susceptibility X ( X ~ \ I ~ , T ) reaches a maximum near s&fu z 0.1 as discussed in Section 5.2, the red-shift of the gap energy in this concentration region is understandable.

Also the conhiderable increase of I dE,/dTI with increasing Mn concentration x M , observed by several authors 157, 25, 64, 1921 can be explained qualitatively on the basis of (23) using the rough approximation X ( S M ~ , T ) - ZM,,/[T + xynO(sH,, = l)] (see 1571 for further discussion).

m:) P I ,

6.3 Mi1 chalcogenides

The influence of the s, p-d exchange interaction on optical properties of the chalcogenides was studied up to now only for MnS with rocksalt structure. Magneto-optical investigations as described for the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals in Section 6.1 are completely missing.

For band-state-related optical properties this influence could be demonstrated by the unusual temperature dependence of the absorption edge [37, 381. As shown in Fig. 34 a strong, nearly step-like shift of the absorption edge to higher energies is found just below the NQel temperature T,, which obviously is connected with the antiferromagnetic ordering of the Mn2+ ion spins due to s, p-d superexchange interaction. Assuming the absorption edge to be caused by optical transitions between valence and conduction band as suggested in Section 2, this effect can be interpreted on the basis of (23). Whereas for T > T, the product x(T) T - T/(T + O(xBIU = 1)) is only slightly temperature dependent, the decrease of x ( T ) below TN leads to a remarkable increase of the gap energy after (23). An essential energy-gap difference between the antiferromagnetic and the paramagnetic phases is also in qualitative agreement with band structure calculations [37, 38, 96, 97, 100, 186, 1871.

On the other hand, various effects of the 9, p-d exchange interaction on the internal optical d-d transitions in MilsRs were suggested. In [62] the occurrence of a magnon- satellite line was reported for the sA1g - 4Tlg absorption band a t lowest temperatures.

I I 1 0 I 700 200 300

Fig. 34. Temperature dependence of the absorption edge for MnS with rocksalt structure (after P I )


A (nm) - bC0 650 460 670

Fig. 35. Fine structure of the 6A1g - 4Alg, IE, absorption band for MnS with rocksalt structure; T = 4.2 K (after ~ 3 1 )

The observed energy difference to the zero-phonon line agrees with the magnon energy a t the Brillouin-zone boundary known from, e.g., neutron scattering measurements. As shown in Fig. 35 also for the 6A16 + (4A1,, 4E,) absorption band a fine structure could be observed [63]. In addi- tion to the lifting of the (4A1g, 4E6) degeneracy by covalency effects and the appearance of phonon satellites, a splitting of the 6Al, -t 4Eg zero-phonon line into two components is found, which can be ascribed to the symmetry reductionfrom 0,, t o DSd

due to the antiferromagnetic ordering of the Mn2+ ion spins (see Fig. 20). It should be mentioned that an increase of the 90” Mil-S-Mn binding angle by about 0.1” in the antiferromagnetic phase could be directly determined by X-ray diffraction analysis [ 1151. Finally, a distinct change of the oscillator strength for the two lowest-energy absorption bands was reported for MnSRs in the temperature range of the magnetic phase transition [ 1881. AS already pointed out in Section 3 the relatively high oscillator strength of about for these symmetry- and spin-forbidden trarisitions must be attributed to the strong S, p-d exchange interaction. The observed increase of the d-d transition probability with increasing temperature in the region of TN supports this suggestion. The thermal activation energy of this process is found to be approximately equal to the magnon energy, i.e. t o the energy of the elementary excitation of the antiferromagnetically ordered Mn2+ spin lattice.

In the light of the recent interesting results for the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals described in Sections 6.1 and 6.2, further detailed optical and, especially, magneto-optical studies of s, p-d exchange-interaction-induced phenomena in the Mn chalcogenides are desirable.

- wave number (?04cm-‘j

7. Optical Properties of Multi-Quantum-Well Structures and Superlatt,ices

7.1 Valence aid rnnduetim band related vrooerties

Recently the first successful preparation of 11-VI semiconductor superlatticeslo) on the basis of the systems CdTe/(Cd, Mn)Te [201, 2021 arid ZnSe/(Zn, Mn)Se [203, 208 to 2101 was reported. Usually the superlattice structures were grown on (100) or (111) GaAs substrates by molecular bearnepitaxy with a high degree of structural quality shown by X-ray diffraction and transmission electron microscope studies

l o ) In accordance with the authors of the papers discussed in this section in the following the terms “superlattice” and “multi-quantum-well structure” are not strictly distinguished.


E (ev) --

Fig. 36. Comparison of the photoluminescence of a) an A1,,,,Ga,,,,As/GaAs/Al~~~~Gao~,, As double heterostructure on n+-GaAs substrate with layer thicknesses 0.4, 0.6, and 0.8 pm, respectively, and b) a C$,,,Mrb,,,Te/Cd,,,Mn~,~Te superlattice (L , = LI, = 10.2 nm) at T = 77 K (after [204])

[201 to 2041. A s suggested by the dependence of the lattice constants of (Cd, Mn)Te and (Zn, Mn)Se on the Mn concentration xMn (see Fig. l), substantial strains exist in these structures which seem to accomodate totally the lattice mismatch [205,206]. The CdTe and ZnSe layers in these so-called strained-layer superlattices act as quantum wells, whereas (Cd, Mn)Te and (Zn, Mn)Se, respectively, are barrier layers as follows from the dependence of the energy gap E , on xM,, given in Fig. 3.

One of the most interesting properties of CdTe/(Cd, Mn)Te superlattices is the observed high efficiency of the low-temperature exciton photoluminescence being two or three orders of magnitude larger than for CdTe or (Cd, Mn)Te thin films or bulk samples. This may partly be caused by the disappearance of the emission band due to donor-acceptor pair recombination, being established in the case of the superlattices [204, 2071. In Fig. 36 the photoluminescence intensities of a superlattice con- sisting of (Cd, Mn)Te layers with different zMn and a liquid-phase epitaxial (Al, Ga)As/GaAs double heterostructure are compared [204]. Under the same excitation conditions the (Cd, Mn)Te superlattice exhibits even a somewhat brighter photoluminescence. The (Al, Ga)As/GaAs heterostructures used for the comparison have good quality as can be concluded from the low threshold currents of 1.5 to 2.5 kA/cm2 for injection lasers made on the basis of this material.

In Fig. 37 a comparison of the photoluminescence spectra is made between a ZnSe/(Zn, Mn)Se superlattice and a (Zn, Mn)Se epilayer with the same XM,, at equal excitation energy in the interband region. In the case of (Zn, Mn)Se epilayers the luminescence band due to internal 4T, + S A , transitions in the Mn2+ ions is the most intensive one, whereas in ZnSe/(Zn, Mn)Se superlattices a blue exciton emission band dominates at low temperatures showing again a much higher efficiency than ZnSe or (Zn, - Mn)Se epilayers [215].

Recently the ability was demonstrated to grow (Cd, Mn)Te superlattices both for (111) and (100) orientation [211, 2131. The observation of a strong esciton localization a t (111) interfaces (see Section 7.2) and the lack of sharp exciton peaks in the luminescence excitation spectra-in the case of (111) orientation with a high Mn concentration in the barrier layers suggest the (111)-oriented superlattices to be probably more disordered near the heterointerfaces [206, 2121.

Optical Properties of (Zn, Mn) and (Cd, Mn) Chalcogenide Mixed Crystals

'-4 1 49

I I I e x a

S 1

I f t 1

Fig. 37. Photoluminescence spectra for a);ZnSe/(Zn, Mn)Se superlattice (zh.ln = 0.33; L, = 9.7 and Lb = 17.5 nm) and b) (zn, Mn)Se epilayer on GaAs (zm, = 0.33) due to exciton (exc) and &Inz+ internal transitions; T =: 6.5 K excitation energy 3.814 eV (after [203])

Now the role of strain and confinement effects are considered. The anion rule suggests zero valence band offset between CdTe and (Cd, Mn)Te in agreement with the results of UV photoemission spectroscopy [89, 2141, already mentioned in Section 4, and leads to the band diagram shown in Fig. 38a. Taking into account the different lattice constants of quantum-well and barrier material, the successive layers in the superlattice are alternately subjected to biaxial tensile and compressive stresses, respectively. Such biaxial stress fields can be considered as a sum of a hydrostatic and a uniaxial stress parallel to the growth direction whose influence on band-gap or

(Cd.MnlJe n b . , .

