Intlt&tigQciónRey;,ta Mexicana de Fúica 40, Na. 6 (1994) 911-922

Dielectric anomalies in improper ferroeleetricMn3B7013X boracitesA.G. CASTELLANOS GUZMÁN*

Laboratorio de Investigación en MaterialesD VTT, Universidad de Cuadalajara

Apartado postal 2-638, 44281 Cuadalajara, Jal., México

VÍCTOR ALTUZAR, J. CAMPA MOLlNA, J. RURIK FARÍAS

Facultad de Ciencias Físico MatemáticasUniversidad de Cuadalajara, México

AND

JUAN REYES GÓMEZCentro de Investigación en Ciencias Básicas

Universidad de ColimaApartado postal 2-1694. 28000 Colima, Col., México

Recibido el 19 de enero de 1994; aceptado el 2 de septiembre de 1994

ABSTRACT.The temperature and frequency dependence of the permittivity in sorne halogenboracites has becn measured in the polar and non polar phases. Mn3B7013CI showed the typicaldielectric anomaly of most boracites whereas Mn3B7013I and Mn3B7013Br exhibited a differentdielectric behavior. The results are discussed using a phenomenological theory of the improperferroelectric phase transition in these compounds.RESUMEN.Se han evaluado la dependencia en la frecuencia y la temperatura en algunas boracitashalógenas, tanto en la fase polar como en la no polar. Mn3B7013Cl mostró la anomalía dieléctricatípica de la mayoría de las boracitas, en tanto que Mn3B7013I y Mn3B7013Br exhibieron un com-portamiento dieléctrico diferente. Los resultados se discuten utilizando una teoría fenomenológicade la transición de fase ferroeléctrica impropia de estos compuestos.

PACS, 77.20.+y

I. INTRODUCTION

Sinee the diseovery oC Cerroeleetrieity in Roehelle Salt (sodium potassium tartrate) byValasek [1]' a vast number oC eompounds has shown to present the phenomenon oC in-version, or reorientation, oC its spontaneous polarization by means oC an applied eleetriefield. Once thought to be a great rarity in nature, the Cerroeleetrie e!feet has been Cound tooeeur not only in inorganics [2,31 but as well in polymers and other organie materials [4,51

.Work partially supported by DGICSA-SESIC-SEP. Also at Facultad de Ciencias Físico Matemá-ticas, Universidad de Guadalajara.

912 A.G. CASTELLANOS GUZMÁNET AL.

and speeulations have merged whether it is present in living matter [6,7J and in high Tesupereonduetors 18,9J.l3esides the existenee of remanent polarization and hysteresis 1001'S, a distineti\'e fea-

ture of ferroeleetries is to display a variety of phase transitions; generally, from a hightemperature non polar phase to one, 01' more, low temperature ferroeleetric phases [10].Thus, for a ferroeleetrie erystal one of the most important eharaeteristies to be evaluatedis the temperature and fregueney dependenee of its eleetrie permitti\'ity siuce its hapeenables one to draw preliminar)' conc1usions as to the nature of the lattice instabilit)'eausing the phase transition.The tirst ferroeleetries to be diseovered, Roehelle salt in 1921 [1], potassium dihydrogen

phosphate in 1935 [111and barium titanate in 1945 112],shared in common: a high value ofthe dieleetrie eonstant (of the order of 10 000 near Te in l3aTi03), a pronounced dieleetrieanomal)' at the phase transition without a ehange in volume of the primitive unit cell,and, aboye Te where ferroeleetricity disappears, the permittivit)' obe)'ed a Curie- \Veisslaw [13]. These are the eharaeteristies of a so-ealled "proper" ferroeleetrie trausition inwhieh the primar)' order parameter is then the spontaneous polarization.However, on the basis of group theory. Indembom [14] pointed out that the po!arization

need not be the primar)' order parameter at a ferroeleetrie phase transition. In such a case,the expeeted dieleetrie behaviour should be different from that of proper ferroeleetries,normall)' no Curie- \Veiss law is obeyed and the primitive unit cell volume will change.Thus the term "improper" was proposed b)' Dvorak [151 to refer to ferroelectrics present-ing these eharaeteristies. Examples of improper ferroeleetries are gadolinium mol)'bdate[Gd2(Mo04h] [16) and boraeites ("le3137013X) [Ji].In this work we are interested in dieleetrie properties of boraeites. The generie ter m

