- Email: [email protected]
Low temperature magnetic behaviour of CuFeS2 from neutron diffraction data
~ ELSEVIER
Journal of Magnetism and Magnetic Materials L62 (1996) 347-354
Low temperature magnetic behaviour of diffraction data
CuFeS 2
Jeurnalof ma|Ntlc materials
from neutron
J.C. W o o l l e y a,*, A.-M. Lamarche a G. Lamarche a M. Quintero b, I.P. Swainson c T.M. Holden c a Physics Department. Ottawa-Carleton Institute for Physics, Unit,ersi~ of Ottawa, Ottawa, Ontario, Canada KIN 6N5 b Departamento de Fisica, Unk:ersidad de Los Andes, M[rida, Venezuela c Atomic Energy of Canada Ltd., Chalk River Laboratories, Chalk RiL'er, Ontario, Canada KOJ lJO
Received 19 October 1995; revised 5 February 1996
Abstract Measurements of neutron diffraction spectra were made at temperatures 4.2, 25, 45, 65, 85, 150 and 300 K on powdered polycrystalline synthetic CuFeS 2. Standard Rietveld profile analysis using GSAS showed that at all temperatures, a good fit to the data could be obtained with both the chemical and magnetic space groups taken as I~,2d, and an antiferromagnetic configuration of the Fe spins, as reported previously by Donnay et al. However, graphs of lattice parameters a and c against temperature showed a distinct change in slope close to 50 K, indicating the presence of a transition. Graphs of integrated intensity of diffraction lines against temperature showed corresponding discontinuities in the case of magnetic and mixed nuclear-magnetic lines but not for nuclear lines, indicating that the transition was magnetic. Detailed calculations of predicted magnetic intensities showed that the intensity variations could be explained by Cu spins, having a paramagnetic arrangement down to 50 K and then ordering to an antiferromagnetic form at lower temperatures. The analysis gave a value of ~ 0.05 i~B for the magnetic moment of the Cu ions. Keywords: Neutron diffraction; Crystal structure; Magnetic structure; Spin ordering - low temperature
I. Introduction The neutron diffraction work of Donnay et al. [1] clearly established the crystal structure of CuFeS 2, the structure now given the general name of chalcopyrite, and showed that the chemical space group was I42d, with the magnetic moments of the Fe atoms being 3.85 IxB, directed along the c-axis. They also confirmed that it was antiferromagnetic at room
Corresponding author. Fax: + 1-613-562-5190; email: [email protected].
temperature, and that the magnetic space group was also I42d. Later, measurements of magnetic behaviour [2] showed that the N6el temperature o f CuFeS 2 was 823 K. At a slightly higher temperature of 830 K, CuFeS 2 undergoes decomposition to pyrite FeS 2 plus a disordered face-centred cubic phase, close in composition to chalcopyrite and structurally very similar to zinc-blende [3]. The isothermal section of the C u - F e - S diagram at 600°C [4] would indicate a molecular ratio of approximately twelve parts of the fcc phase to one of pyrite. Preliminary measurements of magnetic suscepti-
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S0304-8853(96)00252-1
348
J.C. Woolley et al. // Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
bility at low temperatures appeared to indicate some magnetic transition in the vicinity of 50 K. Hence the present neutron diffraction work was carried out to clarify the magnetic behaviour of CuFeS 2 at these lower temperatures.
Spectra were obtained at temperatures of 4.2, 25, 45, 65, 85, 150 and 300 K, observations being made in the range 5 ° < 20 < 120 ° in steps of 0.05 °.
3. Results and analysis
3.1. Symmetry properties of observed phases
2. Sample preparation and neutron diffraction measurements
The powder diffraction spectrum obtained at 25 K is given in Fig. 1. Seventy two lines were observed and are listed in Table 1. This spectrum shows the lines expected for the I42d structure previously reported [1] for both the chemical and magnetic structures of chalcopyrite CuFeS 2. These are listed in Table 2 and are shown to fit very well to a tetragonal structure with a = 0.52804 nm and c = 1.04295 nm. However, in addition to these lines, a number of extra lines of relatively low intensity ( N never greater than 300 in Fig. 1) were observed. Analysis indicated that practically all of these lines belonged to one or the other of two sets (labelled for convenience phase II and phase liD, with only 2 lines remaining unfitted. In Table 1, lines have been labelled I, II and III, where I represents the chalcopyrite phase. The analysis showed that phase II was face-centred cubic with a = 0.5415 nm. These results indicate that this
9 g of sample were prepared from the elements in three separate batches. The appropriate weights of each element were sealed under vacuum in quartz tubes, and were slowly raised in temperature to approximately 1200°C, held at that temperature for about half an hour and were air-quenched to room temperature. The resulting ingot was then annealed at 500°C for several days and again air-quenched to room temperature. Each sample was examined by X-ray diffraction to check that the chalcopyrite form had been obtained. The samples were then combined and powdered, and placed in a 5mm diameter cylindrical vanadium can for the neutron diffraction experiments. Diffraction spectra with a wavelength of 0.15525 nm were obtained on the DUALSPEC C2 powder diffractometer at the Chalk River Laboratories of AECL.
xlO 3
8
Z
4
- - - ,
20
40
60
T r
80
-
100
.
12(
20 Fig. 1. Neutron diffraction spectrum for CuFeS z at 25 K. N is neutron count and A is difference between experimental and calculated values of N: ( + ) experimental data, ( - - ) fit by GSAS analysis, (I) predicted lines for CuFeS 2 .