Ld Te

- - - - - - - - - - - E" E"

Fig. 38. Schematic diagram of the conduction and valence band energies for a CdTe/(Cd, Mn)Te superlattice a) before and b) after including strain effects (- light holes, - - - heavy holes ; af ter [217])

4 physica (b) 146/1


Fig. 39. Scheme of the band structure for a zincblende semiconductor under compressive (eZz<O) and tensile (eZZ > 0) strain (after [216])

exciton energies is well known. In Fig. 39 the strain dependence of the band structure is shown schematically for a zincblende-type semiconductor. The valence band degeneracy at k = 0 caused by the cubic symmetry is removed. The strain parameters for (111) CdTe/(Cd, Mn)Te superlattices were calculated [217] assuming the distor- tion of the layers to minimize the total strain energy. The corresponding valence band energy splitting was determined on the basis of the Bir-Pikus theory [218]. A schematic band diagram for a CdTe/(Cd, Mn)Te superlattice including strain effects is given in Fig. 38b. The strain-induced offset of the heavy-hole band is negligibly small (< 1 meV), whereas the corresponding light-hole band offset is about 80 meV for zJIn = 0.45 [217]. For such a type I1 superlattice a spatial separation of electrons and

Fig. 40. Luminescence spectrum of a CdTe/(Cd, Mn)Te superlattice ( q r n = = 0.06; L, = 15.3, Lb = 16.2 nm) a) in zero magnetic field and b) a t B = 2 T. Excitation energy 2.539 eV, T = 1.8 K (after [219])


light holes should be expected which seems to be in contradiction to the observed high photoluminescence efficiency. A possible non-vanishing valence band offset assumed for the strain-free case could compensate this effect, leading CdTe/(Cd, Mn)Te to be a type I superlattice. Further experimental investigations of this problem are necces- sary.

An experimental verification of the strain-induced splitting between the heavy-hole and light-hole valence bands in the case of a CdTe/(Cd, Mn)Te superlattice with xnIn = 0.06 was provided in [219]. The sharp peaks in the emission and excitation spectra shown in Fig. 40a and 41 a and indicated by X h h and Xlh are identified as the heavy- and light-hole exciton bands, respectively. The lower-energy peak in Fig. 40a is attributed to an impurity-bound exciton. The higher-energy lines in Fig. 41a are ascribed to LO-phonon satellites and excited states as discussed in more detail in [217]. A s found in [219] the Xhl,-Xlh splitting increases for decreasing quantum-well width for the same Mn concentration and nearly the same ratio of the thicknesses of barrier and quantum-well layers. Under these conditions the strain values in the layers should

1580 i 610 I660

1 I I I b

Xhh

7580 7 600 7620

-A (nm)

810 790 770 750 730

L 1550 7600 7650 !700

0

E ieV)

Fig. 41 Fig. 42 €(eV) -

Fig. 41. Excitation spectrum of a CdTe/(Cd, Mn)Te superlattice ( z ~ ~ = 0.06; L, = 15.3, Lb = = 16.2 nm) a) in zero magnetic field and b) at B = 2 T. Emission measured a t a) 1.597 and b) 1.596 eV; T = 1.8 K (after [219])

Fig. 42. Photoluminescence spectra for two (1 11) CdTe/(Cd, IvIn)Te multi-quantum-well structures ( z ~ , , = 0.26; L, = 7.1 (1) and 65.0 nm (2)) in comparison with a CdTe bulk sample (3). The arrow8 denote the free-exciton energies determined from reflect,ion measurements. Excitation energy 1.970 eV, T = 1.8 K (after [206])

4 .


be nearly constant. Therefore, this change of the X),h-Xlh splitting is an indication for hole-confinement effects and supports the assumption that CdTe/(Cd, Mn)Te superlattices are of type I.

Clear evidence for exciton-confinement effects which are mainly due to electron confinement is given in Fig. 42, showing photoluminescence spectra and free-exciton energies from reflection measurements for a CdTe bulk sample and two (111) CdTe/ (Cd, Mn)Te multi-quantum-well structures with different well thicknesses [206, 221, 2221. In the case of a large well thickness the same position for the free-exciton line is found in the reflection and emission spectra as in the bulk sample. On the other hand, for a well thickness in the order of magnitude of the exciton Bohr radius in CdTe (aB ==: 6.0 nm) a remarkable confinement-induced shift of the lines t o higher energies is observed. I n the emission spectrum only a broad band is found which can be attributed to bound exciton transitions (see Section 7.2).

In ZnSe/(Zn, Mn)Se superlattices the ZnSe quantum-well layers are subjected to biaxial expansive strain contrary to the CdTe layers in CdTe/(Cd, Mn)Te superlattices and, therefore, band-gap narrowing is expected (see Fig. 39). A corresponding red- shift of the superlattice luminescence peaks in comparison to (unstrained) ZnSe epilayers was observed in 1203, 2051. For ZnSe/(Zn, Mn)Se superlattices with very narrow ZnSe wells (2.5 t o 5.0 nm; uB = 2.8 nm), however, a net blue-shift of the exciton lines was found because in this case the confinement effect, exceeds the strain-induced red-shift. The problem of type I or I1 behaviour for ZnSe/(Zn, Mn)Se superlattices is not convincingly solved up to now.ll)

In CdTe/(Cd, Mn)Te [223, 2251 and ZnSe/(Zn, Mn)Se [226] multi-quantum-well structures recently also stimulated emission was observed, indicating the rapid pro- gress in the material preparation technique. A schematic cross section of a typical CdTe/(Cd, Mn)Te laser structure is shown in Fig. 43. It consists usually of a CdTe buffer layer grown on a GaAs substrate and the active multi-quantum-well region embedded between (Cd, Mn)Te cladding layers. After removing the GaAs substrate by B special etching procedure [204, 2251 the remaining multilayer structure was cleaved into small bar pieces which were pressed onto indium layers on a copper heat sink and covered by a sapphire window. Pulses of suitable lasers were used for optical pumping. In Fig. 44a, b the emission spectra of CdTe/(Cd, Mn)Te and ZnSe/(Zn,

L,=-75nm Lb =5nm CdTe (Cd,Mn) Je

buffer Cd Je J 2 9 m

substrate ( U J J GaAs

Fig. 43. Schematic diagram of a CdTe/(Cd, Mn)Te multi-quantum- well laser structure (after [223])

11) Recently a valence band offset of 160 meV was claimed for a ZnSe/MnSe/ZnSe heterostructure after UPS measurements [227] with a higher-lying valence band edge for the broader-gap MnSe.


1

h I I

1

I

-: , C i i 7 66 166 7 62 J I

1 I I

7: 5 735 765 n (!In?) - 1

I I I I I I T

b

3 76 Pfh

a(nm)

Fig. 44. Stimulated emission spectra for multi-qnantnm-well structures a t four different power levels. a) CdTe/(Cd, Mn)Te (zAfn = 0.45, T = 25 K, Ptll = 1.35 x lo4 W/cm2) (after [2251); b) ZnSe/(Zn, 1YIn)Se ( ~ 1 ~ = 0.33, T = 5.5 K, P t h = 2.0 x lo5 W/cm2) (after [226])

Mn)Se lasers are shown for various pump intensities. For increasing pump power above the threshold P,, the evolution of a mode structure can clearly be seen. In the case of ZnSe/(Zn, Mn)Se multi-quantum-well structures laser action could be observed up to 80 K [226].

