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Journal of Magnetism and Magnetic Materials 284 (2004) 97–103

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Neutron-diffraction study of the magnetic structureof PrCoAl4

P. Schobinger-Papamantellosa,�, C. Wilkinsonb,c, L.D. Tungd,K.H.J. Buschowe, G.J. McIntyref

aLaboratorium fur Kristallographie, ETH-Zentrum, CH-8092 Zurich, SwitzerlandbDepartment of Chemistry, University of Durham, South Road, Durham DH1 3LE, UK

cInstitut Laue Langevin, BP156, 38042 Grenoble Cedex 9, FrancedDepartment of Physics University of Warwick Coventry CV4 7AL, UK

eVan der Waals-Zeeman Institute, University of Amsterdam Valckenierstr. 65, 1018 XE Amsterdam, The NetherlandsfInstitut Laue Langevin, BP156, 38042 Grenoble Cedex 9, France

Received 24 April 2004; received in revised form 15 June 2004

Available online 10 July 2004

Abstract

The magnetic structure of PrCoAl4 has been studied by neutron diffraction from a single crystal. The Pr moments

order at a temperature near to 20K with a sine-wave longitudinal amplitude-modulated structure. The length of the

wave vector q ¼ ð0 0 qzÞ is almost temperature independent with qz ¼ 0:4087ð5Þ, and only the first harmonic was

observed down to 2K. The amplitude of the wave, 2.05(3) mB/Pr atom at 2K, is reduced compared to the Pr3+ free-ion

moment value g JmB ¼ 3:2mB, due to strong crystal-field effects. One difference between the present and previously

reported neutron powder-diffraction results concerns the wave vector length. The reason for this may lie in the different

magnetic microstructure (stacking faults) of the material depending on the thermochemical history of each sample.

r 2004 Elsevier B.V. All rights reserved.

PACS: 75.25+z; 76.30.kg; 61.12.Ex

Keywords: Rare earth cobalt aluminide; Neutron diffraction; Magnetic structure

- see front matter r 2004 Elsevier B.V. All rights reserve

/j.jmmm.2004.06.023

onding author. Tel.: +41-411-6323-773; fax: +41-

.

address: schobinger@mat.ethz.ch (P. Schobinger-

llos).

1. Introduction and magnetic properties

PrCoAl4, like all light-rare-earth compoundsRCoAl4 (R=La, Ce and Pr), adopts the LaCoAl4type of structure [space group Pmma, a ¼ 7:629 (A,b ¼ 4:037 (A, c ¼ 6:870 (A, Z ¼ 2, R: 2e, (1

40 z),

z ¼ 0:382; Co: 2e, z ¼ 0:816; Al(1): 2a, (0 0 0);

d.

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Fig. 1. Laue diffraction pattern of PrCoAl4 at 11K showing

pairs of satellite reflections with q ¼ ð000:406Þ (e.g. in white

box) in addition to the fundamental reflections. The crystal was

bathed in a quasi-white beam (wavelength range 0.8–3.5 A) at

the end of a thermal-neutron guide. The pattern shown

subtends 1651 around the circumference of the cylindrical

image-plate detector (the horizontal dimension), and 711 along

the length of the detector (the vertical dimension).

P. Schobinger-Papamantellos et al. / Journal of Magnetism and Magnetic Materials 284 (2004) 97–10398

Al(2): 2f, (1412

z), z ¼ 0:043; Al(3): 4j, (x 12

z),x ¼ 0:069, z ¼ 0:02] [1]. Studies of the magneticproperties of a single crystal of PrCoAl4 [2] haveshown that the Co atoms are non-magnetic andthat the Pr moments order antiferromagneticallyat low temperature. The field dependence of themagnetization at 4.2K is strongly anisotropic.Applying a field along the c-axis induces ferro-magnetic order of the Pr moments, after aspin–flop transition at about 0.7 T, which reaches3 mB/Pr atom at the highest field applied (20T).The magnetic isotherms remain linear along the b-and a-axes, and even at 20T the Pr moments arestill far from being parallel. The temperaturedependence of the magnetization measured in afield of 1 T (which is above the spin–flop field) onthe same single crystal [2] has shown that themagnetization adopts only very small values whenmeasured perpendicular to the c direction andmagnetic ordering occurs below about 20K.The magnetic structure of PrCoAl4 has been

studied by some of us by neutron diffraction on apowder sample in the temperature range 1.5–45K[3]. The magnetic reflections are weak down to1.5K in the powder data and are rather broad,possibly due to short-range order effects. Further-more they overlap with nuclear intensities, whichconfuses the interpretation. The analysis of thepowder data led to magnetic ordering model below20K of a simple sine-wave longitudinal-modulatedstructure with wave vector q ¼ ð0 0 qzÞ, where qz ¼