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
phase is pyrite FeS 2, a not-unexpected result since, as indicated above, chalcopyrite CuFeS 2 decomposes at 557°C into pyrite and a zinc-blende type phase close in composition to chalcopyrite [3]. It has been shown [5] that for samples prepared by the present method, it is very difficult to eliminate small amounts of pyrite even with long time annealing at temperatures below 557°C. With regard to phase III, the lines in this case were appreciably wider than those of the chalcopyrite and pyrite phases. Initially, they seemed to fit the chalcopyrite lattice parameters, but detailed analysis
349
indicated that they gave a reasonable fit to a primitive cubic form with a = 0.799 nm and were not consistent with the I42d magnetic structure proposed in this work. One further interesting point was that the phase III lines were observed clearly in only the 4.2 and 25 K spectra and possibly very weakly at 45 K, and if they were present at any higher temperatures, they were hidden in the background noise. Neutron diffraction measurements similar to those described here were made also upon CuFeSe~ and CuFeTe 2 samples and some phase III lines were observed very weakly for these samples also. Thus it
Table 1 Lines observed in neutron diffraction spectrum of CuFeS2sample at 25 K ( Q = 1/d 2 where d is the spacing of the hkl planes) 20
Q ( × 10- 2 ) ( n m - 2)
Phase
20
Q ( × 10- 2) ( n m - 2 )
Phase
18.94 23.96 27.59 28.80 29.61 31.00 31.90 33.30 34.14 34.67 38.46 39.35 41.05 42.55 42.75 45.75 46,76 47.25 47.45 47.80 49.(16 49.43 50.20 52.33 53.05 54.23 55.30 56.80 58.34 59.03 59.50 61.46 64.64 66.70 66.97 69.10
0.0449 0.0715 0.0944 0.1026 0.1084 0.1185 0.1253 0.1362 0.1430 0.1473 0.1800 0.1881 0.2040 0.2185 0.2204 0.2508 0.2613 0.2665 0.2685 0.2724 0.2860 0.2901 0.2986 0.3227 0.3310 0.3447 0.3574 0.3754 0.3942 0.4028 0.4086 0.4333 0.4736 0.5015 0.5051 0.5337
I I III II I I III II I I I I III I III III I III II I I III I I III I II 1 1 II I I III I III
70.00 70.20 71.35 71.91 73.10 74.58 75.10 76.05 77.35 77.85 79.63 80.32 82.06 82.33 84.58 84.80 85.78 89.00 89.25 90.55 92.27 93.05 95.02 96.33 99.50 100.08 101.25 108.37 I 10.70 112.24 113.49 I 16.03 I 17.14 118.61 120.59 121.22
0.5459 0.5487 0.5644 0.5721 0.5885 0.6091 0.6164 0.6297 0.6480 0.6551 0.6804 0.6888 0.7151 0.7186 0.7514 0.7544 0.7687 0.8152 0.8189 I).8377 0.8619 0.8739 0.9023 0.9212 0.9659 {).9742 0.9916 1.0912 1.1230 1.1438 1.1605 1.1939 1.2082 1.2271 1.2520 1.2598
II Ill I11 I 1 I I I II I 1 I I 1 III 1II I11 I1 1 1 1 1 11 1 I I II 1 1 1 II III 11 I I
J.C. Woolley et aL / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
350
appears that phase III is a common impurity phase in all three of these materials. Possibly it undergoes a phase transition somewhere between 25 and 50 K, thus explaining the absence of lines of this phase at higher temperatures.
3.2. Magnetic structure of CuFeS2
Using I4-2d as both the chemical and magnetic space groups of CuFeS 2, as indicated by Donnay et al. [1], a good fit to the experimental data for all
Table 2 Data for the lines observed for phase I (chalcopyrite CuFeS 2) at 25 K. Analysis gave tetragonal with a = 0.52894 nm and c = 1.04261 nm (Q = l / d 2 where d is the spacing of the hkl planes) Q ....
(X
0.0449 0.0715 0.1084 0.1185 0.1430 0.1473 0.1800 0.1881 0.2185 0.2613 0.2860 0.2901 0.3227 0.3310 0.3574 0.3942 0.4028 0.4333 0.4736 0.5051 0.5721 0.5885 0.6091 0.6164 0.6297 0.6804 0.6888 0.7151 0.7186 0.7514 0.8377 0.8619 0.8741 0.9023 0.9659 0.9742 0.9916 1.1230 1.1438 1.1605 1.2520
10 -2 ) ( n m -
2)
hkl
Qfi,, ( x 10- 2) ( n m - 2)
A Q ( X 10- 2) (nm 2)
Nuclear or magnetic
101 110 112 103 200 004 202 211 114 213 220 204 222 301 310 312 116 224 321 314 400 008 402 411 217 332 316 420 404 422 415 424 228 501 512 336 1,1,10 505 440 408 532
0.0449 0.0715 0.1083 0.1185 0.1430 0.1472 0.1798 0.1879 0.2187 0.2615 0.2859 0.2902 0.3227 0.3309 0.3574 0.3942 0.4027 0.4331 0.4738 0.5046 0.5718 0.5888 0.6086 0.6167 0.6295 0.6801 0.6886 0.7148 0.7190 0.7516 0.8376 0.8620 0.8746 0.9027 0.9660 0.9745 0.9915 1.1234 1.1437 1.1606 1.2520
0 0 + 1 0 0 + 1 + 2 + 2 - 2 - 2 + 1 - 1 0 + 1 0 0 + 1 + 2 - 2 +5 +3 - 3 + 5 - 3 +2 + 3 + 2 +3 -4 - 2 + 1 - 1 - 5 -4 - 1 - 3 + 1 -4 + 1 - 1 0
N,M M N N,M N N M N,M M N,M N N M N,M M N N N N,M M N N M N,M N,M N N N N M N,M
N N N,M
N N N N,M N N N
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
temperatures of measurement was obtained with a standard Rietveld analysis using GSAS [6]. The fitted curve for the case of T = 25 K is shown in Fig. 1. The values of lattice parameters obtained from these fits are given in Table 3 and are shown as a function of T in Fig. 2. These graphs of a and c against temperature show a distinct change in slope in the vicinity of 50 K, which would appear to indicate a transition of some type occurring close to that temperature. However, crystallographically the structure retained the IJ,2d symmetry and no extra diffraction lines were observed. Also, the values of c/a in Table 3 show, within the limits of experimental error, a linear variation with T over the whole temperature range, while the x component of the S atoms, the only variable position parameter, was found to be constant with T within computational scatter at a value of 0.735 + 0.02. From measurements of magnetic susceptibility X as a function of temperature T, graphs of 1/X versus T for various samples had indicated that a magnetic transition probably occurred in the vicinity of 50 K. In the susceptibility measurements however, the behaviour was masked, to a greater or lesser extent, by the effects of small quantities of strongly magnetic impurities which were present in the samples, as indicated above, but which gave only very small effects in the neutron diffraction spectrum. In the GSAS analysis mentioned above, the value of the magnetic moment m(Fe) of the iron atoms can be found by using an analytic approximation to the magnetic form factor given by f =
E
Z i exp( - B i sin20/A 2)
+ C,
i = 1,2,3
where A i, B~ can be obtained from neutron diffraction data or by fitting to standard tabulated wave Table 3 Values o f lattice parameters a, c and c / a for C u F e S 2 at different temperatures T T (K)
a (nm)
4.2 25 45 65 85 150 300
0.52885 0.52904 0.52925 0.52926 0.52930 0.52929 0,52940
c (nm)
c/a
1.04267 1.04295 1.04337 1.04337 1.04340 1.04341 1,04340
1.9716 1.9714 1.9714 1.9714 1.9713 1.9713 1.9709
351
1.0436 1.0434
, ~ 1,0432 ~
].0430 1.0428 1.0426
:::::::::::::::::::::::::::::::::::
0.5294
0.5292
0.5290
0.5288
,,, i ....