7.2 Special properties due to M n 3d-states

Also in the case of the considered diluted-magnetic-semiconductor superlattices the magneto-optical propertiesare essentially determined by the Mn 3d-states. In Fig. 40 b and 41 b the luminescence and excitation spectra are shown for a CdTe/(Cd, Mn)Te superlattice with small zMn and, therefore, shallow quantum wells in a magnetic field applied perpendicular to the superlattice layers. A splitting of both the X l h and X h n exciton lines into two components is observed. As shown in Fig. 45, the saturation values of the splitting energies are much smaller than for (Cd, Mn)Te crystals with the same Mn concentration as in the superlattice barriers. Although the excitons are mainly confined within the CdTe quantum wells, the exciton envelope function consider- ably extends into the (Cd, Mn)Te barrier layers leading to s,p-d exchange interaction with the Mn2+ ions. The value of the splitting energy can be used to determine the portion of the esciton wave function in the barriers [219]. Similar exciton energy splittings in a magnetic field are found for ZnSe/(Zn, Mn)Se superlattices. too [220].


I n CdTe/(Cd, Mn)Te superlattices with deep quantum wells, i.e. sufficiently large zMn, only a small shift and practically no splitting of the free-exciton energy is observed in an external magnetic field [206, 219, 221, 2221. In this case the excitons are so strongly confined in the wells that the exchange interaction with the Mn2+ ions in the barriers is negligible and only the usual CdTe g-factor is effective.

A s already mentioned, in (111) CdTe/(Cd, Mn)Te superlattices with sufficiently narrow wells a broad emission band below the free-exciton energy dominates (see Fig. 42). This band was ascribed to localized-exciton transitions as concluded from the temperature dependence of the luminescence intensity [205, 221, 2221. In a magnetic field this band exhibits a strong shift to lower energies and a circular polarization, obviously due to exchange interaction with the Mn2+ ions in the barriers. A s this effect occurs also in the case of deep quantum wells, a binding of the excitons close to the (111) heterointerfaces must be assumed in agreement with the quasi-two-dimensional character of these bound excitons, concluded from the observed anisotropic behaviour in a magnetic field [221, 222, 2281. Mn concentration fluctuations in (Cd, Mn)Te were suggested to induce local fluctuations of the strain and, as a result, of the potential- well depth in thin CdTe regions near to the interfaces which then bind excitons.

If (Cd, Mn)Te is used as quantum-well material, the s, p-d exchange-interaction- enhanced esciton-energy shift is expected to be as large as for bulk crystals. Further- more, a primary shift of the exciton energy into the visible region can be realized by a sufficiently large zfi1,, value. The successful preparation of (Cd, Mn)Te/(Cd, Mn)Te superlattices and the observation of stimulated emission in these structures were reported in [224, 2251. Recently also the possibility of an effective tuning of the energetic position of the laser line by a magnetic field could be demonstrated for these structures (see Fig. 46). The magnetic-field-induced line-shift is found to be linear with the slope BEIBH = 3.4 meV/T which is somewhat smaller than for excitons in bulk (Cd, Mn)Te having the same XnI,, as the wells. However, no saturation of the shift occurs up to 10 T.

B (TI -- Fig. 45

8 (7) - Fig. 46

Fig. 45. Exciton peak energies as a function of the applied magnetic field for a CdTe/(Cd, Mn)Te superlattice ( Z M ~ = 0.06); T = 1.8 K (after [219])

Fig. 46. Magnetic-field dependence of the energy of the stimulated-emission peak for the superlattice laser structure Cd,,8,Mn,,, - TeC&,,M%,,Te; T = 1.9 K (after [232])


The bound-magnetic-polaron effects established for bulk crystals of diluted magnetic semiconductors (see Section 6.2) can also be assumed t o influence the optical and magneto-optical properties of the considered superlattices or multi-quantum- well structures. Especially for CdTe/(Cd, Mn)Te multi-quantum-well structures the role of bound magnetic polarons was discussed in connection with the measured cw and time-resolved luminescence spectra [206,228]. The observed temperature dependence of the exciton energy in a magnetic field, the line-shift in the time-resolved spectra, the decrease of the exciton lifetime, and a pronounced linewidth narrowing in the cw luminescence spectra with increasing magnetic field were attributed to bound-magnetic-polaron effects.

The theoretical treatment of these phenomena in multi-quantum-well structures is quite complicated. I n 12291 the binding energy is calculated for shallow-impurity states in a CdTe well embedded between (Cd, Mn)Te barriers. It is shown that bound magnetic polarons are formed by s,p-d exchange interaction with the Mn2+ ions because the impurity wave function penetrates into the barriers. The binding energy increases if the impurity is placed nearer t o the interface, in contrast to the situation for non-magnetic quantum wells [229]. Similar results were obtained for the exciton energies after variational calculations [230]. It is shown that excitons can be bound in a quasi-two-dimensional state in a region close to the interface. Taking into account also the potential fluctuations near the interface, the exciton-energy shift in a magnetic field is calculated in good agreement with the experimental results [231].

8. Concluding Remarks

The present review has shown the considerable similarities in the optical and magneto- optical properties of the (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals. The variation of the s,p-d exchange interaction inside this family of semimagnetic materials is surprisingly small in comparison to the large band-gap variation. A final conclusion concerning the chemical trend of the p-d exchange-interaction parameter, however, reguires a more precise determination of the sulfide value. The theoretical treatment of the s, p-d exchange interaction in these materials can be expected t o he stimulated by the recent UPS results. Especially calculations exceeding the one-electron approximation are desirable.

The extension of the experimental investigations to the quasi-ternary systems (Zn, Cd, Mn)Te and (Zn, Cd, Mn)Se [234, 2351 completes the knowledge about the considered family of semimagnetic semiconductors but should not lead t o fundamen- tally new results. The growing interest in the Mn chalcogenides as limiting components of the mixed crystals is further enhanced by the recent production of superlattices with quasi-two-dimensional layers of magnetic (MnSe [245]) or semimagnetic ((Cd, Mn)Te [246]) semiconductors. Several open questions of the dynamics of the s, p-d exchange interaction especially in connection with bound magnetic polarons may be answered using modern methods of time-resolved spectroscopy.

The application possibilities of the considered semimagnetic semiconductors are not the subject of this review. It should be pointed out, however, that magnetically tunable lasers [157] and other interesting devices using the outstanding magneto- optical properties of these materials were proposed. For instance, the large Faraday rotation enables the preparation of compact optical isolators, switches, and modulators in the wavelength region 1 1 pm especially for applications in fibre optic systems [244]. In [156] on this basis a design of a very sensitive optical magnetic-field sensor was proposed. The material engineering by superlattices will open further application areas. In [243] special structures were proposed for, e.g., magnetic-field-induced


tuning of resonant tunneling or drastic changes of conductivity, using the strong exchange interaction between band electrons and localized Mn2+ d-electrons.

There is no doubt that the extensively studied and essentially understood (Zn, Mn) and (Cd, Mn) chalcogenide mixed crystals will act as prototypes for other diluted magnetic (semimagnetic) semiconductors as (Hg, Mn), (Pb, Mn), (Zn, Fe), and (Cd, Fe) chalcogenides.

Acknowledgements

We would like to thank Prof. Dr. E. Gutsche for a critical reading of the manuscript and Dr. R. Heise for valuable technical assistance.

References [I] J. A. GAJ, J. Phys. SOC. Japan, Suppl. A 49, 747 (1980). [2] 6. K. FIJRDYNA, J. appl. Phys. 53,7637 (1982). [3] N. B. BRANDT and V. V. MOSHCHaLaOv, Adv. Phys. 33,193 (1984). [4] R. R. GALAZKA, J. Crystal Growth i2,364 (1985). [5] J. K. FURDYNA, J. Vacuum Sci. Technol. A 4,2002 (1986). [6] J. SHAPIRA, S. FONER, D. H. RIDGELEY, K. DWIGHT, and A. WOLD, Phys. Rev. B 30, 4021

[7] R. L. AWARWAL, S. N. JASPERSON, P. BECLA, and R. R. GAFZKA, Phys. Rev. B 32, 5132

[8] A. PAJACZPOWA, Progr. Crystal Growth Charact. 1,289 (1978). [9] 0. GOEDE and DANQ DINH THONG, phys. stat. sol. (b) 124,343 (1984).