0:437ð2Þ and is almost independent of temperature.The two Pr atoms in the cell were found to scatterin phase, with c as the preferred antiferromagneticaxis and m0z ¼ 2:24ð4ÞmB at 1.5K. This result is inagreement with the strong anisotropy found bymagnetization measurements [2].In the present paper, we focus on the low-

temperature magnetic ordering of the single crystalin order to make a more precise estimate of someparameters and to check for the possible existenceof weak higher harmonics of the same wave vectornot detectable in the powder patterns at 1.5K.Laue diffraction measurements have been made inthe temperature range 11–40K on a single crystalof PrCoAl4 on the diffractometer LADI [4] at theInstitut Laue Langevin (ILL), Grenoble. Low-temperature (2K) monochromatic neutron-

diffraction measurements were also made on thesame crystal on the four-circle diffractometer D10at ILL. The crystal was grown by means of amodified tri-arc Czochralski technique describedin Ref. [2].

2. Single-crystal diffraction measurements and data

analysis

2.1. Laue diffraction measurements on LADI

White beam (Laue) diffraction measurementswere made on the LADI diffractometer installed atthe end of the thermal neutron guide H22 at ILL.Neutrons in the wavelength range 0.8–4.5 A wereincident upon the PrCoAl4 single crystal, whichwas in the form of a cylinder 5.5mm long and3.5mm in diameter. Diffraction intensities wererecorded at temperatures between 40 and 11.5K,the minimum temperature achievable by thesingle-stage displex cryostat, which could be fittedon the instrument.Extra satellite reflections were present in the

images at 11.5K (Fig. 1) and were indexed ashaving a propagation vector q ¼ ð0 0 qzÞ withqz ¼ 0:406ð2Þ, differing significantly from the valueqz ¼ 0:437ð2Þ measured from powder data [3].Reflections were integrated and their intensitiesnormalized to the incident spectrum using the

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P. Schobinger-Papamantellos et al. / Journal of Magnetism and Magnetic Materials 284 (2004) 97–103 99

Laue diffraction suite of programs developed atthe Daresbury Laboratory as part of the CCP4suite for X-ray crystallography, with minormodifications to allow for the cylindrical geometryof LADI and the fact that the neutron beam wasunpolarised [5].

2.2. Monochromatic measurements made on D10

Monochromatic measurements were made onthe same crystal on D10 using a wavelength of1.258(1) A, in order to clarify the disparitybetween the Laue and powder diffraction observa-tions and to obtain more precise measurements forthe intensities of the weak magnetic reflections atthe lowest attainable temperature of 2K. For thesemeasurements D10 was used in its four-circle two-axis mode with the scattering detected by a small(ca. 81� 81) position-sensitive detector. With sucha detector, the count distribution around eachreflection is observed in three dimensions inreciprocal space in a single scan. The consequentadvantages for this experiment are optimal deli-neation of the peak from the background, clearobservation of the propagation wave vector, andthe direction of broadening of the magneticreflections.The PrCoAl4 crystal was mounted in a He-flow

cryostat [6] and cooled down to 2K. A total of 109nuclear and 238 magnetic reflections up to siny=l ¼ 0:74 A–1 were scanned. Initial inspectionrevealed that the magnetic reflections were ex-tended along c*, apparently the origin of the largerwidth observed for the magnetic reflections in thepowder-diffraction experiment. The extension ofthe magnetic reflections along c* also led to partialoverlap of the (h k l+qz) and (h k l+1–qz) reflec-tions. To ensure full integration of the magneticscattering, and to aid the extraction of individualmagnetic intensities, the magnetic reflections werecollected by extended Q-scans along c* centered ath k l+0.5 and over a sufficient range to scanthrough both the l+qz and l+1–qz reflections.Selected magnetic reflections were also followedover the temperature range 2–30K. The magneticreflections were much weaker than the nuclearones (by a factor 30 on average) and about 25%had F2p3s(F2).

