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Magnetic structures of R3Cu4Ge4 (R=Tb, Dy, Ho, Er)
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 264 (2003) 192–201
Magnetic structures of R3 Cu4 Ge4 (R=Tb, Dy, Ho, Er) a, ! E. Wawrzynska *, J. Hernandez-Velascob, B. Penca, A. Szytu"aa, A. Zygmuntc ! Poland M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow, b BENSC, Hahn-Meitner Institut, Glienicker StraX e 100, D-14109 Berlin-Wannsee, Germany c W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Dorodna 2, 50-950 Wroc!aw, Poland a
Received 21 November 2002
Abstract Neutron diffraction studies of polycrystalline R3 Cu4 Ge4 (R=Tb, Dy, Ho, Er) intermetallic compounds with the orthorhombic Gd3 Cu4 Ge4 -type crystal structure indicate complex magnetic structures. In these compounds the rare earth atoms occupy two nonequivalent 2d and 4e sublattices. For R=Tb and Er with decreasing temperature the magnetic moments in the 2d sublattice order first; the 4e sublattice magnetic moments order at lower temperatures. For R=Dy, Ho both sublattices order simultaneously although the magnetic moment values are different for each of them. In the compounds with R=Tb and Er a change of the magnetic structure, connected with the 2d sublattice, is observed near the N!eel temperature. This is a transition from the commensurate structure, described by the propagation vector k ¼ ð0; 12; 0Þ at low temperatures to the incommensurate structure with k ¼ ð0; 12 þ d; 0Þ at higher temperatures (still below the N!eel temperature). r 2003 Elsevier Science B.V. All rights reserved. PACS: 61.12.Ld; 75.25.tz; 75.30.Kz Keywords: Rare earth intermetallics; Magnetic ordering; Antiferromagnet; Neutron diffraction
1. Introduction This work is a part of broader studies which are expected to systematize the magnetic properties (including magnetic structures) of the Rm Tn Xp rare earth intermetallic compounds, where R is a rare earth atom, T is a d-electron atom and X is a p-electron atom. Investigated in this work R3 Cu4 Ge4 (R=Tb, Dy, Ho, Er) compounds crystallize in the orthorhombic Gd3 Cu4 Ge4 -type *Corresponding author. E-mail address: [email protected] (E. Wawrzy!nska).
crystal structure (Immm space group). In these compounds the rare earth atoms occupy two different crystallographic sublattices [1]. Similar situation is observed in the RTGe2 compounds (R-heavy rare earth atom, T=Ir, Pd, Pt), which crystallize in the orthorhombic crystal structure (Immm space group) in which the rare earth atoms occupy two nonequivalent sublattices [2]. Neutron diffraction data indicate that the rare earth magnetic moments in different sublattices order at different temperatures and form different magnetic orders [3–5]. The R3 Cu4 Ge4 compounds are a new class materials on which it is possible to find similarity of properties. The magnetic, specific
0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-8853(03)00203-8
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heat and neutron diffraction data for the same R3 Cu4 Ge4 compounds show that these compounds are antiferromagnets with the Ne! el temperatures of 10.3 K (R=Ce) [6], 12 [7] or 8.6 K [8] (R=Gd), 7.7 K (R=Er) [9] and 7.5 K (R=Yb) [8]. For the Ce and Er compounds in the magnetically ordered phases additional phase transitions from the commensurate to the incommensurate structures are observed [6,9]. This work reports the results of X-ray, neutron diffraction and magnetic investigations of structural and magnetic properties of the R3 Cu4 Ge4 compounds (R=Tb, Dy, Ho, Er).
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15 and 12 K for Tb3 Cu4 Ge4 ; Dy3 Cu4 Ge4 ; Ho3 Cu4 Ge4 and Er3 Cu4 Ge4 ; respectively, confirmed that all these compounds crystallize in the orthorhombic structure of Gd3 Cu4 Ge4 -type, described by the Immm space group (see Fig. 1). In this structure the rare earth atoms occupy two inequivalent sites: 2d (12;0,12) with the 2 mm symmetry and 4e (x;0,0) with the mmm symmetry; the Cu atoms are situated at the 8n (x; y;0) positions and the Ge atoms are at 4f (x; 12;0) and 4h (0,y; 12) sites in the crystal unit cell. The determined values of the lattice parameters a; b and c as well as the positional parameters corresponding to the minimum of the reliability factor are listed in Table 1.
2. Experimental procedure The polycrystalline samples, each with the total weight of about 7 g, were synthesized by arc melting of stoichiometric amounts of high purity elements in a Ti/Zr gettered argon atmosphere. The reaction products were annealed at 800 C for a week. The specimens were checked for the presence of parasitic phases by use of x-ray powder diffraction (Cu Ka radiation) and turned out to be single phase within the accuracy of the method. The peaks in the X-ray patterns were indexed in the orthorhombic Gd3 Cu4 Ge4 -type structure. Neutron diffractograms were obtained on the E6 instrument at the BERII reactor, HahnMeitner Institut, Berlin. The incident neutron ( (Tb3 Cu4 Ge4 and Ho3 wavelengths were 2.441 A ( (Dy3 Cu4 Ge4 and Er3 Cu4 Cu4 Ge4 ) and 2.448 A Ge4 ). Diffraction patterns were recorded at different temperatures between 1.5 and 30 K. The Rietveld-type programme: FULLPROF [10] was used for processing the neutron diffraction data. Magnetic data were collected using a SQUID magnetometer in the temperature range 1.5–80 K in external magnetic fields up to 100 Oe.
3.2. Magnetic structure Temperature dependence of magnetization of the R3 Cu4 Ge4 (R=Tb, Dy, Ho, Er) compounds is shown in Fig. 2. In the case of Tb3 Cu4 Ge4 a broad maximum between 10 and 23 K is observed. In the 5–9 K temperature range a jump of magnetization was detected. In the temperature dependence of the magnetization of Dy3 Cu4 Ge4 two maxima at 16.2 and 3.8 K, while for Ho3 Cu4 Ge4 only one at 9.5 K, are observed. Also for Er3 Cu4 Ge4 two maxima at 7.6 and 2.6 K were detected. The determined values of the magnetic transition temperatures are collected in Table 2.