(1984).

(1985).

[lo] D. R. JODER-SHORT, M. DEBSKA, and 5. K. FURDYNA, J. appl. Phys. 58, 4056 (1985). [ l l ] R. NITSCHE, H. V. BOLSTERLI, and M. LICETENSTEIGER, 6. Phys. Chem. Solids 21, 199

[I21 0. GOEDE, w. HEIMBRODT, and v. M 7 ~ ~ ~ ~ ~ ~ ~ , phys. stat. sol. (b) 136, K49 (1986). [13] A. BALZAROTTI, U. CZYZYK, A. KISIEL, N. MOTTA, &I. PODGORNY, and M. ZIMNAL-STAR-

[14] K. Y. LAY, H. NEBF, and K. J. BACHMANN, phys. stat. sol. (a) 92, 567 (1985). [15] Y. R. LEE and A. K. RAMDAS, Solid State Commun. 51,861 (1984). [16] A. TWARDOWSKI, M. NAWROCKI, and J. GINTER, phys. stat. sol. (b) 96, 497 (1979). [17] B. MONTEGU, A. LAUGIER, and R. TRIBOULET, J. appl. Phys. 66, 3061 (1984). [I81 J. A. GAJ, R. R. GALAZKA, and M. NAWROCKI, Solid State Commun. 25, 193 (1978). [19] NQUYEN THE KHOI and J. A. GAJ, phys. stat. sol. (b) 83, K133 (1977). [20] N. BOTTKA, J. STANPIEWICZ, and W. GIRTAT, J. appl. Phys. 52,4189 (1981). [21] M. P. VECCHI, W. GIRIAT, and L. VIDELA, Appl. Phys. Letters 38, 99 (1981). [22] J. STANKIEWICZ, Phys. Rev. B 27, 3631 (1983). [23] P. WI~NIEWSKI and M. NAWROCKI, phys. stat. sol. (b) lli, K43 (1983). [24] S. F. CREEAB and J. C. WOOLLEY, phys. stat. sol. (b) 139, 213 (1987). [25] J. E. MOVALES, W. M. BECKER, and M. DEBSRA, Phys. Rev. B 32, 5202 (1985). [26] W. GIRIAT and J. STANKIEWICZ, phys. stat. sol. (a) 59, K79 (1980). [27] A. TWARDOWSKI, Phys. Letters A 94,103 (1983). [28] Y. R. LEE, A. K. RAMDAS, and R. C. AGGARWAL, Phys. Rev. B 33,7383 (1986). [29] T. DONOFRIO, G. LANARCHE, and J. C. WOOLLEY, J. appl. Phys. 67, 1932 (1985). [30] A. TWARDOWSKI, T. DIETL, and M. DEMIANIUK, Solid State Commun. 48, 845 (1983). [31] L. A. KOLODZIEJBSI, R. L. GUNSIIOR, R. VENPATASUBRAMANIAN, T. C. BONSETT, R. FROH-

NE, S. DATTA, N. OTSUKA, R. B. BYLSMA, W. M. BECPER, and A. V. NURMIKPO, J. Vacuum Sci. Technol. B 4,583 (1986).

(1961).

NAWSKA, Phys. Rev. B 30,2295 (1984).

[32J M. IKED.4, K. ITOH, and H. SATO, J. Phys. SOC. Japan 25,455 (1968). [33] 0. GOEDE, W. HEIMBRODT, V. WEINHOLD, and M. LAMLA, phys. stat.. sol. (b) 146, K65

[34] C. BENECKE, W. BIJSSE, H.-E. GUMLICII, and H. J. MOROS, phys. stat. sol. (b) 142, 301 (1988).

(1987).


R. A. FORD, E. KAUER, A. RABENAU, and D. A. BROWN, Ber. Bunsenges. phys. Chem. 67, 460 (1963). L. D. DEKKER and R. L. WILD, Phys. Rev. B 4,3425 (1971). H. TERASAWA, T. KAMBARA, K. I. GOUDAIRA, T. TERANISHI, and K. SATO, J. Phys. C 13, 6615 (1980). H. H. C H ~ U and H. J. FAN, Phys. Rev. B 10,901 (1974). D. R. HUFFMAN, R. L. WILD, and J. CALLAWAY, J. Phys. Soc. Japan 21, S 623 (1966). D. R. HUFFNAN and R. L. WILD, Phys. Rev. 156, 989 (1967). 0. GOEDE, L. JOHN, and D. HENNIG, phys. stat. sol. (b) 89, 11183 (1978). P. SWIDERSIU and A. TWARDOWSKI, phys. stat. sol. (b) 122, K147 (1984). A. TW.4RDOWSK1, E. ROEITA, and J. A. GAJ, Solid State Commun. 36,927 (1980). S. VENUGOPALAN, A. PETROU, R. R. GAEAZKA, A. K. RABIDAS, and S. RODRIGUEZ, Phys. Rev. B 26,2681 (1982). M. YA. VALAKH and A. P. LITVINCHUK, Fiz. tverd. Tela 27, 1958 (1985). D. L. PETERSON, A. PETROU, W. GIRIAT, A. K. RAAiDAs, and S. RODRIGUEZ, Phys. Rev. B 33,1160 (1986). M. YA. VALAKH and A. P. LITVINCHUK, Fiz. tverd. Tela 25, 2774 (1983). A. OLSZEWSKI, w. WOJDOWSKI, and w. NAZAREWICZ, phys. stat. sol. (b) 104, 11155 (1981). Y. TANABE and S. SUGANO, J. Phys. SOC. Japan 9, 753 (1954). DANG DINH THONG and 0. GOEDE, phys. stat. sol. (b) 120, K145 (1983). W. GIRIAT and J. STANKIEWICZ, preprint (1985). E. MULLER and W. GEBHARDT, phys. stat. sol. (b) 137, 259 (1986). 0. GOEDE, m'. HE~NBRODT, and DANG DINH THONG, phyS. stat. Sol. (b) 126, K159 (1984). E. I. GRANCH-4ROVA, J. P. LASCARAY, J. DIOURI, and J. ALLBGRE, phys. stat. sol. (b) 113, 503 (1982). R. 1: TAO, hf. M. ~L~ORIWAKI, Itr. M. BECKER, and R. R. GALAZKA, J. appl. Phys. 63, 3772 (1982). M. E. AnIRaNI, J. A. LASC.4RAIr, and J. DIOURI, Solid State Commun. 46, 351 (1983). R. B. BYLSMA, W. M. BECKER, J. KOSSUT, and M. DEBsK-4, Phys. Rev. B 33, 8207 (1986). G. REBM.4N, c. RIGAUX, G. BASTARD, M. MENANT, R. TRIBOULET, and w. GIRIAT, Physica l l i / l l 8 B , 452 (1983). H.-E. GUALLICH, R. L. PFROGNER, J. C. SHAFFER, and F. E. WILLIAMS, J. chem. Phys. 44, 3929 (1966). L. L. LOHR and D. S. MCCLURE, J. chem. Phys. 49,3516 (1968). w. GIRIAT, phys. stat. sol. ( b ) 136, K129 (1986). H. MITSUHASHI and H. KOMURA, J. Phys. SOC. Japan 30,895 (1971). H. KOMURA, J. Phys. Soc. Japan 26,1446 (1969). J. I. MORALES TOBO, W. M. BECKER, B. I. WANG, M. DEBSKA, and J. W. RICHARDSON, Solid State Commun. P2,41 (1984). W. GIRIAT and J. STANHIEWICZ, Progr. Crystal Growth Charact. 10, 87 (1985). w. GIRIAT, phys. stat. sol. (b) 132, K131 (1985). MA KE-JUN and W. GIRIAT, Solid State Commun. 60,927 (1986). DANU DINH THONG, w. HEIYBRODT, D. HONMEL, and 0. GOEDE, phys. stat. sol. (a) 81, 695 (1984). . ,

[69] W. BUSSE, H.-E. GUBILICH, M. KRAUSE, H.-J. MOROS, J. SCHLIWINSHI, and D. TSCHIERSE,

[70] H.-E. GUMLICH, J. Lum. 23, 73 (1981). [71] J. BENOIT, P. BENALLOUL, A. GEOFFROY, N. BALBO, C. BARTHOU, J. P. DENIS, and B. BLAN-

[72] P. BENALMUL, J. BENOIT, J. DURAN, P. EVESQUE, and A. GEIFFROY, Solid State Commun.