"boracite" is given to a large number of eompounds all with general formula Me3I37013X,where Me stands for a divalent metal sueh as ;..Ig, Cr, Mn, Fe, Co, Ni, Cu, Zn, 01' Cd andX is gene rally a halogen CI, 131',01' 1. The name is in allusion to the mineral Mg3I37013CIfrom whieh the family takes its name. Although there are substitutions for 1\le and X [18],we will restriet our attention to halogen boraeites with Mn as a eommon metal. In whatfollows we will nse the symbols of the metal and the halogen onl)' to refer to boraeites,i.e., ;..lg3137013CI = "Ig-CI etc.Evidenee for ferroeleetricit)' in ;..Ig-CI was tirst demonstrated by Le Corre [19]. 1I0wever,

there was a eontroversy on this matter for more than 25 years [20-22]. It was only until As-eher et a/. [Jil observed domain wallmotion in Ni-Cl that the tirst undisputed delllonstra-tion of ferroeleetricity in a boracite was given. Since then a large number of studies havebeen earried out on some of these eompounds, not onl)' because its improper ferroeleetrieeharaeter but also beeause Ni-I boraeite displays mutually interaeting ferroeleetrieit)' andferromagnetism; so-ealled ferrolllagnetoeleetricity [23], at low temperatures.Ph)'sieal eharaeterization amI struetura! studies have shown a diversity of struetural

transitions in halogen boraeites: "lost of these eompounds have a piezoeleetrie-high tem-perature eubie phase (point I(roup 43111,space group F4:lc) whieh lransfol'llls lo a lowtcmpcrature orthorhombic pha.se which is ferroelcctric, ft'rroclastic ami pyroclrctric (pointgroup JIl1ll2, spacc group Pca21), al' lo a sequcnce of phases w¡th point groups 111and 3m.The 43m-rnm2 transformatioJl illvolvcs a doubling of the primitive unit ceH (24J confirmingthe impropcr charactcr of thc pitase transit ion in boracites. Thcrc are tluce COl1tllpounds

DIELECTIIIC ANOMALIES IN IMPROPER fERROELECTRIC... 913

(Cr-Br, Cr-I, and Cu-I) whieh remain eubie down to 4 K [25]. Reeently, a new tetragonalphase with point group 42m was found in Cr-CI by Ye et al. [26) and evidenees of a newtransition (point group yet undefined) have also been observed in Mn-Br [27].Besides this diversity of struetural transitions, investigations of the dieleetrie eonstant

behaviour as a funetion of temperature in halogen boracites have demonstrated seriousdifferenees in their transition anomalies.In Fe-I [28), Co-Br [29], Co-I [30) and Mg-CI !I9] for example, as temperature is de-

ereased from the high symmetry phase (43m), the dieleetrie eonstant, 'ro inereases slightlyand at the transition to the orthorhombie phase (mm2) 'r drops abruptly downwards. Forlong time this \Vas thought to be the typieal behaviour for boracites.In the 70's, ho\Vever, it \Vas found that Cu-CI [31] showed an unusual dieleetrie be-

haviour sinee 'r inereased abruptly up\Vards at the eubie-orthorhombic phase transitionon eooling from the high temperature phase. Ni-I [321 and ~ln-I [33] were later found tofollo\V Cu-Cl dieleetrie behaviour.In this \Vork \Ve present results of a eomprehensive experimental study of dieleetrie

properties of Mn-X boraeites. The t\Vo types of dieleetrie anomaly observed in Fe.I audCu.CI boraeites \Vere found to oeeur in this triad of eompounds \Vhieh ha,'e ~In as eommonmetal. Our results also sho\V that Mn-Br is the fourth example of the nnusual dieleetriebehaviour of Cu-Cl.

