ferrimagnetic and antiferromagnetic structures of
TRANSCRIPT
D. E. EASTMAN
In both cases Mn'+ is in an octahedral site, with a4.24-A F=F distance in RbMnFs and a 4.20-AO'—0' distance in MgO. It is interesting to observethat the ratio Gii/Gss is —4.6 for Mn'+ in RbMnF,and —4.7 for Mn'+ in MgO.
The dependence of 61 and 62 on the normalized sub-lattice magnetization 0. is shown in Fig. 7. It has beenassumed that 0. varies with temperature according to aBrillouin function for spin —,'. The temperature de-pendence predicted by the single-ion theory of Callenand Callen'5' is shown by the solid line. According toRefs. 25 and 26, if b1 and b2 are of a single-ion nature,they should vary as
Isis(I. '(0))b(~) = =Is, s(—~),
Ii&s(I. '(0))
where I~+1~~2 is the hyperbolic Bessel function and L, 'is the inverse Langevin function. The above relation
~' K. R. Callen and H. B. Callen, Phys. Rev. 129, 578 (1963).' E. R. Callen, A. E. Clark, B. DeSavage, and |A'. Coleman,
Phys. Rev. 130, 1735 (1963).
results from a classical spin average in the molecularfield approximation. ""A~2 is nearly equal to a' overmost of the range of |T.
According to Callen and Callen, "magnetic dipolarME coupling shouM vary as 0' except at very lowtemperatures. It is seen from Fig. 7 that the experi-mental b1 and b2 are not described by either the I5~2or 0-' curves. These data support the above conclusionsthat both single-ion and magnetic dipolar ME couplingare comparable in magnitude.
ACKNOWLEDGMENTS
It is a pleasure to acknowledge D. T. Teaney andR. J. Joenk for many valuable discussions; D. T.Teaney also supplied the RbMnFs crystals and R. J.Joenk calculated the magnetic dipolar ME constants.A. M. Toxen was of considerable help in furnishingequipment and assistance for the ultrasonic measure-ment of elastic constants.
2' E. Callen and H. B. Callen, Phys. Rev. 139, 455 (1965).
PHYSICAL REVIEW VOLUME 156, NUMBER 2 10 A P R IL 1967
Ferrimagnetic and Antiferromagnetic Structures of QrsSst.
B. VAN LAAR
Reactor Cerftrles Eederlumd, I'etteri, , The Eetherlelds
(Received 14 October 1966)
An investigation of the magnetic and the nuclear structures of Cr~S6 at four different temperatures hasbeen carried out by means of neutron dif'fraction. It has been found that in the nuclear structure, deviationsfrom the idealized structure as given by Jellinek are small at all temperatures. The magnetic structure ofthe antiferromagnetic phase is an antiferromagnetic screw-type spiral with its propagation vector along thec axis. The spin structure in the ferrimagnetic state is collinear and strongly related to the antiferromagneticstructure. Experimental results show that the transition from the antiferromagnetic to the ferrimagneticstate is coupled to the occurrence of a noncollinear component of the moment on the 4f sites.
space group:2 Cr in 2(a):2 Cr in 2(c):2 Cr in 2(b):4 Cr in 4(f):125 in 12(i):
I'31c (Dsg');
0,0,~1;
1 2 1.3&8&4 &
0,0,0; 0,0,2;
8)8) ) 8)8)21 2~. 1 2 1 Swlthg=0
7
&)3'pi Wp" X)si 3' *»)si 3'8'k+si
g=-„y=0, s= —', .t%'os. sponsored jointly by Reactor Centrum Nederland,
The Netherlands and Institutt for Atomenergi, Norway.' F. Jellinek, Acta Cryst. 10, 620 (1957).
INTRODUCTION
'HE crystal structure of Cr5S6 has been deduced
by Jellinek. ' It can be considered as a NiAs-typestructure in which one of each six Cr atoms has been
removed, leading to completely ordered vacancies. Thestructure as given by Jellinek is
At room temperature, the lengths of the unit-cell edgesare u=5.982 A and c=11.509A, and the cell volumeis six times that of the NiAs-type subcell.