[73] H.-E. GUMLICH, R. MOSER, and E. NEUNANN, phys. stat. sol. 24, K13 (1967). [74] CH. EHRLICH, W. BUSSE, H.-E. GUMLICH, and D. TSCHIERSE, J. Crystal Growth i2, 371

[75] &I. M. MORIWAKI, W. M. BECKER, W. GEBHARDT, and R. R. GAL~ZHA, Phys. Rev. B 26,

J. Lum. 31/32,421 (1984).

ZAT, phys. Stat. Sol. (a) 83,709 (1984).

61,389 (1984).

(1985).

3165 (1982).


[76] H. KETT, F. WUNSCH, and W. GEBHARDT, J. Lum. 31/32, 795 (1984). [77] E. MULLER, W. GEBHARDT, and V. GERHARDT, phys. stat. sol. (b) 113, 209 (1982). [78] M. M. MORIWAEI, R. Y. TAO, R. R. GAL~ZKA, W. M. BECKER, and J. W. RICHARDSON, Phys-

[79] V. F. AQEHYAN and F.~N ZUNQ, Fiz. tverd. Tela 27, 1216 (1985). [SO] D. L. DEXTER, J. chem. Phys. 21,836 (1953). [81] M. JOKOTA and 0. TANIYOLO, J. Phys. SOC. Japan 22, 779 (1967). [82] 0. GOEDE, W. HEIMBRODT, V. WEINHOLD, E. S C H N ~ E R , and H. G. EBERLE, phys. stat.

[83] D. W. LANQER, J. C. HELMER, and N. C. WEICHERT, J. Lum. 1/8, 341 (1970). [84] B. A. ORLOWSKI and V. CHAB, Acta Phys. Polon. A67, 329 (1985). [85] A. FRANCIOSI, SHU CHANQ, R. REIFENBERQER, M. DEBSKA, and R. RIEDEL, Phys. Rev.

[86] B. A. ORLOWSKI, K. KOPALKO, and W. CHAB, Solid State Commun. 50, 749 (1984). [87] C. WEBB, M. KAMINSKA, M. LICHTENSTEIQER, and J. LAGOWSKI, Solid State Commun. 40,

[88] P. OELHAFEN, M. P. VECOHI, J. L. FREEOUF, and V. L. MORUZZI, Solid State Commun. 44,

[89] M. TANIQUCEI, L. LEY, R. L. JOHNSON, J. GHIJSEN, and M. CARDONA, Phys. Rev. B 33,

[go] E. SOBCZAK and H. SOMMER, phys. stat. sol. (b) 112, K43 (1982). [91] B. A. ORLOWSKI, phys. stat. sol. (b) 96, K31 (1979). [92] M. ZIMNAL-STARNAWSKA, M. PODGORNY, A. KISIEL ,W. GIRIAT, M. DEMIANIUH, and J. &a-

[93] J. MASEH and B. VELICHP, phys. stat. sol. (b) 140,135 (1987). [94] B. VELIOHP, J. MASEK, G. PAOLUCCI, V. CHAB, M. SURMAN, and K. C. PRINCE, Festkorper-

[95] A. R. WILLIAMS, J. KUBLER, and C. D. GELATT, Phys. Rev. B 19,6094 (1979). [96] T. OQUCH~, K. TERAKURA, and A. R. WILLIAMS, Phys. Rev. B 28, 6443 (1983). [97] T. OGUCHI, K. TERAKURA, and A. R. WILLIAMS, J. appl. Phys. 55, 2318 (1984). [98] B. E. LARSON, K. C. HAW, H. EHRENREICH, and A. E. CARLSSON, Solid State Commun. 56,

[99] K. C. HASS and H. EERENREICH, J. Vacuum. Sci. Technol. A 1, 1678 (1983).

ica 117/118,467 (1983).

sol. (b) 143,511 (1987).

B 3e, 6682 (1985).

609 (1981).

1547 (1982).

1206 (1986).

JA, 5. Phys. C 17, 615 (1984).

probleme 25,247 (1985).

347 (1985).

[loo] SU-HUAI WEI and A. ZUNQER, Phys. Rev. B 35,2340 (1987). [ loll 5. MASER, B. VELICKP, and V. JANIS, Acta phys. Polon. A69, 1107 (1986).

B. VELICKP, 5. MASEK, V. CHLB, and B. A. OREOWSKI, Acta' Phys. Polon. A69,1059 (1986). [I021 L. M. SANDRATSKII, R. F. EQOROV, and A. A. BERDYSHEV, phys. stat. sol. (b) 104,103 (1981).

M. PODGORNY and J. OLESZKIEWICZ, J. Phys. C 16,2547 (1983). [lo31 5. MASER, B. VELICKP, and V. JANIS, J. Phys. C '20, 59 (1987). [lo41 M. E. LINES and E. D. JONES, Phys. Rev. 141,525 (1966). [lo51 L. C. BARTEL, Solid State Commun. 11,55 (1972). [lo61 R. SHANEER and R. A. SINQH, Indian 5. pure appl. Phys. 12, 589 (1974). [lo71 L. JANSEN, R. RIDLER, and E. LOMBARDI, Physica 71, 426 (1974). [lo81 D. M. BARTHOLOMEW, E. K. SUH, S. RODRIQUEZ, A. K. RAMDAS, and R. L. AWARWAL, Solid

[lo91 T. M. GIEBULTOWICZ, J. J. RHYNE, W. L. CHING, and D. L. HUBER, J. appl. Phys. 67, 3415

[LlO] E. D. JONES, Phys. Letters 18, 98 (1965); Phys. Rev. 161, 315 (1966). [ l l l ] R. MACLAREN MURRAY, B. C. FORBES, and R. D. HEYDINQ, Canad. J. Chem. 50, 4059

[112] G. KERNOV and T. A. MAMADOV, Fiz. Metallov i Metallovedenie 28, 188 (1968). [113] P. W. ANDERSON, Solid State Phys. 14,99 (1963). [I141 M. E. LINES, Phys. Rev. 135, A1336 (1964). [115] H. VAN DER HEIDE, C. F. VAN BRUGGEN, G. A. WIEGERS, and C. HAAS, J. Phys. C 16, 855

[116] R. LINDSAY, Phys. Rev. 84,569 (1951).

State Comaun. 62,235 (1987).

(1985).

(1972).

(1983).


[117] L. CORLISS, N. ELLIOTT, and J. HASTINGS, Phys. Rev. 104,924 (1956). [llS] J. W. BATTLES, J. appl. Phys. 42,1286 (1971). [119] D. R. HUFFMAN and R. L. WILD, Phys. Rev. 148,526 (1966). [120] W. S. CARTER and K. W. H. STEVENS, Proc. Phys. Soc. B68, 1006 (1966). [121] M. ESCORNE, A. MAUGER, R. TRIBOULET, and 6. L. THOLENCE, Physica 107B, 309 (1981). [122] A. TWARDoW3KI, M. VON ORTENRERG, M. DEMIANIUK, and R. PAUTHENET, Acts, Phys. Po-

[123] M. A. NOVAE, 0. G. SYMKO, D. J. ZHENG, and S. OSEROFF, Phys. Rev. B 33, 6391 (1986). [124] R. R. GAE~ZKA, S. NAGATA, and P. H. KEESOM, Phys. Rev. B 22, 3344 (1980). [125] S. D. MCALISTER, J. K. FURDYNA, and W. GIRIAT, Phys. Rev. B 29, 1310 (1984). [126] G. DOLLING, T. M. HOLDEN, V. F. SEARS, J. K. FURDYNA, and W. GIRIAT, J. appl. Phys.