i .... 100
i .... T (K)
i .... 200
J,, , 300
Fig. 2. Variation with temperature o f the lattice parameters a and c for CuFeS2: ( Q ) experimental values, (I) estimated relative error, ( - - ) guides to the eye.
functions. Here, data given by Brockhouse et al. [7], from paramagnetic scattering results for Fe 3÷ in octahedral coordination, were used to give values for the coefficients. Refinement analysis was carried out on the data for all temperatures investigated, and the resulting average value of m(Fe) was 3.42 +__0.07 ixB. A value of m(Fe) was also found from the ratio of the intensities of two neighbouring low angle peaks, one purely magnetic and one purely nuclear, thus avoiding any problems in refining thermal factors, etc., and in choosing the appropriate magnetic form factor. This analysis gave a result consistent with that obtained above from the GSAS analysis. Donnay et al. [1] reported a value of 3.87 ix B for m(Fe). Any change in the apparent value of m(Fe) at ~ 50 K was smaller than the uncertainty quoted above, and hence could not be determined from the profile analysis. In another approach to this question, values of the integrated intensity I were plotted against temperature T for a number of different lines in the chalcopyrite spectrum. Typical examples of these plots are shown in Fig. 3-5. Fig. 3 shows the data for typical purely nuclear lines. Here, it is seen that the
352
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354 28 26
.~
24_
i
7
, ,i,,
,i,,
,i ,, ,i , , ,i,,,i
!01 'i ' 7.4
-
O
,,,{,
,
~
220
,,i
60
7-81,
,, ,i,,+i,,
,i,,
40
80
,I.,LI
, , ,I,,
~2o
T(K)
16o
Fig. 3. Variation with temperature of the integrated intensity of typical nuclear lines in the neutron diffraction spectrum of CuFeS2: ( 0 ) experimental values, (I) estimated relative error, ( - - ) guides to the eye.
curves are quite smooth and show no effect close to 50 K. However, in Fig. 4, which shows the data for some purely magnetic lines, it is seen that these curves show a break between 45 and 65 K, the value of the intensity falling a little as the temperature is reduced. Finally, Fig. 5 shows the data for the chalcopyrite type ordering lines, which have both nuclear and magnetic components. In this case, the change between 45 and 65 K is an abrupt increase in intensity as the temperature is reduced. In order to explain the form of these curves, certain effects can be ruled out immediately. Since the nuclear lines (Fig. 3) show no break, any factors which affect the nuclear components of the intensities, e.g. atomic positions, lattice parameters, nuclear Debye-Waller factors etc., can be ruled out. The effect is thus clearly a magnetic one, and one obvious possibility is a change in the mean magnetic moment seen by the neutrons. If this were due to a change in the moments of the Fe atoms, then the changes in Fig. 4 and 5 could be expected to be in the same direction in both cases, which is not as observed. Finally, there is the question of a magnetic moment on the Cu atoms. Donnay et al. [ 1] discussed possible values for the magnetic moment of Cu, and
1"10.
0
40
80T(K)120
160
I ' ' ' I ' ' ' I ' ' ' I K ' ' F ' '
Fig. 4. Variation with temperature of the integrated intensity of typical magnetic lines in the neutron diffraction spectrum of CuFeS2: ( 0 ) experimental values, (I) estimated relative error, ( - - ) guides to the eye.
,,,i,,,i,,,i,,,i,+,1,~,1,,,i,,,
11.s~I ~~. ~ . ~ , . . 11.o
-~ 4.1 ~
3.9--
,.8
1.7 f
,1
0
.i
, , , I , , , I , , ,I
40
, , ,I
, , , I ,,
80
T20
I
t
i
i
160
T (K)
Fig. 5. Variation with temperature of the integrated intensity of typical mixed nuclear-magnetic lines in the neutron diffraction spectrum of CuFeS2: ( 0 ) experimental values, (I) estimated relative error, ( - - ) guides to the eye.
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
'
otl ::---°L--.