The magnetic properties of Cr~S6 have been the sub-ject of many studies. The compound is antiferro-magnetic below 168 K, in the sense that there is no netmagnetic moment, ferrimagnetic between 168 and303 Ky and paramagnetic above 303 K. Kamigaichi
' H. Haraldsen and A. Neuber, Z. Anorg. Allgem. Chem. 234,337 (1937).
'M. Yuzuri, T. Hirone, H. Watanabe, S. Nagasaki, and S.Maeda, J. Phys. Soc. Japan 12, 385 {1957).
T. Kamigaichi, J. Sci. Hiroshima Univ. , Ser. A 24, 371 (1960).' M. Yuzuri, Y. Kang, and Y. Goto, J. Phys. Soc. Japan 17,Suppl. B1, 253 (1962).
6 K. Dwight, R. W. Germann, N. Menyuk, and A. Wo}d, J.Appl. Phys. Suppl, 33, 1341 (1962).' M. Yuzuri and Y. Xakamura, J. Phys. Soc. Japan 19, 1350(1964}.
8 C. F. van Bruggen and F. Jellinek, Colloque International surles derivees semi metalliques du Centre National de la RechercheScientiique, Orsay, 1965 (to be published).
STRUCTURES OF Cr5S6
showed from susceptibility measurements that the spinsshould be in the basal plane in both the ferrimagneticand the antiferromagnetic state, a result which, for theferrimagnetic state, agrees with Jellinek s conclusionsfrom x-ray diffraction patterns of powder samplesoriented in a magnetic field. There are indications' thatthe ferrimagnetism in Cr~S6 disappears when the va-cancies are disordered.
Mechanisms for the transition from ferrimagnetic toantiferromagnetic have been proposed by differentauthors. Yuzuri et al. consider the possibility of somekind of triangular spin arrangement, in which a dis-continuous change of the angles between the spinscould explain the transition. Jellinek gives, as a possiblemechanism, a rearrangement of the spin-order such thatin the ferrimagnetic state the spins are distributed overtwo sublattices in a way different from that in the otherstate.
Finally, Dwight et al. ' consider the two differentchains of Cr ions parallel to the c axis which containthe vacancies, and explain the transition as a shift froma ferromagnetic to an antiferromagnetic interactionbetween these two chains. In the present paper, theresults of a neutron-diffraction study of the two mag-netic phases of Cr5S6 vill be presented, and the spinstructures as deduced from this study will be given.
EXPERIMENTAL
The sample of Cr5S6 used in this investigation hasbeen prepared at the University of Groningen by heatinga mixture of chromium powder (99.99/o) and sulfur(99.9999%%u~) in double-sealed, evacuated quartz tubesfor 48 h at 1000 C. After the heating, it was cooledslowly, powdered, and tempered for some days at300'C. The whole sample consisted of about 25 batchesprepared in this way. Each batch was checked forhomogeneity by x-ray diGraction and by measuring themagnetization-versus-temperature curve before it wasadded to the sample. Only small traces of Cr203 werepresent in the specimen.
Neutron-diffraction patterns were obtained at theFatten high Aux reactor at temperatures of 4.2, 78, 208,and 370'K from a sample contained in a cylindricalsample holder with a diameter of 20 mm.
The neutron wavelength employed was 2.57 A, ob-tained from the (111)planes of a copper monochromat-ing crystal. 'The Soller slits which were placed betweenthe reactor and the monochromator had a horizontalangular divergence of 30'. The angular divergence ofthe slits in front of the BF3 counter was 10' for the dia-grams taken at He and N2 temperatures and 30' forthe other diagrams.
As a second-order 6lter, a block of pyrolytic graphitewith a thickness of 7.5 cm was employed, as describedby Loopstra. ' In addition, in order to study the tran-
9 S.0.Loopstra, Nucl. Instr. Methods 44, 181 (1966).
TAsl.z I. Final structural parameters of Cr5S6 at T=370'K.
zLCr in 4(f)gxLS in 12(z)jyfS in 12(i)jzPS in 12(z)g
B isotropic (Cr)B isotropic (S)2 factor
0.993+0.001
0.337+0.0050.998+0.0030.377+0.002
1.2~0.2 A1.5a0.2 i.2
3 5%
sition from the antiferromagnetic state to the ferri-magnetic state, two sections of the diagram werescanned repeatedly while the sample was allowed towarm up slowly from liquid-nitrogen temperature. Theheating rate was about 10 per hour and the temperaturedifference between the lower and the upper part of thesample, which was contained in an aluminum sampleholder with a wall thickness of 2 mm, was about 3 .