3. Results 3.1. Crystal structure The X-ray patterns recorded at 300 K as well as the neutron diffraction patterns recorded at 28, 30,
Fig. 1. Crystal structure of the R3 Cu4 Ge4 compounds. Only the R and the Cu atoms are presented.
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Table 1 The refined structural parameters of the R3 Cu4 Ge4 where R=Tb, Dy, Ho, Er compounds (space group Immm (No. 71)) obtained from the X-ray diffraction patterns at 300 K (labeled with X) and from the neutron diffraction data collected at lower temperatures (labeled with N) Compound
Tb3 Cu4 Ge4
Method T (K) ( a (A) ( b (A) ( c (A) ( 3Þ V ðA
X 300 13.934(1) 6.6358(5) 4.1981(3) 388.17(5) 0.1309(4) 0.3294(7) 0.187(1) 0.2158(8) 0.193(2)
xR xCu yCu xGe yGe
Dy3 Cu4 Ge4 N 28 13.924(8) 6.636(3) 4.195(2) 387.6(4) 0.126(2) 0.327(1) 0.198(2) 0.223(2) 0.174(3)
X 300 13.8817(9) 6.6264(5) 4.1804(1) 384.54(5) 0.1324(6) 0.3288(9) 0.184(2) 0.217(1) 0.192(2)
Ho3 Cu4 Ge4 N 30 13.863(4) 6.603(2) 4.181(2) 382.7(2) 0.129(2) 0.311(3) 0.205(5) 0.218(3) 0.169(6)
X 300 13.835(1) 6.6163(6) 4.1651(4) 381.24(6) 0.1293(4) 0.3316(6) 0.190(1) 0.2110(7) 0.196(2)
Er3 Cu4 Ge4 N 15 13.79(1) 6.600(7) 4.159(4) 378.7(7) 0.133(3) 0.329(2) 0.183(4) 0.212(2) 0.189(5)
X 300 13.789(1) 6.6050(5) 4.1524(3) 378.18(5) 0.1330(6) 0.3282(9) 0.188(2) 0.212(1) 0.191(2)
N 12 13.924(9) 6.669(4) 4.190(2) 389.0(4) 0.123(3) 0.326(1) 0.207(3) 0.223(2) 0.170(3)
Standard deviations are given in brackets.
Fig. 2. Temperature dependence of magnetization of the R3 Cu4 Ge4 compounds (R=Tb, Dy, Ho, Er) measured at low magnetic fields.
3.2.1. Tb3 Cu4 Ge4 Fig. 3 shows the neutron diffraction patterns of Tb3 Cu4 Ge4 measured at 1.5, 12, 19 and 28 K. With decreasing temperature additional peaks of magnetic origin can be observed. The analysis of these peaks at different temperatures indicates that the magnetic structure changes while changing temperature. The analysis of the topology and intensity of the magnetic reflections reveals the
existence of two main regions of the magnetic ordering. The Tb magnetic moments occupy two crystallographic positions, i.e. 4e and 2d described by the following vectors: *
*
4e sites: M1 ðx; 0; 0Þ; M2 ðx; % 0; 0Þ; M3 ð12 þ x; 12; 12Þ; 1 1 1 M4 ð2 x; 2; 2Þ and 2d sites: M5 ð12; 0; 12Þ; M6 ð0; 12; 0Þ:
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Table 2 Magnetic transition temperatures TN and Tt and the values of the magnetic moments m of the R3 Cu4 Ge4 compounds (R=Tb, Dy, Ho, Er) determined from the magnetic (labeled with M) and the neutron diffraction (labeled with N) measurements. DMM abbreviation states for the direction of the magnetic moment R
TN (K) 2d M
Tb Dy Ho Er
23 16.2 9.5 7.6
Tt (K) 2d N
4e M
4e N 10
8
2.6
3.5
2d M
m (mB ) 2d N 18
7.2
4e M
4e N
2d Exp
4e Exp
Theor
2d DMM
4e DMM
4.2(1) 4.3(9) 7.3(5) 8.9(2)
5.0(1) 3.7(6) 1.6(9) 3.2(2)
9.0 10.0 10.0 9.0
jja jjc jjb jjc
jjc jjc jja jja
Fig. 3. Neutron diffraction patterns of Tb3 Cu4 Ge4 collected at 1.5, 12, 19 and 28 K. The indexes 1 and 2 label the magnetic peaks connected with the propagation vectors k1 and k2 ; respectively.
The analysis of the neutron diffraction patterns gives the following values of the propagation vector components and of the Tb magnetic moment in the 2d sites:
at 1.5 K the peaks of the magnetic origin can be indexed with two propagation vectors: k1 ¼ ð1; 12; 12Þ for the 4e sublattice and k2 ¼ ð0; 12; 0Þ for the 2d sublattice. The Tb moments in the 2d sublattice
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Fig. 4. The low angle part of the neutron diffraction patterns of Tb3 Cu4 Ge4 measured at several selected temperatures (a) and the temperature dependence of integrated intensities of the magnetic peaks (b). The indexes 1 and 2 label the magnetic peaks connected with the propagation vectors k1 and k2 ; respectively.
order ferromagnetically whereas in the 4e sublattice order antiferromagnetically with the sequence of signs + + in the space of the crystal unit cell. The Tb moment values are 5:0ð1Þ mB (along the c-direction) and 4:2ð1Þ mB (along the a-direction) for the 4e and the 2d sublattices, respectively. The thermal evolution of the intensity of the % þ reflections located about 20:3 ð200; 101 1 ; 1001 þ þ þ reflections) and 22:3 ð2002 ; 00 1% 1 ; 01% 01 reflections), presented in Fig. 4, indicates that the peaks connected with the propagation vector k1 disappear at 10 K. This suggests that the magnetic ordering in the 4e sublattice disappears at this temperature. Above 10 K only the 2d sublattice moments remain ordered. The values of the magnetic moments decrease but the direction of the moment does not change: *
*
*
at 12 K the moment is equal to 4:1ð1Þ mB ; k2 ¼ ð0; 12; 0Þ; at 19 K the moment is equal to 2:7ð2Þ mB ; k2 ¼ ð0; 0:516ð1Þ; 0Þ; above 28 K the Tb moments are not ordered.