[127] T. GIERULTOWTCZ, W. MINOR, H. KEPA, J. GINTER, and R. R. GAL+~KA, J. Magnetism mag-

[128] L. DE SEZE, J. Phys. C 10, L 353 (1977). [129] S. B. OSEROFF, Phys. Rev. B 25,6584 (1982). [130] J. SPALEK, A. LEWICRI, Z. TARNAWSKI, 5. K. FURDYNA, R. R. GAL~ZKA, and Z. OBUSZKO,

Phys. Rev. B 33,3407 (1986). [131] R. L. AGGARWAL, S. N. JASPERSON, Y. SHAPIRA, S. FONER, T. SKAKIBARA, T. GOTO, N. MIU-

RA, D. DWIGHT, and A. WOLD, Proc. 17th Internat. Conf. Phys. Semicond. San Francisco, 1984 (p. 1419).

Ion. A67, 339 (1985) ; Solid State Commun. 51, 849 (1984).

53,7644 (1982).

netic Mater. 31/34,1373 (1982).

[132] P. H. KEESOM, Phys. Rev. B 33,6512 (1986). [133] A. V. KOMAROV, S. M. RYABCHENRO, 0. V. TERLETSKII, I. I. ZHERU, and R. D. IVANCHUK,

[I341 J. A. GAJ, R. PLANEL, and G. FISHMAN, Solid State Commun. 29, 435 (1979). 11351 D. HEINAN, Y. SE-~PIBA, and S. FONER, Solid State Commun. 51, 603 (1984). [136] D. HEIMAN, Y. SHAPIRA, and S. FONER, Solid State Commun. 45, 899 (1983).

[138] D. L. PETERSON, A. PETROU, M. DUTTA, A. K. RAMDAS, and 8. RODRIGUEZ, Solid State

[139] J. P. LASCARAY, M. C. D. DERUELLE, and J. COQUILLAT, Phys. Rev. B 35, 675 (1987). [la01 J. A. GAJ, J. GINTER, and R. R. G A L ~ K A , phys. stat. sol. (b) 89, 655 (1978). [141] S. M. RYABCHENKO, 0. V. TERLETSKII, I. B. MIZETSKAYA, and G. S. OLEINIK, Fiz. Tekh.

[142] A. V. KOMAROV, S. M. RYABCHENKO, and N. I. VITRIKHOVSKLI, Zh. eksper. teor. Fiz., Pisma

[143] A. V. KOMAROV, S. M. RYABCHENKO, and Yu. G. SEMENOV, Zh. eksper. teor. Fiz. 70, 1554

[la41 L. BRYJA, M. ARCISZEWSKA, and J. A. GAJ, Acta Phys. Polon. A69, 1051 (1986). [I451 ,4. V. KOMAROV, S. M. RYABCHENRO, and 0. V. TERLETSKII, phys. stat. sol. (b) 102, 603

[146] V. G. ABRAMISEVILI, S. T. GUBAREV, A. V. KoMa~ov, and S. M. RYABCHENKO, Fiz. tverd.

[147] S. I. GUBAREV, Zh. eksper. teor. Fiz. 80, 1175 (1981). [148] S. M. RYABCHENKO, Yu. G. SEMENOV, and 0. V. TERLETSHII, Soviet Phys.-J. exper. theor.

[149] S. I. GUBAREV, phys. stat. sol. (b) 134,211 (1986).

Zh. eksper. teor. Fiz. 73,608 (1977).

[137] Y. SHhPIRA, D. HEIMAN, and s. FONER, Solid state Commun. 44, 1243 (1982).

Commun. 43,667 (1982).

Poluprov. 15,2314 (1981).

27,441 (1978); 28,119 (1978).

(1980).

( 1980).

Tela 26, 1095 (1984).

Phys. 55,557 (1982) (Zh. eksper. teor. Fiz. 82,951 (1982)).

[150] R. L. AGGARWAL, S. N. JASPERSON, J. STANKIEWICZ, Y. SHAPIRA, s. FONER, B. KHAZAT, and A. WOLD, Phys. Rev. B 28,6907 (1983).

215 (1981).

257 (1984).

Rev. Letters 65,1128 (1985).

[151] H. K m r , W. GEBHARDT, V. KREY, and J. K. FURDYNA, J. Magnetism magnetic Mater. 25,

[152] A. MYCIELSKI, C. RIQAUX, M. MENANT, T. DIETL, and M. OTTO, Solid State Commun. 60,

[153] D. D. AWSCHALOM, J.-M. HALBOUT, S. VON MOLNAR, T. SIEGRIST, and F. HOLTZBERG, Phys.

[154] M. A. BUTLER, S. J. MARTIN, and R. J. BAUQHMAN, Appl. Phys. Letters 49, 1053 (1986).

https://www.researchgate.net/publication/235510296_Magnetic_susceptibility_and_EPR_measurements_in_concentrated_spin-glasses_Cd_1-x_Mn_x_Te_and_Cd_1-x_Mn_x_Se?el=1_x_8&enrichId=rgreq-f08f90ae480db0ddda7a98c1dd4d4522-XXX&enrichSource=Y292ZXJQYWdlOzIyODAxMjA2MDtBUzoyNDE2NzU4NjgwNDUzMTJAMTQzNDYzMTQyNTg2NA==

https://www.researchgate.net/publication/235510296_Magnetic_susceptibility_and_EPR_measurements_in_concentrated_spin-glasses_Cd_1-x_Mn_x_Te_and_Cd_1-x_Mn_x_Se?el=1_x_8&enrichId=rgreq-f08f90ae480db0ddda7a98c1dd4d4522-XXX&enrichSource=Y292ZXJQYWdlOzIyODAxMjA2MDtBUzoyNDE2NzU4NjgwNDUzMTJAMTQzNDYzMTQyNTg2NA==

60 0. GEDE and W. HEIMBRODT

[155] D. U. BARTHOLOMEW, J. K. FURDYNA, and A. K. RAMDAS, Phys. Rev. B 34, 6943 (1986). [A561 N. KULLENDORF and B. HOK, Appl. Phys. Letters 46, 1016 (1985). [157] D. HEIMAN, Appl. Phys. Letters 41, 585 (1982); 42, 775 (1983). [158] S. M. RYABCHENKO and Yu. G. SEMENOV, phys. stat. sol. (b) 134,281 (1986). [A591 D. L. ALOV, S. I. GUBAREV, V. B. TIMOFEEV, S. M. RYABCHENKO, and Yu. G. SEMEWOV,

[160] K. DOUGLAS, S. NAKASHIMA, and J. F. SCOTT, Phys. Rev. B 29, 5602 (1984). [161] S. M. RYABCHENKO and Yu. G. SEMENOV, Izv. Akad. Nauk SSSR, Ser. fiz. 50, 260 (1986). [162] D. L. Amv, S. I. GUBAREV, and V. B. TIMOFEEV, Zh. eksper. teor. Fiz. 84, 1806 (1983); 86,

[163] A. PETROU, D. L. PETERSON, S. VENUQOPALAN, R. R. G A ~ K A , A. K. RAMDAS, and S. Ro-

[I641 Yu. G. SEMENOV and S. M. RYABCHENKO, Fiz. Tekh. Poluprov. 17, 2040 (1983). [165] D. L. Awv, S. I. GUBAREV, V. B. TIMOFEEV, andB. I. SHEPEL, Zh. eksper. teor. Fiz., Pisma

[I661 &I. NAWROCKI, R. PLANEL, F. MOLLOT, and M. J. KOZIELSKI, phys. stat. sol. (b) 123, 99

[I671 D. HEIMAN, P. A. WOLFF, and J. WARNOCK, Phys. Rev. B 27, 4848 (1983). [168] M. NAWROCKI, R. PLANEL, G. FISHMAN, and R. R. G A L ~ K A , Phys. Rev. Letters 46, 735

[169] H. EHRENREICH, K. C. HASS, N. F. JOHNSON, B. E. LARSON, and R. J. LEMPERT, Proc.