Q, w;(Q, I.b,—Q„I„i,) '
by a full-matrix refinement technique. Here, p; is thesum over all peaks which can be separated in thediagram, w, is the weight of one peak, and P„ is thesum over the overlapping reflections in such a peak.
The results are given in Table I. It was found thatthe deviations from the idealized structure are signi6-cant only for the s parameter of the Cr in 4(f).
The observed and calculated intensities are listed inTable II. The anal E factor, defined as
was 3.5/q.The value for the coherent nuclear scattering ampli-
tude of sulfur used in the refinement was 0.28)&10—"cm, as given by Menyuk, Dwight, and %old. ' Use ofthe value of 0.31)&10 "cm, listed in the InternationalTables for X-Ray Crystallography, Vol. III, leads toan abnormally high value for the individual isotropictemperature factor of the sulfur atoms. For the chro-mium scattering amplitude, the value of 0.352)(10—"cm was used.
"N. Menynk, K. Dv~ight, and A. Wold, J. Appl, Phys. $li, 1088(1965).
CRYSTALLOGRAPHIC STRUCTURE IN THEPARAMAGNETIC STATE
The structure of CrsSs given by Jellinek is an ideal-ized one, and an attempt was therefore made to de-termine more accurately the s parameter of the Cratoms in 4(f) and the x, y, and s parameters of thesulfur atoms from the neutron intensities obtained at370'K
The above-mentioned structural parameters weredetermined by means of a least-squares program whichminimizes the quantity
656
TABLE II. Calculated and observed intensities of CrqSs in theparamagnetic state (T=370'K).
0 0 20 1 00 1 10 1. 20 1 31 1 00 0 4
1 21 2
0 2 00 20 1 40 2 20 2 30 1 5
1 41 1 4
2 01211 2 10 2 40 0 6122
2 20 1 6123
2 30 3 00 2 50 30 3 21 2 41 2 41 1 61 1 60 3 30 1 70 2 62 2 0
2 52
0 3 4
26
12121262666
121212121266
12121212
2121.21212126
121212121266
1212126
121212
I.sic
27596
594150441
12833
37201467
611579358
24948
53664803
5093
1162110771433
161188
676043
01713033
5701783
025231
481433018
Q„I„),27596
594150
12833
5248
25058
249
1021750
240
9133
7151171
2416
25231
p. Iob'
263 ( 62)146 ( 61)54s ( 70)
74 ( 66)4O8 ( 61)
1312 ( aS)64 ( 57)
5269 (120)
231 ( 56)0( 60)0( 6Q)
io229 (125}0( 60)
121 ( 63)
0( 60)0( 60)
7131 (125)0( 60)
2429 ( 93)
263 ( 76)0( 60)
599 ( 93)
a Numbers in parentheses are estimated standard deviations.
MA65'ETIC STRUCTURES
A'Otiferromagnetic State
In the diagrams obtained at 4.2 and 78 K, manyextra peaks of magnetic origin were found. ThesecouM not be indexed satisfactorily on the basis of aunit cell which was a simple multiple of the nuclear
cell, considering an up to twenty-fivefold increase ofits vohune. This means that there is no simple relationbetween the periodicities of the magnetic and thenuclear structure.
In general, the spin-vector on the uth atom in the ethunit cell in a periodic spin structure can be written asa Fourier sum":
S„„=P,Q„(z) expi~ R .,
where R„„is the position vector of the atom and g thepropagation vector of the Fourier component. Neutron
"D. H. Lyons, F. A. Kaplan, K. Dwight, and N. Menyuk. ,Phys. Rev. 126, 540 (1962).
TABLE DI. Schematic representation of magnitude and rela-tive phase angle of magnetic moments in the magnetic phasesof CrgS6.