] to ( Fig. 6. Unit ceil of CuFeS 2 to show spins on the Fe neighbours of a Cu atom: ( O ) Cu, ( O ) Fe. arrows show spin directions.
from their results indicated that it must be less than 0.2 ix B. Initial calculations indicated that a moment of this magnitude could easily account for the discontinuities observed in the curves of Fig. 4 and 5. The explanation proposed here for the behaviour shown in Fig. 3,4 and 5, is that the Cu spins remain in a paramagnetic disordered state down to ~ 50 K, below which temperature they order to an antiferromagnetic configuration. With the magnetic space group 142d, these spins must also lie along the c-axis. The contribution of the Cu moment to the intensity of the magnetic diffraction lines opposes that of the Fe moment. This ordering of the Cu spins at such a low temperature compared with that for the ordering of the Fe spins can be explained by the low value of the internal field at the Cu atom, as is illustrated by the atomic configuration shown in Fig. 6. Each Cu atom has (i) four Fe neighbours in the form of a square, with spin opposite to that of the Cu, i.e. the C u - F e coupling is antiferromagnetic, and with C u - F e spacing of 0.3740 nm, and (ii) four Fe neighbours in the form of a tetrahedron, with spin parallel to that of the Cu, i.e. the C u - F e coupling is ferromagnetic, and with C u - F e spacing of 0.3714 nm. The next Fe neighbours are two in the z direction from the Cu atom, at a C u - F e spacing of 0.5215 nm and antiparallel Cu to Fe spins. Assuming a type of exchange as proposed by Geetsma et al. [8], which
353
appears to apply in magnetic semiconductors of this type [9] and for which the value of the exchange interaction between any two atoms depends upon their spacing and not on bond-angles, the very similar spacing of equal numbers of spin-up and spindown near-neighbour Fe atoms would result in a relatively small interaction at the Cu, and hence a relatively low spin-ordering temperature. The cation sublattice can thus be considered as sheets of atoms perpendicular to the c-axis. Each sheet has all the Fe moments parallel and all the Cu moments induced antiparallel to the Fe moments, while the direction of the Fe moments are reversed in adjacent sheets. For the spin configuration shown in Fig. 6, following the structure described by Donnay et al. [1], the atomic sites and spin orientations of the Fe atoms can be written as 0 0 1/2 $, 1/2 1,/2 0 1", 1 / 2 0 3 / 4 $, 0 1/2 1 / 4 $. If the spin alignments of the Cu atoms are taken as 0 0 0 $, 1/2 1/2 1 / 2 $, 1/2 0 1 / 4 $, 0 1 / 2 3 / 4 7, it is found that the magnetic contributions to the diffraction lines are proportional to 16[m(Fe)-m(Cu)]2 in the case of the magnetic lines and 8[m(Fe) + m(Cu)] 2 for the mixed nuclear-magnetic lines. Thus the predicted change in the magnetic component of the intensity when the Cu spins order is proportional to -16m(Fe)m(Cu) for the purely magnetic lines, + 8m(Fe)m(Cu) for the mixed nuclear-magnetic lines and, of course, zero for the purely nuclear lines. This is in good agreement with the data shown in Fig. 3,4 and 5. From the values presented in these figures, a simple analysis indicates that the ratio of m(Cu)/m(Fe) has an approximate value of 0.015. Thus using a value of m(Fe) of 3.42 ix B, a value of ~ 0.05 pq~ is obtained for m(Cu). The graphs (Fig. 2) of a and c as a function of T indicate there is a considerable change in the temperature coefficient of expansion at the magnetic transition temperature Tc, the mean value of the coefficient changing from 2.0 × 10 6 / K above Tc to 1.8 × 1 0 - 5 / K below. While these values are both within the normal range for semiconductor materials, it is apparent that the change must be due to effects produced by the ordering of the Cu spins. One effect that could occur with this ordering is a change in the exchange interaction behaviour of the Fe atoms, which would affect various elastic parameters and
354
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
hence could produce the changes in expansion coefficient described above.
4. Conclusions Profile analysis of the neutron diffraction data for the present powder samples indicates that at all temperatures investigated, both the chemical and magnetic space groups of CuFeS 2 are I42d, with antiferromagnetic arrangements of the Fe spins along the c-axis at all temperatures. This is in agreement with the previous data of Donnay et al. obtained for single crystal samples at room temperature. The value found here for the magnetic moment m(Fe) of the Fe atoms was 3.42 _ 0.07 ~B, as compared with the value of 3.85 i~B quoted by Donnay et al. However, the variations of the lattice parameters a and c with temperature showed distinct changes in slope close to 50 K, indicating the presence of some transition. Graphs of integrated intensity of diffraction lines showed different types of behaviour, the nuclear lines showing a smooth variation through 50 K, the magnetic lines showing a sharp fall in intensity as the temperature was lowered through 50 K, and the mixed nuclear-magnetic lines showing an increase in intensity with lowered temperature. This behaviour could not be explained in terms of any change in chemical structure or a change in the value
of the Fe moment m. However, a good fit to the data was obtained by assuming that a small Cu moment orders in an antiferromagnetic manner at ~ 50 K, and the value of the Cu moment was found to be ~ 0.05 ix B. The low temperature of the ordering of the Cu spins can be accounted for by the spin arrangement of the neighbouring Fe atoms, which would give a very low value of molecular field at the Cu atom.
References [1] G. Donnay, L. Corliss, J.D.H. Donnay, N. Elliott and J.M. Hastings, Phys. Rev. 112 (1958) 1917. [2] T. Teranishi, K. Sato and Y. Saito, Inst. Phys. Conf. Ser. No. 35 (1977) 59. [3l J.R. Craig and S.D. ScoU, in: Sulphide Mineralogy, ed. P.H. Ribbe (Mineralog. Soc. Am., 1976) p. CS73. [4] G. Kullerud and H.S. Yoder, Econ. Geol. 54 (1959) 533. [5] R. Brun del Re, J.C. Woolley, M. Quintero and R. Tovar, Phys. Status Solidi (a) 121 (1990) 483. [6] A.C. Larson and R.B. Von Dreele, General Structure Analysis System, (MS-H805) Los Alamos National Laboratory, Neutron Scattering Center (Copyright, The Regent of the University of California, 1993). [7] B.N. Brockhouse, L.M. Corliss and J.M. Hastings, Phys. Rev. 98 (1955) 1721. [8] W. Geertsma, C. Haas, G.A. Sawatsky and G. Vertogen, Phys. B 86-88 (1977) 1093. [9] J.C. Woolley, S. Bass, A.-M. Lamarche and G. Lamarche, J. Magn. Magn. Mater. 131 (1994) 199.