2. EXPEHIMENTAL

The :\ln-CI, Mn-Brand Mn.1 single erystals \Vere gro\Vn by the ehemieal vapour transportmethod of Sehmid [34]. AII measurements \Vere earried out \Vith seleeted eubie (lOO)platelets having no defeets visible in a polarizing mieroseope. Platelets were ground fromas-gro\Vn erystals parallel to a naturally-formed eubie (lOO) faeet and the opposite faeet\Vas polished to a 3 or 1 micron finish using diamond pasle. Semilransparent gold-onehromium electro des \Vere evaporaled on both sides of eaeh sample wil h leads attaehedusing sil ver paste from eolloidal suspension. The purpose of lhe semilransparent eleetrodesis to allow us lo observe, through lhe polarizing mieroseope, the domain slate of thesamples under physical eharaeterization in the entire range of lemperature, as \Vell as locheck the poling process applied lo all samples previous lo dieleetrie measurements. Tlll'starting point for the experimenta! study of a ferroelee!rie is lhe preparation of singleerystals whieh are both single domain eleetrieally and crystallographieally [351. Experi-mental proeedures used for obtaining sueh a eondition are generally kno\Vn as "poling".Ir an eleetrie field is used then the method is ealled "eleetrica! poling", and "meehaniealor dastie poling" if use is made of stress [36). The single domain stale in all samples\Vas obtained by eleetrie poling. This was undertaken by eooling lhe sample throughthe transition temperature under an applied eleetrie field of lhe appropiate magnitudeaecording lo lhe sample under poling. Typieal mlues for lll('se fields as \Vell as sampl,'dimCIlsiolls fOf tlle thrcc compositiolls are dcscrib('d in Table I.For die!"etrie eharaeterization :--ln-Br and ~ln-I single erY'lals \Vere lodged in an espe-

eially modified hOI stage (Leitz 350, see Fig. 1) \Vhieh \Vas in IUrI! mounled in the meehan-ical stagc of an Orthoplall polarizillg microscope, \\-"hile ~ln-Cl sampl('s wcre mOlllltt.'d ina small over provided \Vith qnarlz \Vindo\Vs to allo\V optieal ohservations.

914 A.G. CASTELLANOSGUZMÁNET AL.

TABLEI. Typical sample dimensions and poling fields for Mn.X boracites used in this study.

Com posi tion Area (cm') Thickness (/Lm) Poling field(KV/cm)

Mn3B,Ol3CI 0.019 110 50Mn3B,013Br 0.025 80 30-50Mn3B,0131 0.015 75 5-15

FIGURE1. Modified hot.stage Leitz 350 used to lodge Mn-X boracites for dielectric measurements.1. Chamber with fused quartz windows. 2. Chromel.Alumel Thermocouple. 3. Electric connectionsto sample electrodes.

Permittivity of the free crystal parallel to the spontaneous polarization, P" ¡.e., '33of Mn.X boracites, was derived by measuring the electrical capacitance of the sampleswith either a HP4192 Impedance analyzer or a HP 4172 LCR meter. Temperature wasmeasured by means of a Chromel.Alumel thermocouple placed as close to the sample aspossible (Fig. 1). The absolute error in determining 'r values, falls within 10%. This figureis a result of the rather small size of the samples as well as their thickness (cf. Table I),however, the curve of 'r versus temperature for a given sample could be reproduced withinabout :!: 0.1%.