Atom Position x Moment Phase angle
23456789
10
14,123
31
1
2+83
p
Ij,b
Pap$pgPfPojllf
PfpcJtlf
pO
180'po
180'+rt
PO
+400
scattering from such a spin structure occurs in direc-tions associated with reciprocal-lattice vectors e = H —~;the structure factor will be
F(H, ~) =P„Q„(~)expiH r„,
where 8 is a reciprocal-lattice vector associated with thenuclear structure and r„ is the position vector in thenuclear unit cell of the vth atom. Because of this, themagnetic scattering manifests itself in a number ofsatellites around each nuclear reciprocal-lattice point.There can be as many satellites around each point asthe number of nonzero components in the Fourierexpression for the spin structure. In the diagrams ofCr~S6 in the antiferromagnetic state, no magneticscattering has been observed in directions associatedwith nuclear reciprocal-lattice points, which means thatthere is no component in the spin structure with thesame periodicity as the nuclear structure.
All directions in which magnetic scattering occurscorrespond to lattice spacings d, given by
I/ds= (I s+h~+V) ]a') s+(I ] c*~~ (.[)s.
This shows that only two Fourier components are non-zero, one with propagation vector +~ and one with
propagation vector —~, parallel with the c~ axis.The existence of only two Fourier components im-
mediately rules out the possibility of an antiphase-domain-type structure. Kamigaichi's observation4 thatthe spins should be in the basal plane leaves a screw-typespiral structure as the remaining possibility. In such anarrangement, the manner in which the spin componentvaries from one unit cell to the next is given by thepropagation vector c. In each crystallographic unit cell,a phase angle p„can be assigned to each magnetic atom.
The intensities of the satellite rejections in a screw-
type spiral structure are given by
I(H, —~) =JL(q')F'(H —~)exp( —8/2d') for e= H+g
I(H, +~)=jL(q')F'(H +~)exp( —8/2d') for e=H —q
where
F(H, &~)=0.2695 P„f„(H, +~)p„expi(H r„~g„).
In these expressions, f„(e) is the form factor of the
657
TABLE IV.. Final structural anura an'
parameters fan magneticne lc states.
0
S~RUCq UR FS OF
It should belar
be mentioned that in1 tio factors a e
n, rat er
PPrameters. As a result the
e i erent
the diffett dfi d th an the se ar
en
and str
'erent position Is. n Table IV
parate moment fs 0
as ructural param tmeters are l
, the 6nal maa neticd
Ant'nh erromagnet'
T =4.2oK T =77'K
(5.962 +0.003)(11 509+0 011) g (11.506 +0.005) g
A (53.25 &0.32) A
Ferrimagnetic
T =208'Z
(S.974 a0.012) A(11.509 &0.028) g
Spiralperiodicity
z PCr in 4(f)js LS in 12(i)gy LS in 12(i)&z LSin 12(i)$
papbpopf
0.993+0.0010.331&0.0030.998+0.0020.376 +0.001
(2.98 +0.25)ps(2.VV +0.12)pg(2.78 +0.10(2 57~0,)PB
(2.73 +0.04)pg
(129.1 +2.7) '0 A~
0.995 +0.0010.328 +0.0030.998+0.0020.378 &0.001
(2.87 +0.84(2,66&0 5( .56+0.19)pg
o I 6)pg
(2.34 &0.32)pgg
(2.ss +0.06)p~
(131 2~9 2) o
(0.3 +0.1) A&
4 7'Fo8 over-a11R factor
) C3
I
gp, a
~'D E Cox %'
eman for Cr'+.
. Cox, W. J.Takei, and G. Sh', . ys. hCox, W. . ', . lrane, J.Phys. Chys. hem. Solids
an . J. Freeman, Acta Crc a ryst. 14, 27 (1961).
p, b
b
Fxo. 1.vacan
' ntderromagn tth lattice a
elc s inlce are represented be y open squares.