Journal of Magnetism and Magnetic Materials L62 (1996) 347-354
Low temperature magnetic behaviour of diffraction data
CuFeS 2
Jeurnalof ma|Ntlc materials
from neutron
J.C. W o o l l e y a,*, A.-M. Lamarche a G. Lamarche a M. Quintero b, I.P. Swainson c T.M. Holden c a Physics Department. Ottawa-Carleton Institute for Physics, Unit,ersi~ of Ottawa, Ottawa, Ontario, Canada KIN 6N5 b Departamento de Fisica, Unk:ersidad de Los Andes, M[rida, Venezuela c Atomic Energy of Canada Ltd., Chalk River Laboratories, Chalk RiL'er, Ontario, Canada KOJ lJO
Received 19 October 1995; revised 5 February 1996
Abstract Measurements of neutron diffraction spectra were made at temperatures 4.2, 25, 45, 65, 85, 150 and 300 K on powdered polycrystalline synthetic CuFeS 2. Standard Rietveld profile analysis using GSAS showed that at all temperatures, a good fit to the data could be obtained with both the chemical and magnetic space groups taken as I~,2d, and an antiferromagnetic configuration of the Fe spins, as reported previously by Donnay et al. However, graphs of lattice parameters a and c against temperature showed a distinct change in slope close to 50 K, indicating the presence of a transition. Graphs of integrated intensity of diffraction lines against temperature showed corresponding discontinuities in the case of magnetic and mixed nuclear-magnetic lines but not for nuclear lines, indicating that the transition was magnetic. Detailed calculations of predicted magnetic intensities showed that the intensity variations could be explained by Cu spins, having a paramagnetic arrangement down to 50 K and then ordering to an antiferromagnetic form at lower temperatures. The analysis gave a value of ~ 0.05 i~B for the magnetic moment of the Cu ions. Keywords: Neutron diffraction; Crystal structure; Magnetic structure; Spin ordering - low temperature
I. Introduction The neutron diffraction work of Donnay et al. [1] clearly established the crystal structure of CuFeS 2, the structure now given the general name of chalcopyrite, and showed that the chemical space group was I42d, with the magnetic moments of the Fe atoms being 3.85 IxB, directed along the c-axis. They also confirmed that it was antiferromagnetic at room
Corresponding author. Fax: + 1-613-562-5190; email: [email protected].
temperature, and that the magnetic space group was also I42d. Later, measurements of magnetic behaviour [2] showed that the N6el temperature o f CuFeS 2 was 823 K. At a slightly higher temperature of 830 K, CuFeS 2 undergoes decomposition to pyrite FeS 2 plus a disordered face-centred cubic phase, close in composition to chalcopyrite and structurally very similar to zinc-blende [3]. The isothermal section of the C u - F e - S diagram at 600°C [4] would indicate a molecular ratio of approximately twelve parts of the fcc phase to one of pyrite. Preliminary measurements of magnetic suscepti-
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S0304-8853(96)00252-1
348
J.C. Woolley et al. // Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
bility at low temperatures appeared to indicate some magnetic transition in the vicinity of 50 K. Hence the present neutron diffraction work was carried out to clarify the magnetic behaviour of CuFeS 2 at these lower temperatures.
Spectra were obtained at temperatures of 4.2, 25, 45, 65, 85, 150 and 300 K, observations being made in the range 5 ° < 20 < 120 ° in steps of 0.05 °.
3. Results and analysis
3.1. Symmetry properties of observed phases
2. Sample preparation and neutron diffraction measurements
The powder diffraction spectrum obtained at 25 K is given in Fig. 1. Seventy two lines were observed and are listed in Table 1. This spectrum shows the lines expected for the I42d structure previously reported [1] for both the chemical and magnetic structures of chalcopyrite CuFeS 2. These are listed in Table 2 and are shown to fit very well to a tetragonal structure with a = 0.52804 nm and c = 1.04295 nm. However, in addition to these lines, a number of extra lines of relatively low intensity ( N never greater than 300 in Fig. 1) were observed. Analysis indicated that practically all of these lines belonged to one or the other of two sets (labelled for convenience phase II and phase liD, with only 2 lines remaining unfitted. In Table 1, lines have been labelled I, II and III, where I represents the chalcopyrite phase. The analysis showed that phase II was face-centred cubic with a = 0.5415 nm. These results indicate that this
9 g of sample were prepared from the elements in three separate batches. The appropriate weights of each element were sealed under vacuum in quartz tubes, and were slowly raised in temperature to approximately 1200°C, held at that temperature for about half an hour and were air-quenched to room temperature. The resulting ingot was then annealed at 500°C for several days and again air-quenched to room temperature. Each sample was examined by X-ray diffraction to check that the chalcopyrite form had been obtained. The samples were then combined and powdered, and placed in a 5mm diameter cylindrical vanadium can for the neutron diffraction experiments. Diffraction spectra with a wavelength of 0.15525 nm were obtained on the DUALSPEC C2 powder diffractometer at the Chalk River Laboratories of AECL.
xlO 3
8
Z
4
- - - ,
20
40
60
T r
80
-
100
.
12(
20 Fig. 1. Neutron diffraction spectrum for CuFeS z at 25 K. N is neutron count and A is difference between experimental and calculated values of N: ( + ) experimental data, ( - - ) fit by GSAS analysis, (I) predicted lines for CuFeS 2 .