3. RESULTS

The temperature dependence and results at 3 frequencies of the electric permittivityin single domain, single crystals of Mn.I boracite are shown in Figs. 2 and 3. 'r has aroom temperature value of about 8 (typical among halogen boracites) and it increases

DIELECTRIC Al'mlALIES 11' I~IPROPER FERROELECTRIC... 915

markedly as tempera! ure is raised. It reaches a maximum value at the 43m-mm2 phasetransition (T, = 400 K) and at that temperature the dielectric constant falls abruptlydown to a value of about 15. Above the transition, in the non-polar (paraelectric) cubil'phase the magnitude of the permitti,'ity remains rather constan!. Our results are in goodagreement with an independent measurement made at 10 kHz [3i]. However, our (r peakvalue is lower than that rep0rled in a previous work on Mn-X boracite [33). This dilfer-ence could be due to the fact that at low frequencies the non-ferroelectrie/ferroeleetriephase bonndary at a first order transition, as theoretieally predieted for boraeites, mayoseillate in a small AC eleetric field allll thus mimic a high intrinsic permittivity dneto the alternati,'e appearance and disappearence of a tiny fraction of the spontaneouspolarization.As it is seen in Figs. 2 and 3, the dielectric beha,'iour of ~ln-I. independently of fre-

quency, follows that of Cu-CI boracite: (r inereases abrnp!ly npwards at the transitionwhen eooling the erystal from the high temperature phase.The temperature dependenee of the stress-free permittivity, parallel to P" in single

domain, single erystals of ~ln-Br boraeite at 3 ~lHz. and 5 ~lHz. frequencies is shown inFig. 4. The eleetrie permittivity in this boraeite inereases very slowly from a room te m-perature value of about 8 to a maximum peak value of about 15 at the eubic-orthorhombicphase transition. At such a temperature, T, = 535 K, (r drops down to a value of about12.5 and remains eonstant in the eubie paraelectric phase. This drop, however, is smootherthan in ~In-I or Cn-CI boraeit"s. In spite that one could argue that there is no divergeneeof the permittivity in ~In-Br, it is cI,'ar from Fig. 4 that the permittivity increases upwardsat the transition when the crystal is eooled from the high temperature cubie phase. ThusMn-Br is the fourth example of the unusual dielectrie anomaly of Cu-Cl boraeite. Theelfect of lhe aforem<'lltioned oscillations of lhe phase boundary on the (r peak is clearlyillustrated by this boracite, if one compares Fig. 4 in this work with Fig. 3 of Re£. [38) inwhich a much higher peak was observed, the origin of which was idenlified by the mergiugof a complieated domain structure a few degrees near the transition.The temperature dependenee of the permittivity in single domain, single erystals of

Mn-Cl boracile at a frequency of 1 ~lHz, is shown in Fig. 5. The permittivity rises slowlyfrom a room lemperat.ure value of 9 up lo a 13 as the 43m-mm2 phase lransition isapproached (T, = 680 K), a lemperalnre al which (r increases npwards to a maximumvalue of 16. Above T" in the paraeleclrie cubie phase, lhe permiltivily in Mn-CI variesslowly wit h temperature. The lypieal behaviour of mosl boracites is clearly obser\'Cd inMn-C!, i.e., (r decreases downwards al the pha$e lransilion on cooling the erystal fromthe high temperature pha$e.It shonld be pointed onl that the transition temperature of these eompounds, as de ter-

milll'd optieally (as the temperature where the single domain structnre disappears whenentering the cnbic phase) and diclectrically (as the temperature where the maximum of thepermittivity occurs) resulted to be: 680 K (Mn-CI), 535 K (Mn-Br) and 400 (Mn-I) withinexperimental uncertainty. Diserepancies in lhe lransilion temperature as determined bythese two melhods rtln from 4 K for ~ln-Cl and Mn-I up to 13 K for Mn-Br. In Mn-Br,for example, Ascher el al. [1iJ had already found lhat T, for lhis boraeile could be wilhina range of temperalure fmm 523 K lo 569 K. The origin of these dilferences is thoughtto be lhe presence of growth seetors whieh shift the transition lemperature to higher

916 A.G. CASTELLANOS GUZMÁN ET AL.

30

FREQUENCY:25 -

,

Mn-I

,

>-1-

>1-1-

::E""weL

20

15

lO

o 1 KHz

5250

30

,300

,

350

TEMPERATURE (K),

400 450

FREQUENCY

>-1-

>1-1-

::E""WeL

25

20

15

lO

o

Mn-I

10KHz

..,0.00---0-----' o"O) .. o~'-

o~6161/1

¿P ~~o

o

5250 300 350 400 450

TEMPERATURE (K)

FIGURE 2. Stress-free permittivity of Mn-j as a function of temperature at 1 KHz and 10 KHzfrequencies.