0.992 +0.004
nd calculaisted whil
t t i h0.991+0,007
---F 1
0.379 +0.004
(1.70 +0.34)paFerrimagnetic State
paver age
(1.69 +0.20)p~ n t ediagram og, obtained at 208'Kthb' fhth d'
.-., l
ase, it was deduc d te antiferro-
P'
f'
g'
h
man ' 'ngnetic ion v and
Fn, n p„is its ma nThe
P fo s
um is taken ov
p' struc u e w
uc ure.
ni ce".
spins in the basuc a
e basal plane is
ver all equivalent reflec-„ f„(H)p„K„expiH.~ s v Pz fy
2 —1g =
g 1+cos 7/) i
av a equivalent
n anced by its h'
vector in the d' 'e
, which is st
f thbl h th
hlsho
e same meaninng as before. It
tio b do re ative an
can be
n e educed from owdn e om powder data.
a icaly considering all os' ' ' '
t b de eterminede magnetic
ii
o rin
n addition, one orP e ers should also
~ ~
io rmined.e re6nement of both ma ne
're ot magnetic and str t
carrie out a a'ructura
p g'
by ull-magram. This resulted in
fo th d tI'A band 78 K
p
l L
o ained form
atson and Fre
jIL
C
B. vAN LAA R
Ter.z V. Calculated and observed intensities of Cr5S6 in the antiferromagnetic state. The column s indicateswhether the intensity is nuclear (s=o), or magnetic (s=+1).
00001
11111
1110
1
00111
1222
2121222212
21
1022222222022210222122122
+1—1+0+1+0
+1—1+0+1—1+0+1—1+0—1+0—1+1+1+0+1—1+0+0—1+1+0—1+1—1+0+0+1+1+0+1—1—1+0
+0+1+0+0+1+1—1—1+0—1+1—1+0+0+0+0+1+1—1
+1+0+0+1+0—1—1+1+0+0
2222666
12121212121212122666
1222
1266
1212666
121212121212121212
1212121266
12122
12121212241212122
24
2412
2121224122412121212
616373
722
42400
2781696
1084620231
4291514745971337
473756
1717
22670
23115594517
101
8600
38456197
15368
3188182
2695957
5
5913454
17089158791389
083
13400
2728839017845
11003
23442118
398
1682052ii2770
1302551677
426278
16961084620231
4291514745971337
47
315 (130)190 (120)
1659 (120)10530 (160)20791 (250)
359 (100)14783 (170)4972 (135)1384 (110)
40 (100)
3790226
7
23
1607610
186
038
3196182
2695957
5834
5913454
3833 (120)327 ( 90)
0( 70)0( 70)
45 ( 80)
15999 (170)0( 70)0( 70)
45 ( /0)
0( 70)30 ( 70)
510 ( 90)ruSS ( 95)
3140 (115)107 ( 85)
2634 (110)1001 (100)
0( 70)800 (110)30 ( 60)
380 (100)30 ( 60)
1500 (200)138 ( 80)
0 ( 70)
100 ( 70)20 ( 70)
2000 1936 (120)
4447 {160)0( 60)
300 (100)1836 (130)
70 ( 50}
7=4.2'K
6163 6165 (400)73 250 (150)
722 614 (135)
Ioa,1o
435
27300
107862
43949140
20871501955574
191820
1275
1
54322235
21900
14240
65613
140590
1214382
34422
10116
85527150495
0520
153189131
7398
0876766
1414776959
2491
471
T= 77'Kg, I„),
275107862
43949140
20871501955574
19
140790
1214
15702495
0
250
Er Job:
0( 60)490 ( 68)
136 ( 60)0( 60)
774 ( 66)4465 (100)9119 (410)
189 ( 52)7164 (112)1916 ( 68)593 ( 59)
0( 60)
1768 { /0)95 ( 70)0( 60)0( 60)0( 60)
0 ( 60)0( 60)
182 47)574 47)
1395 ( 64)0( 60)
1133 ( 60)
493 ( 61)
388 ( 57)
139 ( 44)
16131 (470)484 ( 60)
0( 60)0( 60)0( 60)
0 ( 60)
785 ( 80)
1893 ( 90)931 ( 75)
0{60}
156 STRUCTURES OF Cr5S6 659
TAsx.E V. (coltcliied).