In Fig. 4b the thermal evolution of 000þ 2 ; þ % þ %þ % þ 200=101 1 =1001 and 2002 =0011 =0101 magnetic peaks intensities is shown. One can estimate ordering temperature values to be about 10 K for the 4e sublattice and about 22.5 K for the 2d sublattice. The analysis of the position of the 000þ magnetic peak (see Fig. 4a) reveals an 2 additional transition from the commensurate to the incommensurate structure at Tt of about 18 K. 3.2.2. Dy3 Cu4 Ge4 In the neutron diffraction pattern of Dy3 Cu4 Ge4 collected at 1.5 K some additional peaks of magnetic origin are observed (Fig. 5). The analysis of the magnetic peak intensities indicates that: at 1.5 K the magnetic peaks can be indexed with the propagation vector k ¼ ð0; ky ; 0Þ where ky is equal to 0.521(1). The Dy moments in both, the 4e and the 2d, sites order ferromagnetically. The moment values are 3:7ð6Þ mB and 4:3ð9Þ mB for the 4e and the 2d sublattices, respectively. Both moments are directed along the c-axis.
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Fig. 5. Neutron diffraction patterns of Dy3 Cu4 Ge4 collected at 1.5 and 30 K.
At higher temperatures (but still below the Ne! el temperature) the type of the ordering remains unchanged but the Dy moment values decrease (in both sublattices) and the value of the 4e sites moment becomes dominant. The value of ky changes in comparison to the value at 1.5 K: at 10 K the moment values are: 3:6ð3Þ mB and 2:2ð6Þ mB for the 4e and the 2d sublattices, respectively, whereas ky is equal to 0.526(2), at 13.5 K the moment values are: 3:1ð3Þ mB and 1:6ð6Þ mB for the 4e and the 2d sublattices, respectively, whereas ky is equal to 0.526(2), at 30 K the Dy moments become not ordered. The above results show that the magnetic structure does not change with increasing temperature. This is in contradiction with the magnetic data which indicate the existence of a further transition at 3.8 K (see Fig. 2).
3.2.3. Ho3 Cu4 Ge4 The Ho3 Cu4 Ge4 magnetic structure resulting with additional peaks in the neutron diffraction pattern is observed at low temperatures (see Fig. 6). The analysis reveals that: at 1.5 K the magnetic peaks can be indexed with the propagation vector k ¼ ð0; 12; 0Þ: The Ho moments, in both the 4e and the 2d sites, order magnetically but the relative orientation of the Ho magnetic moments in the body-centered sublattice is undefinable on the basis of our data. The magnetic moment values are 1:6ð9Þ mB (parallel to the a-axis) and 7:3ð5Þ mB (along the b-axis) for the 4e and the 2d sublattices, respectively. At higher temperatures the type of magnetic ordering remains unchanged and the moment values change as follows: at 6 K are: 1:6ð8Þ mB and 7:0ð5Þ mB for the 4e and the 2d sublattices, respectively.
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Fig. 6. Neutron diffraction patterns of Ho3 Cu4 Ge4 collected at 1.5 and 15 K.
at 8 K are: 2:0ð6Þ mB for the 4e sites and 5:6ð6Þ mB for the 2d sublattice, both oriented along the b-axis. above 15 K the Ho moments are not ordered. 3.2.4. Er3 Cu4 Ge4 In the neutron diffraction pattern of Er3 Cu4 Ge4 at 1.5 K additional peaks of magnetic origin are observed (Fig. 7). The Er magnetic moments occupy two sites in the crystal unit cell. The analysis of the neutron diffraction patterns indicates that: at 1.5 K the magnetic peaks can be indexed with two propagation vectors: k1 ¼ ð0; 0:883ð2Þ; 0Þ for the 4e subblatice and k2 ¼ ð0; 12; 0Þ for the 2d sublattice. The Er moments in both sublattices form an antiferromagnetic ordering. The sequences of signs for the Er moments in the crystal unit cell are as follows: + + + + for the 4e
sublattice (the magnetic moments are parallel to the a-axis) and + in the 2d sites (along the caxis). The amplitudes of the magnetic moments are equal to 3:2ð2Þ mB and 8:9ð2Þ mB for the 4e and the 2d sublattices, respectively. The diffraction patterns of Er3 Cu4 Ge4 for 2y ranging from 7 to 25 and for temperatures between 1.5 and 12 K are shown in Fig. 8a. In this 2y range new magnetic peaks appear at 7.5 K. At about 7 K a change in their angular position is observed. Below 3 K an additional peak of magnetic origin is observed. In Fig. 8b the temperature dependence of the intensities of some of the magnetic peaks presented in Fig. 8a is shown. These dependencies give the Ne! el temperature of 3.5 K for the 4e and 8 K for the 2a sublattices. Analysis of the angular positions of the magnetic peaks leads to the magnetic ordering in the 2d sublattice described by the wave vector k ¼
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Fig. 7. Neutron diffraction patterns of Er3 Cu4 Ge4 collected at 1.5, 5.5, 7.5 and 12 K. The indexes 1 and 2 label the magnetic peaks connected with the propagation vectors k1 and k2 ; respectively.
ð0; 12; 0Þ in the temperature range 1.5–7 K, which at 7.5 K changes into k ¼ ð0; 0:519ð1Þ; 0Þ: The best fits to the experimental data at different temperatures give the following parameters of the magnetic structure: at 5.5 K the Er magnetic moment value in the 2d sites equals 8:6ð1Þ mB (still along the c-axis) and k2 ¼ ð0; 12; 0Þ; at 7.5 K the Er magnetic moment value in the 2d sites equals 4:0ð2Þ mB (still along the c-axis) and k2 ¼ ð0; 0:519ð1Þ; 0Þ; above 12 K the Er moments are not ordered. 4. Discussion The neutron diffraction data for R3 Cu4 Ge4 compounds (R=Tb, Dy, Ho, Er), presented in
this work, confirm the crystal structure resulting from the X-ray data and lead to complex magnetic structure models for these compounds. All of the investigated compounds crystallize in the orthorhombic Gd3 Cu4 Ge4 -type structure. Rare earth atoms occupy two nonequivalent 2d and 4e crystallographic positions. The magnetic moments in the high-symmetry sites order at relatively high temperatures whereas the magnetic moments in the low-symmetry sites order at lower temperatures. The observed reduction of the values of the magnetic moments in both sublattices is caused by the crystal electric field (CEF) effect. In the case of the Ho and Er compounds a large difference between the magnetic moments values in the two inequivalent sites is detected. Similar dependence is observed in Tb5 Sb3 [11] while in
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Fig. 8. The low angle part of the neutron diffraction patterns of Er3 Cu4 Ge4 measured at several selected temperatures (a) and the temperature dependence of integrated intensities of the magnetic peaks (b). The indexes 1 and 2 label the magnetic peaks connected with the propagation vectors k1 and k2 ; respectively.