2.3. Crystal structure

For the nuclear reflection intensities collected onD10, background corrections were made by amethod that minimizes the value of the ratios(Iobs)/Iobs in three dimensions, where Iobs is thebackground corrected integrated intensity ands(Iobs) is its estimated uncertainty [7]. The crystalstructure was refined against the nuclear intensitiesusing the program FullProf [8], with a singleparameter for the correction of the extinction. Sixof the strongest reflections were excluded from therefinements as they were very poorly fitted due tosevere extinction. Also excluded were twelvesystematically absent nuclear reflections; theirnon-zero observed values were attributed to multi-ple scattering. The results of the crystal-structurerefinements summarized in Table 1, confirm thePrCoAl4 structure [1]. This refinement providedthe scale factor to allow determination of themagnitude of the magnetic moment from the D10magnetic reflection intensities, and the nucleardiffraction intensities recorded on LADI were usedto fix the scale factor for the magnetic reflectionsmeasured in the Laue diagrams.

2.4. Magnetic ordering

All observed magnetic satellite reflections in themonochromatic D10 data were distributed oneither side of allowed nuclear reflections in the c*

direction at a distance qz ¼ 0:4087ð5Þ r.l.u., inagreement with the 11.5K Laue data. No higherharmonics of the propagation vector could bedetected. Because of the partial overlap of thel+qz and l+1–qz reflections in each scan, theirintegrated intensities were obtained by fitting twopeaks to the projection of the three-dimensionalcount distribution of the scan onto c*, with theappropriate Lorentz correction applied to obtainthe observed squared structure amplitude [9]. In allthese scans the profile of the magnetic reflectionscould be approximated by a Lorentzian profile,while that of the nuclear reflections by a consider-ably narrower Gaussian (Fig. 2). Fitting the scanthrough the (2 0 0)7q satellites to a pair ofLorentzians convoluted with the Gaussian thathad been fitted to the scans through (2 0 0) and

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Table 1

Refined parameters of PrCoA14 from monochromatic single-crystal neutron data at 2K and powder data at 1.5K

Pmma 2K, D10 Single crystal data 1.5K, Powder data

Atom/site X z Bi(A)2 x z Bi(A)

2

Pr: 2e (140 z) 0.25 0.3834(2) 0.21(2) 0.25 0.386(1) 0.32

Co: 2e 0.25 0.8121(5) 0.17(3) 0.25 0.807(1) 0.30

Al1: 2a (0 0 0) 0 0 0.34(2) 0 0 0.51

Al2: 2f (1412

z) 0.25 0.0419(3) 0.22(2) 0.25 0.037(1) 0.41

Al3: 4j (140 z) 0.0681(2) 0.7007(2) 0.22(2) 0.0677(7) 0.696(1) 0.26

qz, moz (mB) 0.4087(5) 2.05(3) 0.437(3) 2.24(4)

a, b, c (A) 7.630(3), 4.0416(5), 6.869(2) 7.644(1) 4.0431(4) 6.8717(8)

RF2, RF2w, RF(%), w2nucl.: 3.8, 4.8, 2.8, 11.7 RB, Rm(%) 5.8,13.8

RF2, RF2w, RF(%), w2magn.: 13, 20.5, 9, 2.4 Rwp,Rexp(%) 13.7, 3

The Bi are the individual temperature factors, which were refined in the analysis of the single-crystal data. The Bi values of the 1.5K

powder data were those obtained in the paramagnetic state at 65K [3]. moz (mB), is the refined Pr3+ amplitude of the sine wave with the

wave vector q=(00 qz).

0

40

80

120

0 0.2 0.4 0.6 0.8 1

obscalc

c* (r.l.u.)

(2 0 0)+

(2 0 1)-

(2 0 1)(2 0 0)

580

Fig. 2. Scan along c* through the (2 0 0) nuclear reflection, the

(2 0 0)+and (2 0 1)- magnetic satellites and the (2 0 1) nuclear

reflection. The nuclear reflections are fitted with Gaussian

profiles, the magnetic satellites with Lorentzians convoluted

with a Gaussian with width equal to the average of the widths

fitted to the (2 0 0) and the (2 0 1) nuclear reflections.