0 3 00 3 00 3 00 2 5
2 30 30 2 50 3 2
1 60 3 21 2 40 3 2
2 41 2 41 1 61 1 60 1 71 2 40 2 61 1 60 3 30 1 70 2 60 1 7
2 50 2 60 3 42 2 02 2 02 2 0
2 51 2 50 0 80 3 41 2 50 3 42 2 22222 2 20 0 82 2 21 3 01 3 01 3 01 3 11 3 10 1 8
+0
+1+0+1+0+1—1—1+0—1+1+0+0+0+0—1+1—1+1+0+0+0+1+1—1+1—1+1+0+0—1+0+1+1—1+0+0+0+1+0—1+1+1+0—1
Jl
666
122412121212122412121266
1224121212121212241212666
1212
212241212662
12121212122
12
I~lo
2370122
139460
5813
22554
20
135133
22776424355
31031
100
96110339
2729
141672
11
15293
720
T=4.2'KQ„I ),
23845460
5813
57520
93253
1031
97110339
2
26627
20
Zr Iobs'
23755 (200)40 ( 60)o( 7o)
7Oo (13O)20 ( 60)
600 (130)o( 7o)0 ( 70)
9412 (140)o( 7o)
1206 (150)
847 (12s)ioo ( 6o)30 ( 60)o( 7o)
2480 (2oo)o( 7o)
63 ( 85)
lcale
1102911
92100
15902
31600
7766
9023182
1020
26920
34947
1178
3773
00
9570
114
13000
119529173634
0134
001
320
T= 77'KQ„I„l,
111340
15902
31600
10888 (130)0( 60)
125 40)0 60)o( 6o)0( 60)0( 60)0( 60)
43280
4154 (110)0( 60)
62047
71
1783
442 ( 7s)o ( 60)0( 60)0( 60)
40 ( 60)50 ( 60)
94014
1300
8oo (iio)o( 6o)0( 60)0( 60)
0( 60)
7880 8073 (150)
' Numbers in parentheses are estimated standard deviations.
The model in Table III gives the best fit to the intensi-ties also in this case. While in the antiferromagneticstate, the quantity P has a value different from 180',the data for the ferrimagnetic phase 6tted perfectly amodel in which this phase angle was 6xed at 180'.
Figure 2 shows the ferrimagnetic spin structure. Aleast-squares refinement of structural and magneticparameters resulted in an R factor of 3.9/o. The ob-tained form factor in this refinement was very close tothe Cr'+ form factor of Watson and Freeman. "Thiswould suggest that the moments are somewhat lessspread out than in the antiferromagnetic state, but it isvery doubtful whether such a quantitative interpre-tation is justihed.
In Table IU, the 6nal parameters are shown, and thecalculated and observed intensities are given in TableVI. Here again, rather large correlation factors were
computed between the magnetic parameters, particu-larly between p, ~ and pj, where this factor was close to—1. As a result, the sum of these moments is welldefined [(3.13+0.38)yiij, while the separate momentshave large standard deviations. Also, the net momentper unit cell is very ill defined [(0.2+10.7)ic~f. Thevalue found by means of magnetization measurementsin a field of 8530 Oe, carried out at the University ofGroningen, ' is 0.98 p~.
TRANSITION FROM THE ANTIFERROMAGNETICSTATE TO THE FERMMAGNETIC STATE
Apart from the magnitude of the moments, there areonly two differences between the spin structures of thetwo magnetic phases. Firstly, in the antiferromagnetic
'4 C. F. van Bruggen (to be published).
Too . IR ion
156
. o obtain the variationIR ion ersus ten1peraturc. en was e satellites
expenment, the tern
sate, arate intensitiesn ese
a t es were obtained.e o owing quantities wc l lculated.