Ce5 Si3 [12] and Ce5 Sn3 [13] compounds the magnetic ordering exists in the high-symmetry sites while the low-symmetry sites are nonmagnetic. For R=Tb and Er with decreasing temperature the 2d sublattice magnetic moments order first and then at lower temperatures, the 4e sublattice orders. For R=Dy and Ho both sublattices order simultaneously but with different moment values. In R3 Cu4 Ge4 (R=Tb and Er) a further phase transition from commensurate collinear magnetic structure (described by the wave vector k ¼ ð0; 12; 0Þ) to the incommensurate sine-wave modulated structure with the propagation vector k ¼ ð0; 12 þ d; 0Þ (d is equal to 0.16(1) for R=Tb and 0.19(1) for R=Er) is observed about the Ne! el temperature. This effect is also reported in a large number of other rare earth intermetallics [14,15]. It results from temperature-dependent free energy for different propagation vectors in the presence of magnetocrystalline anisotropy. The results of preliminary neutron diffraction measurements of Er3 Cu4 Ge4 reported in Ref. [9] are in a good agreement with our data. The results for
R3 Cu4 Ge4 (R=Tb and Er) confirm the results obtained for RTGe2 (T= Ir, Pt, Pd) [3–5]. In these compounds the rare earth magnetic moments in different sublattices order at different temperatures and with different types of magnetic ordering. ( suggest that Large R3þ –R3þ distances (X3:8 A) the direct magnetic interactions are highly improbable. Stability of the observed magnetic ordering schemes may thus be considered as being due to interactions via conduction electrons (the RKKY model). Thermal dependence of resistivity indicates metallic character of the isostructural stannides [16]. In the RKKY model the Ne! el temperature is proportional to the de Gennes factor G ¼ ðgJ 1Þ2 JðJ þ 1Þ [17]. However, the Ne! el temperatures of the R3 Cu4 Ge4 (R=Gd–Er) compounds do not follow the de Gennes scalling (see Fig. 9). This suggests that the main interaction leading to the magnetic ordering in these systems is not purely of RKKY-type but is modified by crystalline electric field effects, which can significantly influence the magnitude of the Ne! el temperature [18].
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State Committee for Scientific Research in Poland within the confines of the Grant 2P03B 113 23. The authors (E.W., B.P. and A.S.) would like to express their gratitude to the management of the Berlin Neutron Scattering Centre for financial support and kind hospitality.
References
Fig. 9. The N!eel temperature vs. de Gennes function for the R3 Cu4 Ge4 (R=Gd, Tb, Dy, Ho, Er) compounds. The value of TN for Gd3 Cu4 Ge4 was taken from Refs [7,8].
In all the investigated compounds the rare earth magnetic moments in the 2d sublattice are parallel to the c-axis while the direction of the moments in the 4e sublattice is different for different compounds. This is connected with the different point symmetry of the 2d and the 4e crystallographic positions (mmm and 2mm, respectively). The magnetic ordering in the low-symmetry sites (observed at low temperatures) occurs due to the intersite interactions.
Acknowledgements This work was supported by the European Commission under the Access to Research Infrastructures of the Human Potential Programme (contract no HPRI-CT-1999-00020) and IHP II Programme (project no: 466) and by the
[1] W. Rieger, Mon. Chem. 101 (1970) 449. [2] M. Fran@ais, G. Venturini, E. McRae, B. Malaman, B. Rogues, J. Less-Common Met. 128 (1987) 249. [3] D. Schmitt, D. Ouladdiaf, Ch.D. Routsi, J.K. Yakinthos, H. Gamari-Seale, J. Alloys Compounds 292 (1999) 21. [4] B. Penc, M. Hofmann, A. Szytu"a, A. Zygmunt, J. Phys.: Condens. Matter 13 (2001) 4471. [5] A. Gil, B. Penc, M. Hofmann, A. Szytu"a, A. Zygmunt, J. Alloys Compounds 322 (2001) 21. [6] O. Zaharko, L. Keller, C. Ritter, J. Magn. Magn. Mater. 253 (2002) 130. [7] H. Oestrreicher, Phys. Stat. Sol. A 39 (1977) K75. [8] S.K. Dhar, S. Sigh, B. Bonville, C. Mazumdar, P. Manfrinetti, A. Palenzona, Physica B 312–313 (2002) 446. [9] O. Zaharko, L. Keller, Scientific Report 2001, Paul Scherrer Institute, Villigen, 2001, p. 24. [10] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [11] J.K. Yakinthos, I.P. Semitelou, E. Roudout, Solid State Commun. 59 (1986) 227. [12] M. Kontani, M. Senda, M. Nakano, J.M. Lawrence, K. Adachi, J. Magn. Magn. Mater. 70 (1987) 378. [13] J.M. Lawrence, M.F. Hundley, J.D. Thompson, G.H. Kwei, Z. Fisk, Phys. Rev. B 43 (1991) 11057. [14] A. Szytu"a, J. Leciejewicz, Handbook of Crystal Structure and Magnetic Properties of Rare Earth Intermetallics, Chemical Rubber Company Press, Boca Rotan, Fl, 1994. [15] D. Gignoux, D. Schmitt, Phys. Rev. B 48 (1993) 12682. [16] R.V. Sholozdra, Stannides of Rare Earth and Transition Metal, Svit, Lviv, Ukraina, 1993, p. 200. [17] P.G. de Gennes, J. Phys. Radium 23 (1962) 510, 630. [18] D.R. Noakes, G.H. Shenoy, Phys. Lett. A 91 (1982) 35.