DIELECTRIC ANOMALIES IN IMPROPER FERROELECTRIC... 917

30 , ,

F'REQUENCY Mn-[

25 ra 100 KHz

~'"~>- 20 f-f-

2:f-f-

::;; 15 f-n:: aw llllCL a

~a10 f- a~a

co_o-o-o-

5 ,250 300 350 400 450

TEMPERATURE (K)FIGURE 3. Stress-free permittivity af Mn-! as a functian af temperture at a frequency of 100 KHz.

values. Growth sectors are common in synthetic crystals grown by methods such as thatof Schmid [34] permitting the free development of growth facets.

4. PHENOMENOLOGY OF TIIE D1ELECTRIC ANOMALY ON MN-X BORACITES

The free energy describing macroscopic properties of the cubic and orthorhombic phasesof halogen boracites has been determined independently by Dvorak [15], Dvorak andPetzelt [39), Kobayashi el al. [401, Gufan and Sakhnenko [41], Sannikov [42), Levanyukand Sannikov [43] and Toledano el al. [251. None of these models has been able to explainthe whole set of experimental data on boracites. However, it has been shown [44] that atleast the temperature variation of permittivity in halogen boracites can be derived witha sufficient accuracy from a simplified Gibbs potential:

where TI is the true order para meter, a primary structural distortion which double thevolume of the primitive unit cell and it is associated with the normal coordinates at azone boundary "soft" mode, while the polarization, P, merges as a secondary effect drivenby such a primary distortion. T and E are the temperatnrc and c!ectric ficld, 0, {J, "Y, Xo,al and a2 are assumed to be independent of temperature.

918 A.G. CASTELLA:<OS GUZMÁN ET AL.

600,

550500,

450,

400

./o/L._.- ,- ..-_.-.._-. ----' .._~---.•

,350

TEMPERATURE ( K )

• 3 MHz

FREQUENCY

• •

,300

,---,----,_'---....-,-~-,_,---,---_r---_,Mn-8r

30

25•.....•.",- 20.••..••..>-f-

> 15f-f-

:::Eo:: 10Wa...

5

O250

30Mn-8r

25•.....•.- FREQUENCY'".••..••..

>- 20 • 5 MHzf-

>f-f- 15:::E .Ao::wa... .'0/"''''' ••10 .--- .----

.._.'__.__e--e-.-

5250 300 350 400 450 500 550 600

TEMPERATURE ( K )

FIGURE 4. Stress. Free pcrmittivity af Mn-Dr as a function oC temperature and freqllcncy.

DIELECTRICANOMALlESIN IMPROPERFERROELECTRIC... 919

20FREQUENCY MIl-CI

181 MHz

~ 16"'"~

>- 14>-->>-->-- 12:::<~wa.. 10

8

6300 360 420 480 540 600 660 720

TEMPERATURE (K)

FIGURE5. Temperature dependen ce of the stress-free permittivity of Mil-el Doradte.