660
TABLE pl . Calculated and observed'
o served intensitiesr o
l~& p) ill
8 ~ &AN
g etic state (E=20
h k J Ie calo I@a calc
0 0 2 2 307
c ts calc Itot calc
130 45 17455 587 1242
403 163 567
1 1 2 6 1506 0 15060 3599
33 7 4096 188
0 2 2 12 5757 1132 1189
0 1 5 12 2222 131 1534562 0 4562
0 5578 102931 5 50
163 34 19739 34 7248 6 54
2 2 32612212 ' '2
12 39 403 44112 39 883
0 3 0 6 69616961 0 6962
0 30311200 0 7517
1 2 3936 2 39
I 1 6 6 569 069 0 569 26040 0 0 0
026 12 8 2' "' "922O 6 478 0 478
5 18 230341280 8 602
Z. Itot "1. tot obs
239 ( 55)174 222 ( 55)
1248 ( 7o)6043 6056 (100)
567 611 ( 50)123O 1237 ( 65)
42 ( 5O)
5105 4970 (100)0 ( 60)
I'C Ca
(~&»r &/0 2695&&f)'== (~.—2~i »n4)',
(F&Ou+)/0 2695.X
198 ( 55
f) glp+2pr slug)
1255 ( 65)) I'om th.c int cnsltlcs below thc tI'
43o ( 6o)
w c tI'RQsltlon point, Rnd2791189
(Fou/0. 2695Xf)2= p,—PC
10474 (125) from the inten" '
83 ( 4O tin ensities above the tr
t esc quantities aree transition point, . In
is gure, it can bI sus tcInpcI'Rtuic. Fl
graduall t e to the
733 ( 70)As both quantitiesuantities, ~posing~ and . a
s o say that the beha'
p . This will be discussed
For the lnterpretatio
ough it is therefore i
one magnetic state to the other is of r i imental re y avor such a
a N Q1T1N'iimbers in parentheses are een eses are estimated stand d d' ' s.ar eviations.
phase a helical orderin, r eI'in alue of the spiralha r erlng with a unite valc ln the fcl I
periodicity ls I 6 0' g b'»ls zero in the ferrimagnetic stat -h'
ln t~c Rntifcrromastudy experiment ll
e transition point.e ers ln the vicinity of
The variation of the m'
hVCCtOI C
o e magnitude of thr c as a function of tern ep
inuously the (012u ic by
peaks while warmrming up slowlsR e ltc
between these tw
and (012+) sat 11'
wo peaks provides ay. Thc angular dl tis ance
c . The temperatuure resolution er1 CS R 11CCt 1Tleasure f1C Oi
per run was about 3 .e separation of these p kpea s at
In Fig. 4, the resultincs ting curve of versus tempera-gures ows that ~ d
y to zero when thCCI'CRSCS Con-
transition point.pcrature approaches
C
Qp, a
FIG. 2. Ferrimagnetic s inspin arrangement ln i gSG.
STRUCTU RES OF Cr5S6 661
1000l
109o K 159o K
E500
th
o0'I—
UJx0
M
Ul
I/
~ ~ ~ ~~ ~ Q
I I
~ Not ~ t tl ~I~ 1~
I I I
I
~o~ Oyo ~ gt4 ~
~01~
I I I I
166o K
r~ lyO~ Ops
I I I I'
I
~' 1700 K
1000—
500
/|l/ .
r'l
sV ~ ~
~ yyyyO ~1~ ~ ~ 00 ~ ~ 00000
I I I I I I
38 40 4236
I~ 001yy ~OOgs
I I I
36 38
I~ ~
~ ~'i ~ Itelo 01~
40- 42
COUNTER ANGLE (2e )
Fro. 3. Typical examples of the angular separation of the (012 )and (Oj.2+) peaks at four different temperatures in Cr~S6.
DISCUSSION
If the assumption that Cr5S6 is purely ionic is valid,it can be expected that there are six Cr'+ ions and fourCr'+ ions in the crystallographic unit cell, with spin-only values for the magnetic moments of 4' and 3',respectively, which results in an average moment of 3.6p~ per Cr ion. In the present work, the observed averagemoment at 4.2'K is (2.73&0.04)p~, and no moment ashigh as 4@~ has been found. This probably means that
the purely ionic model is not correct, and that metallicCr-Cr bonds are present, as pointed out by Jellinek. '
This is supported by the fact that metallic conductionhas been observed by Kamigaichi' in specimens ofCrS with 1.13&x&1.20.