Journal of Magnetism and Magnetic Materials 264 (2003) 192–201
Magnetic structures of R3 Cu4 Ge4 (R=Tb, Dy, Ho, Er) a, ! E. Wawrzynska *, J. Hernandez-Velascob, B. Penca, A. Szytu"aa, A. Zygmuntc ! Poland M. Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Krakow, b BENSC, Hahn-Meitner Institut, Glienicker StraX e 100, D-14109 Berlin-Wannsee, Germany c W. Trzebiatowski Institute of Low Temperature and Structure Research, Polish Academy of Sciences, Dorodna 2, 50-950 Wroc!aw, Poland a
Received 21 November 2002
Abstract Neutron diffraction studies of polycrystalline R3 Cu4 Ge4 (R=Tb, Dy, Ho, Er) intermetallic compounds with the orthorhombic Gd3 Cu4 Ge4 -type crystal structure indicate complex magnetic structures. In these compounds the rare earth atoms occupy two nonequivalent 2d and 4e sublattices. For R=Tb and Er with decreasing temperature the magnetic moments in the 2d sublattice order first; the 4e sublattice magnetic moments order at lower temperatures. For R=Dy, Ho both sublattices order simultaneously although the magnetic moment values are different for each of them. In the compounds with R=Tb and Er a change of the magnetic structure, connected with the 2d sublattice, is observed near the N!eel temperature. This is a transition from the commensurate structure, described by the propagation vector k ¼ ð0; 12; 0Þ at low temperatures to the incommensurate structure with k ¼ ð0; 12 þ d; 0Þ at higher temperatures (still below the N!eel temperature). r 2003 Elsevier Science B.V. All rights reserved. PACS: 61.12.Ld; 75.25.tz; 75.30.Kz Keywords: Rare earth intermetallics; Magnetic ordering; Antiferromagnet; Neutron diffraction
1. Introduction This work is a part of broader studies which are expected to systematize the magnetic properties (including magnetic structures) of the Rm Tn Xp rare earth intermetallic compounds, where R is a rare earth atom, T is a d-electron atom and X is a p-electron atom. Investigated in this work R3 Cu4 Ge4 (R=Tb, Dy, Ho, Er) compounds crystallize in the orthorhombic Gd3 Cu4 Ge4 -type *Corresponding author. E-mail address: [email protected] (E. Wawrzy!nska).
crystal structure (Immm space group). In these compounds the rare earth atoms occupy two different crystallographic sublattices [1]. Similar situation is observed in the RTGe2 compounds (R-heavy rare earth atom, T=Ir, Pd, Pt), which crystallize in the orthorhombic crystal structure (Immm space group) in which the rare earth atoms occupy two nonequivalent sublattices [2]. Neutron diffraction data indicate that the rare earth magnetic moments in different sublattices order at different temperatures and form different magnetic orders [3–5]. The R3 Cu4 Ge4 compounds are a new class materials on which it is possible to find similarity of properties. The magnetic, specific
0304-8853/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0304-8853(03)00203-8
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heat and neutron diffraction data for the same R3 Cu4 Ge4 compounds show that these compounds are antiferromagnets with the Ne! el temperatures of 10.3 K (R=Ce) [6], 12 [7] or 8.6 K [8] (R=Gd), 7.7 K (R=Er) [9] and 7.5 K (R=Yb) [8]. For the Ce and Er compounds in the magnetically ordered phases additional phase transitions from the commensurate to the incommensurate structures are observed [6,9]. This work reports the results of X-ray, neutron diffraction and magnetic investigations of structural and magnetic properties of the R3 Cu4 Ge4 compounds (R=Tb, Dy, Ho, Er).
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15 and 12 K for Tb3 Cu4 Ge4 ; Dy3 Cu4 Ge4 ; Ho3 Cu4 Ge4 and Er3 Cu4 Ge4 ; respectively, confirmed that all these compounds crystallize in the orthorhombic structure of Gd3 Cu4 Ge4 -type, described by the Immm space group (see Fig. 1). In this structure the rare earth atoms occupy two inequivalent sites: 2d (12;0,12) with the 2 mm symmetry and 4e (x;0,0) with the mmm symmetry; the Cu atoms are situated at the 8n (x; y;0) positions and the Ge atoms are at 4f (x; 12;0) and 4h (0,y; 12) sites in the crystal unit cell. The determined values of the lattice parameters a; b and c as well as the positional parameters corresponding to the minimum of the reliability factor are listed in Table 1.
2. Experimental procedure The polycrystalline samples, each with the total weight of about 7 g, were synthesized by arc melting of stoichiometric amounts of high purity elements in a Ti/Zr gettered argon atmosphere. The reaction products were annealed at 800 C for a week. The specimens were checked for the presence of parasitic phases by use of x-ray powder diffraction (Cu Ka radiation) and turned out to be single phase within the accuracy of the method. The peaks in the X-ray patterns were indexed in the orthorhombic Gd3 Cu4 Ge4 -type structure. Neutron diffractograms were obtained on the E6 instrument at the BERII reactor, HahnMeitner Institut, Berlin. The incident neutron ( (Tb3 Cu4 Ge4 and Ho3 wavelengths were 2.441 A ( (Dy3 Cu4 Ge4 and Er3 Cu4 Cu4 Ge4 ) and 2.448 A Ge4 ). Diffraction patterns were recorded at different temperatures between 1.5 and 30 K. The Rietveld-type programme: FULLPROF [10] was used for processing the neutron diffraction data. Magnetic data were collected using a SQUID magnetometer in the temperature range 1.5–80 K in external magnetic fields up to 100 Oe.
3.2. Magnetic structure Temperature dependence of magnetization of the R3 Cu4 Ge4 (R=Tb, Dy, Ho, Er) compounds is shown in Fig. 2. In the case of Tb3 Cu4 Ge4 a broad maximum between 10 and 23 K is observed. In the 5–9 K temperature range a jump of magnetization was detected. In the temperature dependence of the magnetization of Dy3 Cu4 Ge4 two maxima at 16.2 and 3.8 K, while for Ho3 Cu4 Ge4 only one at 9.5 K, are observed. Also for Er3 Cu4 Ge4 two maxima at 7.6 and 2.6 K were detected. The determined values of the magnetic transition temperatures are collected in Table 2.