P. Schobinger-Papamantellos et al. / Journal of Magnetism and Magnetic Materials 284 (2004) 97–103100

(2 0 1) nuclear reflections gave a mean Lorentzianfull-width at half-height of 0.0306(10) in l whichcorresponds to a correlation length of 225(7) Aalong c.The absence of (0 0 l)7q satellites, including the

(0 0 0)7q satellites, suggests either an anti-parallelarrangement of the magnetic atoms within theelementary cell or a moment direction along the c-axis as proposed in Ref. [3]. Symmetry analysissuggests that for the Pmma space group under the

action of the wave vector q ¼ ð0 0 qzÞ the two Pratoms at 2e related by the center of symmetrybelong to two distinct orbits and could thereforehave different moment values and orientations.There are three irreducible representations allow-ing uniaxial structures with u, v or w components.The refinement of the magnetic structure, againusing FullProf [8], converged for a parallelarrangement of the moments on the two Pr sitesalong c within the chemical cell and confirmed thelongitudinal amplitude-modulated structure. Themoment component of the Pr atoms in the nth cellis given by the expression

mnj ¼ mojzcos ð2pqRn þ fjÞ

where z is the unit vector in the direction of thevarying moment component parallel to c. moj is theamplitude of the sinusoidal variation, Fj is thephase factor of the jth atom relative to the originof the wave and Rn ¼ n1a þ n2b þ n3c for the nthcell (n is integer). In the Fullprof fit, the phases F2,F2 of the two Pr moments were found to be almostequal and were subsequently constrained to be so,while the moments m01 and m02 were fixed to beequal and found to have a value of m0 ¼2:05ð3ÞmB=Pr atom at 2K (Table 1). A similarFullprof refinement of the magnetic satelliteintensities of the Laue diffraction data from LADIgave a value mo ¼ 1:62ð4ÞmB=Pr atom at 11.5K.

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2.5. Temperature dependence of magnetic ordering

The temperature dependence of the integratedintensity of the magnetic satellites measured onD10 (see Fig. 3) and the (unchanged) position ofseveral nuclear reflections with temperature giveno indication of a structural phase transitionbelow 200K. The amplitude of the sine wavecalculated from the fits to the profiles of the(2 0 0)+ and (2 0 1)� magnetic satellites measuredfrom the D10 data changes smoothly withtemperature, as shown in Fig. 4a. Long-rangeordering of the Pr moments sets in below 20K andthere is evidence of short-range ordering of themoments at temperatures just above 20K. Fromthe change in position of the two magneticsatellites (Fig. 4b), one may observe a smallincrease of the wave vector length with tempera-ture, in good agreement with the results obtainedfrom the powder data [3]. The half-width of themagnetic satellites displays little change between 2

13.7

13.9

14.1

0 50 1

(2 0 0)

(a)

140

160

180

200

0 50 1

T

(2 0 0)

(b)

Inte

grat

ed I

nten

sity

Posi

tion

degr

ees

Fig. 3. Thermal variation of the value of the scan angle O at the pea

intensity (b).

and 10K, but then increases rapidly from 10 to17K (Fig. 4c).

3. Discussion

The refined amplitude modulated structure andthe thermal evolution of magnetic ordering corre-spond to the same model found in our previousstudy based on powder data [3]. One importantresult of the present study is that the single-crystaldata are also described by a single harmonic, aswere the powder data. This means that the sine-wave longitudinal structure persists down to 1.5Kand does not undergo a squaring-up transition atlower temperatures to an equal-amplitude anti-phase domain structure, where the moments with-in a block have equal value, changing sign fromone block to the next in the direction of the wavevector.

00 150 200

PrCoAl4

00 150 200

(K)

k of the nuclear (2 0 0) reflection (a) and its integrated nuclear

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0

1

2

0 5 10 15 20 25

PrCoAl4

(2 0 0)+(2 0 1)-

(a)

0.4

0.5

0.6

0 5 10 15 20 25

(201)-

(201)+

(b)

0.01

0.02

0.03

0.04

0.05

0 5 10 15 20 25

T(K)(c)

Am

plit

ude

(l -

q)

(r.l.

u.)