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
phase is pyrite FeS 2, a not-unexpected result since, as indicated above, chalcopyrite CuFeS 2 decomposes at 557°C into pyrite and a zinc-blende type phase close in composition to chalcopyrite [3]. It has been shown [5] that for samples prepared by the present method, it is very difficult to eliminate small amounts of pyrite even with long time annealing at temperatures below 557°C. With regard to phase III, the lines in this case were appreciably wider than those of the chalcopyrite and pyrite phases. Initially, they seemed to fit the chalcopyrite lattice parameters, but detailed analysis
349
indicated that they gave a reasonable fit to a primitive cubic form with a = 0.799 nm and were not consistent with the I42d magnetic structure proposed in this work. One further interesting point was that the phase III lines were observed clearly in only the 4.2 and 25 K spectra and possibly very weakly at 45 K, and if they were present at any higher temperatures, they were hidden in the background noise. Neutron diffraction measurements similar to those described here were made also upon CuFeSe~ and CuFeTe 2 samples and some phase III lines were observed very weakly for these samples also. Thus it
Table 1 Lines observed in neutron diffraction spectrum of CuFeS2sample at 25 K ( Q = 1/d 2 where d is the spacing of the hkl planes) 20
Q ( × 10- 2 ) ( n m - 2)
Phase
20
Q ( × 10- 2) ( n m - 2 )
Phase
18.94 23.96 27.59 28.80 29.61 31.00 31.90 33.30 34.14 34.67 38.46 39.35 41.05 42.55 42.75 45.75 46,76 47.25 47.45 47.80 49.(16 49.43 50.20 52.33 53.05 54.23 55.30 56.80 58.34 59.03 59.50 61.46 64.64 66.70 66.97 69.10
0.0449 0.0715 0.0944 0.1026 0.1084 0.1185 0.1253 0.1362 0.1430 0.1473 0.1800 0.1881 0.2040 0.2185 0.2204 0.2508 0.2613 0.2665 0.2685 0.2724 0.2860 0.2901 0.2986 0.3227 0.3310 0.3447 0.3574 0.3754 0.3942 0.4028 0.4086 0.4333 0.4736 0.5015 0.5051 0.5337
I I III II I I III II I I I I III I III III I III II I I III I I III I II 1 1 II I I III I III
70.00 70.20 71.35 71.91 73.10 74.58 75.10 76.05 77.35 77.85 79.63 80.32 82.06 82.33 84.58 84.80 85.78 89.00 89.25 90.55 92.27 93.05 95.02 96.33 99.50 100.08 101.25 108.37 I 10.70 112.24 113.49 I 16.03 I 17.14 118.61 120.59 121.22
0.5459 0.5487 0.5644 0.5721 0.5885 0.6091 0.6164 0.6297 0.6480 0.6551 0.6804 0.6888 0.7151 0.7186 0.7514 0.7544 0.7687 0.8152 0.8189 I).8377 0.8619 0.8739 0.9023 0.9212 0.9659 {).9742 0.9916 1.0912 1.1230 1.1438 1.1605 1.1939 1.2082 1.2271 1.2520 1.2598
II Ill I11 I 1 I I I II I 1 I I 1 III 1II I11 I1 1 1 1 1 11 1 I I II 1 1 1 II III 11 I I
J.C. Woolley et aL / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
350
appears that phase III is a common impurity phase in all three of these materials. Possibly it undergoes a phase transition somewhere between 25 and 50 K, thus explaining the absence of lines of this phase at higher temperatures.
3.2. Magnetic structure of CuFeS2
Using I4-2d as both the chemical and magnetic space groups of CuFeS 2, as indicated by Donnay et al. [1], a good fit to the experimental data for all
Table 2 Data for the lines observed for phase I (chalcopyrite CuFeS 2) at 25 K. Analysis gave tetragonal with a = 0.52894 nm and c = 1.04261 nm (Q = l / d 2 where d is the spacing of the hkl planes) Q ....
(X
0.0449 0.0715 0.1084 0.1185 0.1430 0.1473 0.1800 0.1881 0.2185 0.2613 0.2860 0.2901 0.3227 0.3310 0.3574 0.3942 0.4028 0.4333 0.4736 0.5051 0.5721 0.5885 0.6091 0.6164 0.6297 0.6804 0.6888 0.7151 0.7186 0.7514 0.8377 0.8619 0.8741 0.9023 0.9659 0.9742 0.9916 1.1230 1.1438 1.1605 1.2520
10 -2 ) ( n m -
2)
hkl
Qfi,, ( x 10- 2) ( n m - 2)
A Q ( X 10- 2) (nm 2)
Nuclear or magnetic
101 110 112 103 200 004 202 211 114 213 220 204 222 301 310 312 116 224 321 314 400 008 402 411 217 332 316 420 404 422 415 424 228 501 512 336 1,1,10 505 440 408 532
0.0449 0.0715 0.1083 0.1185 0.1430 0.1472 0.1798 0.1879 0.2187 0.2615 0.2859 0.2902 0.3227 0.3309 0.3574 0.3942 0.4027 0.4331 0.4738 0.5046 0.5718 0.5888 0.6086 0.6167 0.6295 0.6801 0.6886 0.7148 0.7190 0.7516 0.8376 0.8620 0.8746 0.9027 0.9660 0.9745 0.9915 1.1234 1.1437 1.1606 1.2520
0 0 + 1 0 0 + 1 + 2 + 2 - 2 - 2 + 1 - 1 0 + 1 0 0 + 1 + 2 - 2 +5 +3 - 3 + 5 - 3 +2 + 3 + 2 +3 -4 - 2 + 1 - 1 - 5 -4 - 1 - 3 + 1 -4 + 1 - 1 0
N,M M N N,M N N M N,M M N,M N N M N,M M N N N N,M M N N M N,M N,M N N N N M N,M
N N N,M
N N N N,M N N N
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
temperatures of measurement was obtained with a standard Rietveld analysis using GSAS [6]. The fitted curve for the case of T = 25 K is shown in Fig. 1. The values of lattice parameters obtained from these fits are given in Table 3 and are shown as a function of T in Fig. 2. These graphs of a and c against temperature show a distinct change in slope in the vicinity of 50 K, which would appear to indicate a transition of some type occurring close to that temperature. However, crystallographically the structure retained the IJ,2d symmetry and no extra diffraction lines were observed. Also, the values of c/a in Table 3 show, within the limits of experimental error, a linear variation with T over the whole temperature range, while the x component of the S atoms, the only variable position parameter, was found to be constant with T within computational scatter at a value of 0.735 + 0.02. From measurements of magnetic susceptibility X as a function of temperature T, graphs of 1/X versus T for various samples had indicated that a magnetic transition probably occurred in the vicinity of 50 K. In the susceptibility measurements however, the behaviour was masked, to a greater or lesser extent, by the effects of small quantities of strongly magnetic impurities which were present in the samples, as indicated above, but which gave only very small effects in the neutron diffraction spectrum. In the GSAS analysis mentioned above, the value of the magnetic moment m(Fe) of the iron atoms can be found by using an analytic approximation to the magnetic form factor given by f =
E
Z i exp( - B i sin20/A 2)
+ C,
i = 1,2,3
where A i, B~ can be obtained from neutron diffraction data or by fitting to standard tabulated wave Table 3 Values o f lattice parameters a, c and c / a for C u F e S 2 at different temperatures T T (K)
a (nm)
4.2 25 45 65 85 150 300
0.52885 0.52904 0.52925 0.52926 0.52930 0.52929 0,52940
c (nm)
c/a
1.04267 1.04295 1.04337 1.04337 1.04340 1.04341 1,04340
1.9716 1.9714 1.9714 1.9714 1.9713 1.9713 1.9709
351
1.0436 1.0434
, ~ 1,0432 ~
].0430 1.0428 1.0426
:::::::::::::::::::::::::::::::::::
0.5294
0.5292
0.5290
0.5288
,,, i ....