[170] J. P. LASCARAY, M. NAWROCKI, J. M. BROTO, M. RAKOTO, and M. DEMIANIUK, Solid State

[I711 J. P. LASCARAY, A. BRUNO, &I. NAWROCKI, J. M. BROTO, J. C. OUSSET, S. ASKENAZY, and

[172] G. BARILERO, C. RIGAUX, NGUYEN H Y HAU, J. C. PICOCHE, and W. GIRIAT, Solid State

[173] P. A. WOLFF and J. WARNOCK, J. appl. Phys. 66,2300 (1984). [174] J. WARNOCK, R. N. KERSHAW, D. RIDGELY, K. DWIGET, A. WOLD, and R. R. GALAZKA,

[175] J. SPALEK and J. KOSSUT, Solid State Commun. 61, 483.(1987). [A761 J. KOSSUT and W. M. BECKEE, Phys. Rev. B 33,1394 (1986). [I771 J. OKA, K. NARAMURA, I. SOUMA, and H. FUJISAKI, see [169] (p. 1771). [178] A. GOLNIK, J. A. GAJ, M. NAWROCKI, R. PLANEL, and C. BENOIT ;S LA GUILLAUYE, J. Phys.

[179] P. A. WOLFF, Acta phys. Polon. A67,287 (1985). [A801 J. WARNOCK, Acta phys. Polon. A6i, 345 (1985). [181] T. DIETL and J. SPALER, Phys. Rev. B 28, 1548 (1983); Phys. Rev. Letters 48, 355 (1982). [182] TRAN HONG NHUNG, R. PLANEL, C. BENOIT i LA GUILLAUME, and A. K. BHATTACHABJEE,

[ 1831 C. BENOIT 1 LA GUILLAUME, Europhys. Letters 2, 563 (1986).

Izv. Akad. Nauk SSSR, Ser. fiz. 47,2338 (1983).

1124 (1984).

DRIGUEZ, Phys. Rev. B 27, 3471 (1983).

34,76 (1981).

(1984).

(1981).

18th Internat. Conf. Phys. Semicond. Vol. 2, Stockholm 1986 (p. 1751).

Commun. 61,401 (1987).

R. TI~IBOULET, Phys. Rev. B 36,6860 (1987).

Commun. 62,345 (1987).

J. Lum. 34,25 (1985).

SOC. Japan, Suppl. A 49,819 (1980).

Phys. Rev. B 31,2388 (1985).

[184] D. SC?LLBERT, M. NAWROCKI, c. BENOIT 1 LA GUILLAUME, and J. CERNOGORA, Phys. Rev. B 33,4418 (1986).

(1984). [185] R. PLANEL, TRAN HONG NHUNG, G. FISHMAN, and M. NAWROCKI, J. Physique 45, 1071

[I861 K. TERAKURA, T. Oaucm, A. R. WILLIAMS, and J. KUBLER, Phys. Rev. B 30, 4734 (1984). [A871 A. FAZZIO, M. J. CALDAS, and A. ZUNGER, Phys. Rev. B 30,3430 (1984). [l88] D. R. HUFFMAN, J. appl. Phys. 40, 1334 (1969). [189] T. DIETL, J. SPALEK, and L. SWIERKOWSKI, Phys. Rev. B 33,7303 (1986). [190] A. GOLNIE and J. SPALEK, J. Magnetism magnetic Mater. 64/67,1207 (1986). [191] D. SCALBERT, M. NAWROCRI, J. CERNOGORA, and C. BEKOIT h LA GU~LLAUME, see [169]

[192] J. DIOURI, J. P. LASCARAY, and M. EL AMRANI, Phys. Rev. B 31, 7795 (1985). [193] D. D. AWSCHALOM, J. WARNOCK, and S. VON M O L N ~ , Phys. Rev. Letters 68, 812 (1987).

(p. 1679).

https://www.researchgate.net/publication/235572356_Many-electron_multiplet_effects_in_the_spectra_of_3d_impurities_in_heteropolar_semiconductors?el=1_x_8&enrichId=rgreq-f08f90ae480db0ddda7a98c1dd4d4522-XXX&enrichSource=Y292ZXJQYWdlOzIyODAxMjA2MDtBUzoyNDE2NzU4NjgwNDUzMTJAMTQzNDYzMTQyNTg2NA==




[194] D. D. AWSCHALOM, J. WARNOCK, J. R. ROZEN, and M. B. KETCHEN, J. appl. Phys. 61,3532

[195] J. H. HARRIS and A. V. NURMIKKO, Phys. Rev. Letters 51, 1472 (1983). [196] J. J. ZAYKOWSKI, C. JAGANNATH, R. N. KERSHAW, D. RIDCILEY, K. DWIGHT, and A. WOLD,

[197] L. LEY, M. TANrauc~r, J. GHIJSEN, and R. L. JOHNSON, Phys. Rev. B 35,2839 (1987). [198] K. HOCHBERGER, H. H. OTTO, and W. GEBHARDT, Solid State Commun. fXZ, 11 (1987). [199] M. TANIGUCHI, M. FUJIMORI, M. FUJISAWA, M. MORI, I. SouRrA, and Y. 09.4, Solid State

Commun. 62,431 (1987). [200] A. FRANCIOSI, A. WALL, S. CHANG, P. PHILIP, R. REIFENBERGER, F. POOL, and J. K. FUR-

DYNA, see [169] (p. 1763). [201] R. N. BICLNELL, R. W. YANKA, N. C. GTLES-TAYLOR, D. U. BLANKS, E. L. BUCKLAND, and

6. F. SCHETZINA, Appl. Phys. Letters 45,92 (1984). [202] L. A. KOLODZIEJSKI, T. C. BONSETT, R. L. GUNSAOR, S. DATTA, R. B. BYLSMA, W. M. BEK-

KER, and N. OTSIJRA, Appl. Phys. Letters 45,440 (1984). [203] L. A. KOLODZIEJSKI, R. L. GUNSHOR, T. C. BONSETT, R. VENKATASUBRAMANIAN, S. DATTA,

R. B. BYLSMA, W. M. BECKER, and N. OTSUKA, Appl. Phys. Letters 4i , 169 (1985).

T. SAKAMOTO, R. B. BYLSMA, W. M. BECKER, and R'. OTSUKA, J. Vacuum Sci. Technol. B 3, 714 (1985).

[205] L. A. KOLODZIEJSKI, R. L. GUNSHOR, N. OTSUKA, s. DATT.~, W. M. BECHER, and A. \'. NUR- NIKKO, IEEE J. Quantum Electronics 22, 1666 (1986).

[206] A. V. NURMIHKO, R. L. GUNSHOR, and L. A. I~OLODZIEJSKI, IEEE J. Quantum Electronics 22, 1785 (1986).

[207] R. N. BICKNELL, N. C. GILES-TAYLOR, D. U. BLANKS, R. W. YANKA, E. L. BUCKLAND, and J. F. SCHETZINA, J. Vacuum Sci. Technol. B 3, 709 (1985).

[208] Y. HEFETZ, W. C. GOLTSOS, A. V. NURMIRKO, L. A. KOLODZIEJSKI, and R. L. GUNSHOR, Appl. Phys. Letters 48, 372 (1986).

[209] X.-C. ZHANG, Y. HEFETZ, S.-K. CHANG, J. NAKAHARA, L. A. KOLODZIEJSKI, R. L. GUNSROR, and S. DATTA, Surface Sci. 174,292 (1986).