3. Results 3.1. Crystal structure The X-ray patterns recorded at 300 K as well as the neutron diffraction patterns recorded at 28, 30,
Fig. 1. Crystal structure of the R3 Cu4 Ge4 compounds. Only the R and the Cu atoms are presented.
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Table 1 The refined structural parameters of the R3 Cu4 Ge4 where R=Tb, Dy, Ho, Er compounds (space group Immm (No. 71)) obtained from the X-ray diffraction patterns at 300 K (labeled with X) and from the neutron diffraction data collected at lower temperatures (labeled with N) Compound
Tb3 Cu4 Ge4
Method T (K) ( a (A) ( b (A) ( c (A) ( 3Þ V ðA
X 300 13.934(1) 6.6358(5) 4.1981(3) 388.17(5) 0.1309(4) 0.3294(7) 0.187(1) 0.2158(8) 0.193(2)
xR xCu yCu xGe yGe
Dy3 Cu4 Ge4 N 28 13.924(8) 6.636(3) 4.195(2) 387.6(4) 0.126(2) 0.327(1) 0.198(2) 0.223(2) 0.174(3)
X 300 13.8817(9) 6.6264(5) 4.1804(1) 384.54(5) 0.1324(6) 0.3288(9) 0.184(2) 0.217(1) 0.192(2)
Ho3 Cu4 Ge4 N 30 13.863(4) 6.603(2) 4.181(2) 382.7(2) 0.129(2) 0.311(3) 0.205(5) 0.218(3) 0.169(6)
X 300 13.835(1) 6.6163(6) 4.1651(4) 381.24(6) 0.1293(4) 0.3316(6) 0.190(1) 0.2110(7) 0.196(2)
Er3 Cu4 Ge4 N 15 13.79(1) 6.600(7) 4.159(4) 378.7(7) 0.133(3) 0.329(2) 0.183(4) 0.212(2) 0.189(5)
X 300 13.789(1) 6.6050(5) 4.1524(3) 378.18(5) 0.1330(6) 0.3282(9) 0.188(2) 0.212(1) 0.191(2)
N 12 13.924(9) 6.669(4) 4.190(2) 389.0(4) 0.123(3) 0.326(1) 0.207(3) 0.223(2) 0.170(3)
Standard deviations are given in brackets.
Fig. 2. Temperature dependence of magnetization of the R3 Cu4 Ge4 compounds (R=Tb, Dy, Ho, Er) measured at low magnetic fields.
3.2.1. Tb3 Cu4 Ge4 Fig. 3 shows the neutron diffraction patterns of Tb3 Cu4 Ge4 measured at 1.5, 12, 19 and 28 K. With decreasing temperature additional peaks of magnetic origin can be observed. The analysis of these peaks at different temperatures indicates that the magnetic structure changes while changing temperature. The analysis of the topology and intensity of the magnetic reflections reveals the
existence of two main regions of the magnetic ordering. The Tb magnetic moments occupy two crystallographic positions, i.e. 4e and 2d described by the following vectors: *
*
4e sites: M1 ðx; 0; 0Þ; M2 ðx; % 0; 0Þ; M3 ð12 þ x; 12; 12Þ; 1 1 1 M4 ð2 x; 2; 2Þ and 2d sites: M5 ð12; 0; 12Þ; M6 ð0; 12; 0Þ:
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Table 2 Magnetic transition temperatures TN and Tt and the values of the magnetic moments m of the R3 Cu4 Ge4 compounds (R=Tb, Dy, Ho, Er) determined from the magnetic (labeled with M) and the neutron diffraction (labeled with N) measurements. DMM abbreviation states for the direction of the magnetic moment R
TN (K) 2d M
Tb Dy Ho Er
23 16.2 9.5 7.6
Tt (K) 2d N
4e M
4e N 10
8
2.6
3.5
2d M
m (mB ) 2d N 18
7.2
4e M
4e N
2d Exp
4e Exp
Theor
2d DMM
4e DMM
4.2(1) 4.3(9) 7.3(5) 8.9(2)
5.0(1) 3.7(6) 1.6(9) 3.2(2)
9.0 10.0 10.0 9.0
jja jjc jjb jjc
jjc jjc jja jja
Fig. 3. Neutron diffraction patterns of Tb3 Cu4 Ge4 collected at 1.5, 12, 19 and 28 K. The indexes 1 and 2 label the magnetic peaks connected with the propagation vectors k1 and k2 ; respectively.
The analysis of the neutron diffraction patterns gives the following values of the propagation vector components and of the Tb magnetic moment in the 2d sites:
at 1.5 K the peaks of the magnetic origin can be indexed with two propagation vectors: k1 ¼ ð1; 12; 12Þ for the 4e sublattice and k2 ¼ ð0; 12; 0Þ for the 2d sublattice. The Tb moments in the 2d sublattice
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Fig. 4. The low angle part of the neutron diffraction patterns of Tb3 Cu4 Ge4 measured at several selected temperatures (a) and the temperature dependence of integrated intensities of the magnetic peaks (b). The indexes 1 and 2 label the magnetic peaks connected with the propagation vectors k1 and k2 ; respectively.
order ferromagnetically whereas in the 4e sublattice order antiferromagnetically with the sequence of signs + + in the space of the crystal unit cell. The Tb moment values are 5:0ð1Þ mB (along the c-direction) and 4:2ð1Þ mB (along the a-direction) for the 4e and the 2d sublattices, respectively. The thermal evolution of the intensity of the % þ reflections located about 20:3 ð200; 101 1 ; 1001 þ þ þ reflections) and 22:3 ð2002 ; 00 1% 1 ; 01% 01 reflections), presented in Fig. 4, indicates that the peaks connected with the propagation vector k1 disappear at 10 K. This suggests that the magnetic ordering in the 4e sublattice disappears at this temperature. Above 10 K only the 2d sublattice moments remain ordered. The values of the magnetic moments decrease but the direction of the moment does not change: *
*
*
at 12 K the moment is equal to 4:1ð1Þ mB ; k2 ¼ ð0; 12; 0Þ; at 19 K the moment is equal to 2:7ð2Þ mB ; k2 ¼ ð0; 0:516ð1Þ; 0Þ; above 28 K the Tb moments are not ordered.