i .... 100
i .... T (K)
i .... 200
J,, , 300
Fig. 2. Variation with temperature o f the lattice parameters a and c for CuFeS2: ( Q ) experimental values, (I) estimated relative error, ( - - ) guides to the eye.
functions. Here, data given by Brockhouse et al. [7], from paramagnetic scattering results for Fe 3÷ in octahedral coordination, were used to give values for the coefficients. Refinement analysis was carried out on the data for all temperatures investigated, and the resulting average value of m(Fe) was 3.42 +__0.07 ixB. A value of m(Fe) was also found from the ratio of the intensities of two neighbouring low angle peaks, one purely magnetic and one purely nuclear, thus avoiding any problems in refining thermal factors, etc., and in choosing the appropriate magnetic form factor. This analysis gave a result consistent with that obtained above from the GSAS analysis. Donnay et al. [1] reported a value of 3.87 ix B for m(Fe). Any change in the apparent value of m(Fe) at ~ 50 K was smaller than the uncertainty quoted above, and hence could not be determined from the profile analysis. In another approach to this question, values of the integrated intensity I were plotted against temperature T for a number of different lines in the chalcopyrite spectrum. Typical examples of these plots are shown in Fig. 3-5. Fig. 3 shows the data for typical purely nuclear lines. Here, it is seen that the
352
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354 28 26
.~
24_
i
7
, ,i,,
,i,,
,i ,, ,i , , ,i,,,i
!01 'i ' 7.4
-
O
,,,{,
,
~
220
,,i
60
7-81,
,, ,i,,+i,,
,i,,
40
80
,I.,LI
, , ,I,,
~2o
T(K)
16o
Fig. 3. Variation with temperature of the integrated intensity of typical nuclear lines in the neutron diffraction spectrum of CuFeS2: ( 0 ) experimental values, (I) estimated relative error, ( - - ) guides to the eye.
curves are quite smooth and show no effect close to 50 K. However, in Fig. 4, which shows the data for some purely magnetic lines, it is seen that these curves show a break between 45 and 65 K, the value of the intensity falling a little as the temperature is reduced. Finally, Fig. 5 shows the data for the chalcopyrite type ordering lines, which have both nuclear and magnetic components. In this case, the change between 45 and 65 K is an abrupt increase in intensity as the temperature is reduced. In order to explain the form of these curves, certain effects can be ruled out immediately. Since the nuclear lines (Fig. 3) show no break, any factors which affect the nuclear components of the intensities, e.g. atomic positions, lattice parameters, nuclear Debye-Waller factors etc., can be ruled out. The effect is thus clearly a magnetic one, and one obvious possibility is a change in the mean magnetic moment seen by the neutrons. If this were due to a change in the moments of the Fe atoms, then the changes in Fig. 4 and 5 could be expected to be in the same direction in both cases, which is not as observed. Finally, there is the question of a magnetic moment on the Cu atoms. Donnay et al. [ 1] discussed possible values for the magnetic moment of Cu, and
1"10.
0
40
80T(K)120
160
I ' ' ' I ' ' ' I ' ' ' I K ' ' F ' '
Fig. 4. Variation with temperature of the integrated intensity of typical magnetic lines in the neutron diffraction spectrum of CuFeS2: ( 0 ) experimental values, (I) estimated relative error, ( - - ) guides to the eye.
,,,i,,,i,,,i,,,i,+,1,~,1,,,i,,,
11.s~I ~~. ~ . ~ , . . 11.o
-~ 4.1 ~
3.9--
,.8
1.7 f
,1
0
.i
, , , I , , , I , , ,I
40
, , ,I
, , , I ,,
80
T20
I
t
i
i
160
T (K)
Fig. 5. Variation with temperature of the integrated intensity of typical mixed nuclear-magnetic lines in the neutron diffraction spectrum of CuFeS2: ( 0 ) experimental values, (I) estimated relative error, ( - - ) guides to the eye.
J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
'
otl ::---°L--.