[a101 R. L. GUNSHOR, L. A. KOLODZIEJSKI, N. OTSUKA, and S. DATTA, Surface Sci. l i 4 , 5 2 2 (1986). [211] L. A. KOLODZIEJSKI, R. L. GUNSEOR, N. OTSUKA, X.-C. ZHANG, 8.-K. CHANG, and A. V.

[212] S.-K. CHANG, A. V. NURMIKKO, L. A. KOLODZIEJSKI. and R. L. GUNSHOR, Phys. Rev. B 33,

[213] R. L. GUNSHOR, L. A. KOLODZIEJSKI, N. OTSUKA, S.-K. CHANG, and A. V. NURMIKKO,

[214] M. PESSA and 0. JYLHA, Appl. Phys. Letters 45,646 (1984). [215] Y. HEFETZ, W. C. GOLTSOS, A. V. NURMIKKO, L. A. I<OLODZIEJSKI, and R. L. GnnsHoR,

[216] P. VOISIN, Surface Sci. 168, 546 (1986). [217] D. K. BLANKS, R. N. BICKNELL, N. C. GILES-TAYLOR, J. F. SCHETZINA, A. PETROU, and

J. WARNOCK, J. Vacuum Sci. Technol. A 4,2120 (1986). [218] G. L. BIR and G. E. PIKUS, Symmetry and Deformation Effects in Semiconductors, Chap. V,

Wiley, New York 1974. [219] J. WARNOCK, A. PETROU, R. N. BICRNELL, X . C. GILES-TAYLOR, D. U. BLANKS, and J. F.

SCHETZINA, Phys. Rev. B 32, 8116 (1985). [220] Y. HEFETZ, J. NAKAHARA, A. V. NURMIRKO, L. A. KOLODZIEJSKI, R. L. GUNSHOR, and

S. DATTA, -4ppl. Phys. Letters 47,989 (1985). "2213 A. V. NURMIKKO, X.-C. ZJZANG, S.-I<. CHANG, L. A. KOLODZIEJSKI, R. L. GUNSHOR, and

S. DATTA, J. Lum. 14,89 (1985). [222] X.-C. ZHANG, S.-K. CHANG, A. V. NURMIKKO, L. A. KOMDZIEJSKI, R. L. GUNSHOR, and

S. DATTA, Phys. Rev. B 31,4056 (1985). [223J R. N. BICKNELL, N. C. GILES-TAYLOR, J. F. SCHETZINA, N. G. ANDERSON, and W. D. LAI-

DIG, Appl. Phys. Letters 46, 238 (1985).

(1987).

Solid State Commun. 56,941 (1985).

[204] L. A. KOLODZIEJSRI, R. L. GUNSHOR, s. DATT-4, T. C. BONSETT, M. YAMANISHI, R. ~ O H N E ,

NURMIKRO, Appl. Phys. Letters 47, 882 (1985).

2589 (1986).

J. Vacuum Sci. Technol. A 4,2117 (1986).

Superlattices and Microstructure 2,455 (1986).

62 0. GOEDE and W. HEIMBRODT: Optical Properties of Mixed Chalcogenides

[224] R. N. BICKNELL, N. C. GILES-TAYLOR, J. F. SCHETZINA, N. G. ANDERSON, and W. D. LAI-

[225] R. N. BICKNELL, N. C. GILES-TAYLOR, J. F. SCHETZINA, N. G. ANDERSON, and W. D. LAI-

[226] R. B. BYLSMA, W. M. BECKER, T. C. BONSETT, L. A. KOLODZIEJSKI, R. L. GUNSHOR,

[227] H. ASONEN, J. LILJA, A. VUORISTO, M. ISHIKO, and M. PESSA, Appl. Phys. Letters 60, 733

[228] A. V. NURYIKKO, X.-C. ZHANG, S.-K. CHANG, L. A. BOLODZIEJSRI, R. L. GUNSHOR, and

[229] C. E. T. GONCALVES DA SILVA, Phys. Rev. B 39,6962 (1985). [230] C. E. T. GONCALVES DA SILVA, Phys. Rev. B 33,2923 (1986). [231] JI-WEI Wv, A. V. NURMIKPO, and J. J. QUINN, Phys. Rev. B 34, 1080 (1986). [232] E. D. ISAACS, D. HEIMAN, J. J. ZAYHOWSKI, R. N. BICKNELL, and J. F. SCIIETZINA, Appl.

[233] R. BUCKER, H.-E. GUMLICH, and M. KRAUSE, J. Phys. C 18, 661 (1985). [234] CH. JUNG, E. FLACH, H.-E. GUMLICH, M. KRAUSE, and A. KROST, see [169] (p. 1767). [235] R. BRUN DEL RE, T. DONOFRIO, J. AVON, J. MAJID, and J. C. WOOLLEY, Nuovo Cimento ED,

DIQ, Appl. Phys. Letters 46, 1122 (1985).

DIQ, J. Vacuum Sci. Technol. A 4,2126 (1986).

M. YAMANISEI, and S. DATTA, Appl. Phys. Letters 47, 1039 (1985).

(1987).

S. DATTA, Surface Sci. K O , 665 (1986).

Phys. Letters 48, 275 (1986).

1911 (1983). T. DONOFRIO, G. LAMARCHE, and J. C. WOOLLEY, J. appl. Phys. 5 i , 1937 (1985). S. MANHAS, A. MANOOGIAN, G. LAMARCHE, and J. C. WOOLLEY, phys. stat. sol. (a) 94, 213 (1986). 6. C. WOOLLEY, S. F. CHEHAB, T. DONOFRIO, S. MANHAS, G. LAMARCHE, and A. MANOOGIAN, J. Magnetism magnetic Mater. 61, 13 (1986).

[236] D. THEIS, Phys. Letters A 59, 154 (1976). [237] W. GEBIIARDT, Excited-State Spectroscopy in Solids, Editrice Compositori, Bologna 1987

[238] S. VES, K. STROSSNER, W. GEBHARDT, and M. CARDONA, Phys. Rev. B 33,4077 (1986). I<. STROSSNER, S. VES, W. HONLE, W. GEBHARDT, and M. CARDONA, see [l69] (p. 1717).

[239] E. D. ISAACS and P. A. WOLFF, see [169] (p. 1791). [240] Y. R. LEE, A. RAMDAS, and R. L. AGGARWAL, see [169] (p. 1759). [241] T. GIEBULTOWICZ, B. LEBECH, B. BURAS, 1%'. MINOR, H. KEPA, and R. R. G A L ~ Z K A , J. appl.

[242] E. JAHXE, 0. GOEDE, and V. WEINHOLD, phys. stat. sol. (b) 146, No. 2 (1988). [243] S. DATTA, J. K. FURDYNA, and R. L. GUNSHOR, Superlattices and Microstructures 1, 327

[244] A. E. TURNER, R. L. GUNSHOR, and S. DATTA, Appl. Optics 92, 3152 (1983). [245] R. L. GUNSHOR, L. A. KOLODZIEJSKI, N. OTSUKA, B. P. Gn, D. LEE, J. HEFETZ, and A. V.

NURMIKKO, Superlattices and Microstructures 3, 5 (1987); Appl. Phys. Letters 48, 1482 (1986).

[246] D. D. AWSCHALOM, J. &I. HONG, L. L. CHANO, and G. GRINSTEIN, Phys. Rev. Letters 69, 1733 (1987).

[247] J. K. BURDYNA and N. SAMARTH, J. appl. Phys. 61, 3526 (1987).

(p. 111).

Phys. 55,2305 (1984).

(1985).

(Received November 2,1987)

Optical Properties of (Zn, Mn) and (Cd, Mn) Chalcogenide Mixed Crystals and Superlattices

Documents

Transcript of Optical Properties of (Zn, Mn) and (Cd, Mn) Chalcogenide Mixed Crystals and Superlattices