To illustrate the behavior of the two quan. titiesr ~r
andr pf sing
rwhen the temperature is varied, and in
order to of'fer a possible explanation for the existence oftwo magnetic phases, we will consider the Heisenbergenergy of the system. . The interactions which will betaken into account can be divided into three groups:(a,) interactions between nearest neighbors in (00l)planes; (b) interactions between nearest neighbors alongthe L00l] direction; (c) interactions between momentsat distances (+-sr, &s, -„') Lapart from the small devia-tion from zero of the z-parameter of Cr in 4(f)]. Theanion-anion-cation angles for these three types of inter-actions in the idealized structure are, respectively,89', 72, and 132 . In the actual structure, these anglesdeviate slightly from these values.ls As it is dificult to say which one of these interactionsis of predominant importance, we will take them allinto consideration. The Heisenberg energies resultingfrom these three groups of interactions are
L~', = —2Csy cosp —Crf cos2&+C«,
Eg=+2C~ cossn —2Ccf cos(n+Q) )
L~', = —2Cs, c osn+2 Cy cos(n+P)+2C,r' cos(n —Q) —2C,f cos(n —P) .
The energy for the whole system is
&a.a.i= ~.+~b+~'In these formulas, C;;=J,;p;p;, where J;;is the exchangeintegral for the interaction between the moments p,; andp; at the crystallographic positions i and j.
0.2 5
Fn. 4. Variation of the wavevector r with temperature inCr~S6. The left-hand ordinate ivesthe wave vector in units of c~r,the right-hand ordinate the spiralperiodicity in units of rcr. Theopen and 6lled circles representtwo different warming runs.
0.20
0.1 5
0.10
0.05
0 --i75 100
I
125 150 175
TEMPERATURE ( DEGREES K)
O—5
D—6
i——7 (J
oC3
—9—10
-15—20
V)
—30-50
200
B. vAN LAAR 156
40
ijt sin ('f 1
e 30m
"lA
CV
~ 20X
LAChCDP4
CD
h. EO
P4
Fxo. S. Variation of F' ofthe (011-) and (011+) re-Qections helot the tran-sition point and of the(011) re6ection above thispoint. The 611ed circle indi-cates the value of p,2 asobtained from the diagramat T=78'K.
I
100
~011: ( )jc- 2 yt s in ('f )
0 O O
1 I I
f50 175 200
TEMPERATURE ( OEGREES K )
C,r stands for interactions over a dists, nce (st, ~„—' —s),C,r' for interactions over (—'„—rs, rs+s), C.f for inter-actions over (s, ~» sr+s), and C,f' for interactions over
(0, 0, sr —s). a, the turn angle of the spiral between. twoadjacent Cr layers, isde6ned asn=(~~~/(c*~)X2s-, and
P has the same meaning as in Table III.We will assume the interactions of group (c) to be
positive and the interactions of the two other groups tobe negative. It can be shorn that, if the absolute valuesof the quantities C,f and Cf~ are not too large, the energyis minimized for n=0' and &=180o, as is the case forthe ferrimagnetic structure. When, for some reason, theabove-mentioned quantities become relatively more im-
portant, the minilnum energy is no longer obtained forn=0 and &=180', and P will deviate from 180'. Theturn angle 0. is then given by
(C f—C,y'+C.r—C,r')singkgo,'=—
(C.r+C.x C r —C r')cos4' —Cs.+C.s
From this, it is seen that a goes to zero when~ pr sing~
approaches zero. This 6ts the observed behavior with
varying temperature of these t%o quantities.The fact that ~yr sing~ is zero. above the transition
point means that &=180' in the ferrirnagnetic state.Although, in this state, the observed moment p~ does
not differ signi6cantly from zero, the observed valuefor the sum of the moments pr and ps of (3.13+0.38)psis too large to be attributed. to pg only.
ACKNDWLEDGME5TS
The author wishes to thank Professor F. Jellinekfor the suggestion of the problem and for his interestin the work, Dr. C. F. van Bruggen for providing themagnetization data and for the elaborate checking ofthe sample, and A. Bruiniag for the preparation of thespecimen. The valuable assistance of J. F. Strang with
the experiment. al work is gratefully acknowledged,