] to ( Fig. 6. Unit ceil of CuFeS 2 to show spins on the Fe neighbours of a Cu atom: ( O ) Cu, ( O ) Fe. arrows show spin directions.
from their results indicated that it must be less than 0.2 ix B. Initial calculations indicated that a moment of this magnitude could easily account for the discontinuities observed in the curves of Fig. 4 and 5. The explanation proposed here for the behaviour shown in Fig. 3,4 and 5, is that the Cu spins remain in a paramagnetic disordered state down to ~ 50 K, below which temperature they order to an antiferromagnetic configuration. With the magnetic space group 142d, these spins must also lie along the c-axis. The contribution of the Cu moment to the intensity of the magnetic diffraction lines opposes that of the Fe moment. This ordering of the Cu spins at such a low temperature compared with that for the ordering of the Fe spins can be explained by the low value of the internal field at the Cu atom, as is illustrated by the atomic configuration shown in Fig. 6. Each Cu atom has (i) four Fe neighbours in the form of a square, with spin opposite to that of the Cu, i.e. the C u - F e coupling is antiferromagnetic, and with C u - F e spacing of 0.3740 nm, and (ii) four Fe neighbours in the form of a tetrahedron, with spin parallel to that of the Cu, i.e. the C u - F e coupling is ferromagnetic, and with C u - F e spacing of 0.3714 nm. The next Fe neighbours are two in the z direction from the Cu atom, at a C u - F e spacing of 0.5215 nm and antiparallel Cu to Fe spins. Assuming a type of exchange as proposed by Geetsma et al. [8], which
353
appears to apply in magnetic semiconductors of this type [9] and for which the value of the exchange interaction between any two atoms depends upon their spacing and not on bond-angles, the very similar spacing of equal numbers of spin-up and spindown near-neighbour Fe atoms would result in a relatively small interaction at the Cu, and hence a relatively low spin-ordering temperature. The cation sublattice can thus be considered as sheets of atoms perpendicular to the c-axis. Each sheet has all the Fe moments parallel and all the Cu moments induced antiparallel to the Fe moments, while the direction of the Fe moments are reversed in adjacent sheets. For the spin configuration shown in Fig. 6, following the structure described by Donnay et al. [1], the atomic sites and spin orientations of the Fe atoms can be written as 0 0 1/2 $, 1/2 1,/2 0 1", 1 / 2 0 3 / 4 $, 0 1/2 1 / 4 $. If the spin alignments of the Cu atoms are taken as 0 0 0 $, 1/2 1/2 1 / 2 $, 1/2 0 1 / 4 $, 0 1 / 2 3 / 4 7, it is found that the magnetic contributions to the diffraction lines are proportional to 16[m(Fe)-m(Cu)]2 in the case of the magnetic lines and 8[m(Fe) + m(Cu)] 2 for the mixed nuclear-magnetic lines. Thus the predicted change in the magnetic component of the intensity when the Cu spins order is proportional to -16m(Fe)m(Cu) for the purely magnetic lines, + 8m(Fe)m(Cu) for the mixed nuclear-magnetic lines and, of course, zero for the purely nuclear lines. This is in good agreement with the data shown in Fig. 3,4 and 5. From the values presented in these figures, a simple analysis indicates that the ratio of m(Cu)/m(Fe) has an approximate value of 0.015. Thus using a value of m(Fe) of 3.42 ix B, a value of ~ 0.05 pq~ is obtained for m(Cu). The graphs (Fig. 2) of a and c as a function of T indicate there is a considerable change in the temperature coefficient of expansion at the magnetic transition temperature Tc, the mean value of the coefficient changing from 2.0 × 10 6 / K above Tc to 1.8 × 1 0 - 5 / K below. While these values are both within the normal range for semiconductor materials, it is apparent that the change must be due to effects produced by the ordering of the Cu spins. One effect that could occur with this ordering is a change in the exchange interaction behaviour of the Fe atoms, which would affect various elastic parameters and
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J.C. Woolley et al. / Journal of Magnetism and Magnetic Materials 162 (1996) 347-354
hence could produce the changes in expansion coefficient described above.
4. Conclusions Profile analysis of the neutron diffraction data for the present powder samples indicates that at all temperatures investigated, both the chemical and magnetic space groups of CuFeS 2 are I42d, with antiferromagnetic arrangements of the Fe spins along the c-axis at all temperatures. This is in agreement with the previous data of Donnay et al. obtained for single crystal samples at room temperature. The value found here for the magnetic moment m(Fe) of the Fe atoms was 3.42 _ 0.07 ~B, as compared with the value of 3.85 i~B quoted by Donnay et al. However, the variations of the lattice parameters a and c with temperature showed distinct changes in slope close to 50 K, indicating the presence of some transition. Graphs of integrated intensity of diffraction lines showed different types of behaviour, the nuclear lines showing a smooth variation through 50 K, the magnetic lines showing a sharp fall in intensity as the temperature was lowered through 50 K, and the mixed nuclear-magnetic lines showing an increase in intensity with lowered temperature. This behaviour could not be explained in terms of any change in chemical structure or a change in the value
of the Fe moment m. However, a good fit to the data was obtained by assuming that a small Cu moment orders in an antiferromagnetic manner at ~ 50 K, and the value of the Cu moment was found to be ~ 0.05 ix B. The low temperature of the ordering of the Cu spins can be accounted for by the spin arrangement of the neighbouring Fe atoms, which would give a very low value of molecular field at the Cu atom.
References [1] G. Donnay, L. Corliss, J.D.H. Donnay, N. Elliott and J.M. Hastings, Phys. Rev. 112 (1958) 1917. [2] T. Teranishi, K. Sato and Y. Saito, Inst. Phys. Conf. Ser. No. 35 (1977) 59. [3l J.R. Craig and S.D. ScoU, in: Sulphide Mineralogy, ed. P.H. Ribbe (Mineralog. Soc. Am., 1976) p. CS73. [4] G. Kullerud and H.S. Yoder, Econ. Geol. 54 (1959) 533. [5] R. Brun del Re, J.C. Woolley, M. Quintero and R. Tovar, Phys. Status Solidi (a) 121 (1990) 483. [6] A.C. Larson and R.B. Von Dreele, General Structure Analysis System, (MS-H805) Los Alamos National Laboratory, Neutron Scattering Center (Copyright, The Regent of the University of California, 1993). [7] B.N. Brockhouse, L.M. Corliss and J.M. Hastings, Phys. Rev. 98 (1955) 1721. [8] W. Geertsma, C. Haas, G.A. Sawatsky and G. Vertogen, Phys. B 86-88 (1977) 1093. [9] J.C. Woolley, S. Bass, A.-M. Lamarche and G. Lamarche, J. Magn. Magn. Mater. 131 (1994) 199.