The equilihrium conditions ac/ap = o and aC/iJr¡, yield for the spontaneous polar-ization P(T) in the ferroelectric phase (below Te):

(2)

and for the inverse dielectric susceptibility, X(T)-l in the ferroelectric phase:

where r¡(T) is determined by the equation

2a2xr¡2 2a a2v21¡4(T "') +!J 2+ 4 1 + 2~1~.'__ Oa -'O r¡ 1r¡ - = .(1 + 2a2X0r¡2) (1 + 2a2X01¡2)2

(3)

(4)

In the paraelectric phase, P = O, r¡ = O and :'( = :'(0 is temperature independent. Ageneral solution for Eq. (4) is not simple and a qllantitative comparison of onr exper-imental reslllts with the predictions of this free energy is still in progress. However agood deal ofinsight has been obtained [441 for halogen bOTad tes based on approxima-tions.From the stability condition a2c / a,¡2 > O it follows that (!J + 211/2) > O therefore

the last term on the r¡ght hand side of Eq. (3) can only accollnt for a decrease of X

920 A.G. CASTELLANOS GUZMÁN ET AL.

in the transition to the non polar phase. However, when az < O the ter m 2az7}z maylead to a reduction of this decrease or even to an increase of X in that transition.Hence, the magnitude and the sign of the jump of X at the transition is determinedby the relative magnitudes of the last two terms in Eq. (3). As the transition is closeto the second order type, the contribution of the third term on the right-hand side ofEq. (3) becomes more significant and the contribution of the second term becomes lesssignificant In this case a decrease of X in the transition to the non polar phase can beexpected.

The form of the free energy requires that the cubic-orthorhombic transition be firstorder, and in a large number of boracites it has such a pronounced first order character.However, the spontaneous polarization behaviour versus temperature in Mn-Br [381seemsto indicate a second-order type transition, this also would explain the magnitude decreaseof the permittivity observed in this boracite. It also has been shown that the cubic-orthorhombic phase transition in Mn-I and Cu-CI [45-461seems to be closer to secondorder, but then this contradicts theoretical expectations of this model concerning themagnitude of the €r at the transition in these compounds.

It is interesting to mention that the model of Sannikov [42) based on considerations ofdouble phase transitions, can also explain the two types of dielectric anomalies observedin this family of compounds. It also predicts the absence of dielectric divergence at thephase transition, a point that should be further explored due to the large number ofboracites which have not yet been characterized.

5. CONCLUSIONS

Our experimental results have shown that Mn-X exhibit the two types of dielectric anoma-lies reported previously for crystals of this large family of compounds: Mn-CI followed thetypical dielectric behaviour of most boracites in which the permittivity drops downwardsat the phase transition when cooling from the high temperature phase, while in Mn-Brand Mn-I the permittivity increases upwards, an unusual dielectric behaviour among thesecompounds firstly observed in Cu-CI boracite [31).

An attempt was made to describe these dielectric anomalies by a simplified thermody-namic potential which can explain both types of dielectric behaviour observed in boracites.However, fits of our data to the free energy expressions of such a mode! involve moredegrees of freedom in the theory than can be determined from the dielectric data alone.The theoretical model used to analyze qualitatively our experimental results explainsboth types of dielectric anomalies, but it fails to account successfully for the magnitudeof the jumps in €r in Mn-X boracites when taking in consideration the order of the phasetransition in these compounds. The order of the transition itself is yet unclear for Mn-Xboracites. Taking Mn-Br as example, from pyroelectrics measurements [38] the 43m-mm2transition seems to be close to second order, but this is in opposition to results fromthermal measurements [461 that shows a typical first order behaviour. This situationreflects the striking differences in physical properties of boracites which are awaiting fora satisfactory theoretical description.

DIELECTRIC ANOMALIES IN IMPROPER FERROELECTRIC... 921

ACKNOWLEDGEMENTS

Work partially supported by DGICSA-SESIC-SEP and the Director of DVTT UDEG.We would like to thank M. Roland BouteJlier (Univearsité de Geneve) for his technicalassistance in modifying our hot stage 350 and for taking the photograph iIlustrating Fig. l.Thanks are also due to Mr. Mónico Briseño and his group from Centro de Cómputo yTelecomunicaciones DCA- UDEG for access to their computing facilities.

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922 A.G. CASTELLAKOS GUZMÁ:< ET AL.

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