In Fig. 4b the thermal evolution of 000þ 2 ; þ % þ %þ % þ 200=101 1 =1001 and 2002 =0011 =0101 magnetic peaks intensities is shown. One can estimate ordering temperature values to be about 10 K for the 4e sublattice and about 22.5 K for the 2d sublattice. The analysis of the position of the 000þ magnetic peak (see Fig. 4a) reveals an 2 additional transition from the commensurate to the incommensurate structure at Tt of about 18 K. 3.2.2. Dy3 Cu4 Ge4 In the neutron diffraction pattern of Dy3 Cu4 Ge4 collected at 1.5 K some additional peaks of magnetic origin are observed (Fig. 5). The analysis of the magnetic peak intensities indicates that: at 1.5 K the magnetic peaks can be indexed with the propagation vector k ¼ ð0; ky ; 0Þ where ky is equal to 0.521(1). The Dy moments in both, the 4e and the 2d, sites order ferromagnetically. The moment values are 3:7ð6Þ mB and 4:3ð9Þ mB for the 4e and the 2d sublattices, respectively. Both moments are directed along the c-axis.
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Fig. 5. Neutron diffraction patterns of Dy3 Cu4 Ge4 collected at 1.5 and 30 K.
At higher temperatures (but still below the Ne! el temperature) the type of the ordering remains unchanged but the Dy moment values decrease (in both sublattices) and the value of the 4e sites moment becomes dominant. The value of ky changes in comparison to the value at 1.5 K: at 10 K the moment values are: 3:6ð3Þ mB and 2:2ð6Þ mB for the 4e and the 2d sublattices, respectively, whereas ky is equal to 0.526(2), at 13.5 K the moment values are: 3:1ð3Þ mB and 1:6ð6Þ mB for the 4e and the 2d sublattices, respectively, whereas ky is equal to 0.526(2), at 30 K the Dy moments become not ordered. The above results show that the magnetic structure does not change with increasing temperature. This is in contradiction with the magnetic data which indicate the existence of a further transition at 3.8 K (see Fig. 2).
3.2.3. Ho3 Cu4 Ge4 The Ho3 Cu4 Ge4 magnetic structure resulting with additional peaks in the neutron diffraction pattern is observed at low temperatures (see Fig. 6). The analysis reveals that: at 1.5 K the magnetic peaks can be indexed with the propagation vector k ¼ ð0; 12; 0Þ: The Ho moments, in both the 4e and the 2d sites, order magnetically but the relative orientation of the Ho magnetic moments in the body-centered sublattice is undefinable on the basis of our data. The magnetic moment values are 1:6ð9Þ mB (parallel to the a-axis) and 7:3ð5Þ mB (along the b-axis) for the 4e and the 2d sublattices, respectively. At higher temperatures the type of magnetic ordering remains unchanged and the moment values change as follows: at 6 K are: 1:6ð8Þ mB and 7:0ð5Þ mB for the 4e and the 2d sublattices, respectively.
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Fig. 6. Neutron diffraction patterns of Ho3 Cu4 Ge4 collected at 1.5 and 15 K.
at 8 K are: 2:0ð6Þ mB for the 4e sites and 5:6ð6Þ mB for the 2d sublattice, both oriented along the b-axis. above 15 K the Ho moments are not ordered. 3.2.4. Er3 Cu4 Ge4 In the neutron diffraction pattern of Er3 Cu4 Ge4 at 1.5 K additional peaks of magnetic origin are observed (Fig. 7). The Er magnetic moments occupy two sites in the crystal unit cell. The analysis of the neutron diffraction patterns indicates that: at 1.5 K the magnetic peaks can be indexed with two propagation vectors: k1 ¼ ð0; 0:883ð2Þ; 0Þ for the 4e subblatice and k2 ¼ ð0; 12; 0Þ for the 2d sublattice. The Er moments in both sublattices form an antiferromagnetic ordering. The sequences of signs for the Er moments in the crystal unit cell are as follows: + + + + for the 4e
sublattice (the magnetic moments are parallel to the a-axis) and + in the 2d sites (along the caxis). The amplitudes of the magnetic moments are equal to 3:2ð2Þ mB and 8:9ð2Þ mB for the 4e and the 2d sublattices, respectively. The diffraction patterns of Er3 Cu4 Ge4 for 2y ranging from 7 to 25 and for temperatures between 1.5 and 12 K are shown in Fig. 8a. In this 2y range new magnetic peaks appear at 7.5 K. At about 7 K a change in their angular position is observed. Below 3 K an additional peak of magnetic origin is observed. In Fig. 8b the temperature dependence of the intensities of some of the magnetic peaks presented in Fig. 8a is shown. These dependencies give the Ne! el temperature of 3.5 K for the 4e and 8 K for the 2a sublattices. Analysis of the angular positions of the magnetic peaks leads to the magnetic ordering in the 2d sublattice described by the wave vector k ¼
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Fig. 7. Neutron diffraction patterns of Er3 Cu4 Ge4 collected at 1.5, 5.5, 7.5 and 12 K. The indexes 1 and 2 label the magnetic peaks connected with the propagation vectors k1 and k2 ; respectively.
ð0; 12; 0Þ in the temperature range 1.5–7 K, which at 7.5 K changes into k ¼ ð0; 0:519ð1Þ; 0Þ: The best fits to the experimental data at different temperatures give the following parameters of the magnetic structure: at 5.5 K the Er magnetic moment value in the 2d sites equals 8:6ð1Þ mB (still along the c-axis) and k2 ¼ ð0; 12; 0Þ; at 7.5 K the Er magnetic moment value in the 2d sites equals 4:0ð2Þ mB (still along the c-axis) and k2 ¼ ð0; 0:519ð1Þ; 0Þ; above 12 K the Er moments are not ordered. 4. Discussion The neutron diffraction data for R3 Cu4 Ge4 compounds (R=Tb, Dy, Ho, Er), presented in
this work, confirm the crystal structure resulting from the X-ray data and lead to complex magnetic structure models for these compounds. All of the investigated compounds crystallize in the orthorhombic Gd3 Cu4 Ge4 -type structure. Rare earth atoms occupy two nonequivalent 2d and 4e crystallographic positions. The magnetic moments in the high-symmetry sites order at relatively high temperatures whereas the magnetic moments in the low-symmetry sites order at lower temperatures. The observed reduction of the values of the magnetic moments in both sublattices is caused by the crystal electric field (CEF) effect. In the case of the Ho and Er compounds a large difference between the magnetic moments values in the two inequivalent sites is detected. Similar dependence is observed in Tb5 Sb3 [11] while in
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Fig. 8. The low angle part of the neutron diffraction patterns of Er3 Cu4 Ge4 measured at several selected temperatures (a) and the temperature dependence of integrated intensities of the magnetic peaks (b). The indexes 1 and 2 label the magnetic peaks connected with the propagation vectors k1 and k2 ; respectively.