HW

HM

(r.

l.u)

P. Schobinger-Papamantellos et al. / Journal of Magnetism and Magnetic Materials 284 (2004) 97–103102

In rare-earth compounds when the rare-earthatoms have odd numbers of unpaired electrons(Kramer’s ions), amplitude-modulated structuresbecome unstable at T ¼ 0K, and if the anisotropyis of Ising type, higher harmonics of the mainvector appear in the diffraction pattern at thesquaring-up transition towards a long-periodcommensurate structure [10]. In the case ofHeisenberg anisotropy the modulated structuremay persist down to 0K. The structure descriptionwith a sine-wave function applies only to the long-range order, other components remain in adisordered state most likely due to frustrationmechanisms. In the case of Pr3+ which has an evennumber of unpaired electrons (non-Kramer’s ion)the ground state, may be non-magnetic if thelowest electric-crystal-field level is a singlet; in thiscase the sinusoidal structure may be stable downto 0K.It is difficult to give a precise TN from the

variation with temperature of the value of thefitted moment (Fig. 4a) due to the presence ofshort range order at temperatures near 20K. Theneutron powder diffraction experiment [3] alsoindicated that the onset of magnetic orderingcommenced at approximately 20K. The dramaticincrease in the width of the (2 0 0)+and (2 0 1)�satellites between 16 and 17K indicated in Fig. 4cmay, however, hint that the antiferromagneticphase transition temperature could lie in thisregion.The ordered moment amplitude of 1.64 mB/Pr

atom interpolated at 11.5K from Fig. 4a (D10data) agrees well with the value of 1.62(4) mB/Pratom determined from the Laue data. The refinedamplitude of the wave at 2K from D10 data is

Fig. 4. The temperature dependence of the parameters deter-

mined from a fit to the profiles of the (2 0 0)+and

(2 0 1)�magnetic satellites. Lines have been added through the

data points to act as a guide for the eye. The amplitude of the

moment in mB is shown in 4(a) and the variation of qz and 1�qz

is shown in (b). The variation of the half-width at half-

maximum (HWHM) of the (2 0 0)+and (2 0 1)�magnetic

satellites (which were constrained to be equal) is shown in

4(c). For temperatures above 17K, the values of the HWHM

and qz and 1�qz were constrained to be the values obtained

from the 17K fit.

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2.05(3) mB/Pr atom, comparable to 2.24(4) mB/Pratom obtained from the powder sample but isconsiderably less than the Pr3+ free-ion momentvalue g JmB ¼ 3:2mB, most likely due to crystal-field effects. Heat-capacity measurements [11] in amagnetic field on the same PrCoAl4 single crystalhave shown that the crystal-field effect is strong inall RCoAl4 compounds. The ground state inPrCoAl4 is a singlet, and well separated by a gapof about 135K from the next excited state. Such acrystal-field level scheme evidently supports thestability of the sinusoidal magnetic structureobserved at the lowest temperature and thereduced moment values. Similar behavior has beenreported for the modulated structure of thetetragonal compound PrNi2Si2 [12,13], which doesnot display a magnetic transition at low tempera-tures.The increased width of the magnetic reflections

found in the powder data analysis [3] was taken toindicate a small domain size, and the broadeningof the magnetic reflections compared to thenuclear reflections in the c* direction in the singlecrystal data (Fig. 2) supports the existence ofstacking faults in the magnetic structure in thisdirection. The D10 and the LADI single-crystaldata give fitted values of qz of 0.4087(5) at 2K and0.406(2) at 11.5K, respectively. The different qz

component of the wave vector derived frompowder data (qz ¼ 0:437ð3Þ) measurements is mostlikely related to the different microstructures of thetwo samples, which in turn depend on theirthermochemical history. The powder and single-crystal samples were prepared under differentconditions; the powder should have a betterlong-range chemical order because of the longannealing at 8001C, while the single-crystal was

obtained directly from the melt. There are smalldifferences in the lattice parameters of the powderand the single-crystal samples, and attempts weremade to refine the Al/Co site occupation para-meters from the D10 nuclear reflection data, butno evidence could be found for atomic disorder onAl and Co sites. A different sequence of magneticstacking faults in the single crystal and in thepolycrystalline sample could, however, led to theobserved difference in the magnetic wave vector.

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