Ce5 Si3 [12] and Ce5 Sn3 [13] compounds the magnetic ordering exists in the high-symmetry sites while the low-symmetry sites are nonmagnetic. For R=Tb and Er with decreasing temperature the 2d sublattice magnetic moments order first and then at lower temperatures, the 4e sublattice orders. For R=Dy and Ho both sublattices order simultaneously but with different moment values. In R3 Cu4 Ge4 (R=Tb and Er) a further phase transition from commensurate collinear magnetic structure (described by the wave vector k ¼ ð0; 12; 0Þ) to the incommensurate sine-wave modulated structure with the propagation vector k ¼ ð0; 12 þ d; 0Þ (d is equal to 0.16(1) for R=Tb and 0.19(1) for R=Er) is observed about the Ne! el temperature. This effect is also reported in a large number of other rare earth intermetallics [14,15]. It results from temperature-dependent free energy for different propagation vectors in the presence of magnetocrystalline anisotropy. The results of preliminary neutron diffraction measurements of Er3 Cu4 Ge4 reported in Ref. [9] are in a good agreement with our data. The results for
R3 Cu4 Ge4 (R=Tb and Er) confirm the results obtained for RTGe2 (T= Ir, Pt, Pd) [3–5]. In these compounds the rare earth magnetic moments in different sublattices order at different temperatures and with different types of magnetic ordering. ( suggest that Large R3þ –R3þ distances (X3:8 A) the direct magnetic interactions are highly improbable. Stability of the observed magnetic ordering schemes may thus be considered as being due to interactions via conduction electrons (the RKKY model). Thermal dependence of resistivity indicates metallic character of the isostructural stannides [16]. In the RKKY model the Ne! el temperature is proportional to the de Gennes factor G ¼ ðgJ 1Þ2 JðJ þ 1Þ [17]. However, the Ne! el temperatures of the R3 Cu4 Ge4 (R=Gd–Er) compounds do not follow the de Gennes scalling (see Fig. 9). This suggests that the main interaction leading to the magnetic ordering in these systems is not purely of RKKY-type but is modified by crystalline electric field effects, which can significantly influence the magnitude of the Ne! el temperature [18].
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State Committee for Scientific Research in Poland within the confines of the Grant 2P03B 113 23. The authors (E.W., B.P. and A.S.) would like to express their gratitude to the management of the Berlin Neutron Scattering Centre for financial support and kind hospitality.
References
Fig. 9. The N!eel temperature vs. de Gennes function for the R3 Cu4 Ge4 (R=Gd, Tb, Dy, Ho, Er) compounds. The value of TN for Gd3 Cu4 Ge4 was taken from Refs [7,8].
In all the investigated compounds the rare earth magnetic moments in the 2d sublattice are parallel to the c-axis while the direction of the moments in the 4e sublattice is different for different compounds. This is connected with the different point symmetry of the 2d and the 4e crystallographic positions (mmm and 2mm, respectively). The magnetic ordering in the low-symmetry sites (observed at low temperatures) occurs due to the intersite interactions.
Acknowledgements This work was supported by the European Commission under the Access to Research Infrastructures of the Human Potential Programme (contract no HPRI-CT-1999-00020) and IHP II Programme (project no: 466) and by the
[1] W. Rieger, Mon. Chem. 101 (1970) 449. [2] M. Fran@ais, G. Venturini, E. McRae, B. Malaman, B. Rogues, J. Less-Common Met. 128 (1987) 249. [3] D. Schmitt, D. Ouladdiaf, Ch.D. Routsi, J.K. Yakinthos, H. Gamari-Seale, J. Alloys Compounds 292 (1999) 21. [4] B. Penc, M. Hofmann, A. Szytu"a, A. Zygmunt, J. Phys.: Condens. Matter 13 (2001) 4471. [5] A. Gil, B. Penc, M. Hofmann, A. Szytu"a, A. Zygmunt, J. Alloys Compounds 322 (2001) 21. [6] O. Zaharko, L. Keller, C. Ritter, J. Magn. Magn. Mater. 253 (2002) 130. [7] H. Oestrreicher, Phys. Stat. Sol. A 39 (1977) K75. [8] S.K. Dhar, S. Sigh, B. Bonville, C. Mazumdar, P. Manfrinetti, A. Palenzona, Physica B 312–313 (2002) 446. [9] O. Zaharko, L. Keller, Scientific Report 2001, Paul Scherrer Institute, Villigen, 2001, p. 24. [10] J. Rodriguez-Carvajal, Physica B 192 (1993) 55. [11] J.K. Yakinthos, I.P. Semitelou, E. Roudout, Solid State Commun. 59 (1986) 227. [12] M. Kontani, M. Senda, M. Nakano, J.M. Lawrence, K. Adachi, J. Magn. Magn. Mater. 70 (1987) 378. [13] J.M. Lawrence, M.F. Hundley, J.D. Thompson, G.H. Kwei, Z. Fisk, Phys. Rev. B 43 (1991) 11057. [14] A. Szytu"a, J. Leciejewicz, Handbook of Crystal Structure and Magnetic Properties of Rare Earth Intermetallics, Chemical Rubber Company Press, Boca Rotan, Fl, 1994. [15] D. Gignoux, D. Schmitt, Phys. Rev. B 48 (1993) 12682. [16] R.V. Sholozdra, Stannides of Rare Earth and Transition Metal, Svit, Lviv, Ukraina, 1993, p. 200. [17] P.G. de Gennes, J. Phys. Radium 23 (1962) 510, 630. [18] D.R. Noakes, G.H. Shenoy, Phys. Lett. A 91 (1982) 35.