- Email: [email protected]
Neutron diffraction study of NdCrGe3
Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
Contents lists available at SciVerse ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Neutron diffraction study of NdCrGe3 P. Lemoine a,n, J.M. Cadogan b, B.R. Slater c, A. Mar c, M. Avdeev d a
Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada, R3T 2N2 School of Physical, Environmental and Mathematical Sciences, The University of New South Wales, Canberra ACT BC2610, Australia Department of Chemistry, University of Alberta, Edmonton, AB, Canada, T6G 2G2 d Bragg Institute, ANSTO, PMB 1, Menai, NSW 2234, Australia b c
a r t i c l e i n f o
abstract
Article history: Received 18 July 2012 Received in revised form 15 August 2012 Available online 29 August 2012
The hexagonal perovskite (BaNiO3-type) structure of NdCrGe3 and its ferromagnetic order at TC ¼ 122 K have been confirmed by neutron powder diffraction measurements. The magnetic structure is characterized by an axial ferromagnetic arrangement of both the Cr and Nd sublattices below TC. The relatively high Curie temperature of this compound is mainly driven by the magnetic ordering of the Cr sublattice with Nd–Cr magnetic interactions also playing a role. The magnetic ordering of the Nd sublattice, deduced from the thermal variation of the magnetic moments, occurs at around TE 70 K. The absence of a spin reorientation of the Nd and Cr magnetic order allows us to conclude that the complex magnetic behaviour previously observed at low temperatures in macroscopic magnetic measurements is a consequence of strong magnetocrystalline anisotropy effects. Crown Copyright & 2012 Published by Elsevier B.V. All rights reserved.
Keywords: Rare-earth intermetallic compound Hexagonal perovskite-type structure Neutron powder diffraction Magnetic structure
1. Introduction Among the RTX3 compounds (R ¼rare earth; T¼transition metal; X ¼p-block element), the ternary germanides RTiGe3 (R¼La–Pr) [1], RVGe3 (R¼ La–Nd) [2] and RCrGe3 (R¼La–Nd, Sm) [3] represent unusual instances of intermetallic phases adopting the hexagonal perovskite structure (BaNiO3-type, P63/mmc). This structure consists of one-dimensional chains of face-sharing TX6 octahedra along the c axis (Fig. 1) linked by triangular X3 clusters and is normally found for chalcogenides and halides [4]. Due to their quasi-one-dimensional structure, the BaNiO3-type intermetallic compounds show interesting magnetic properties which are dependent on the transition metal. For example, CeTiGe3 orders ferromagnetically at low temperature (TC ¼14 K) [1], while the RVGe3 (R¼Ce–Nd) compounds have low temperature antiferromagnetic ordering with TN ranging from 4 K for CeVGe3 to 15 K for PrVGe3 [2]. The magnetic properties of the RCrGe3 compounds are also varied due to the magnetic ordering of both the rare-earth and transition metal sublattices, leading to ferromagnetic order at relatively high temperatures (TC ranges from 66 K for CeCrGe3 to 155 K for SmCrGe3) and complex magnetic behaviours at low temperature [3]. For example, macroscopic magnetic measurements performed on powdered NdCrGe3 show a divergence of the susceptibility between the ZFC and FC measurements below TE70 K and a metamagnetic transition
n
Corresponding author. E-mail addresses: [email protected] (P. Lemoine), [email protected] (J.M. Cadogan).
with strong hysteresis at 2 K (Fig. 2), suggesting a possible spin reorientation at low temperature. The ferromagnetic order of the Cr sublattice was recently confirmed by neutron powder diffraction on LaCrGe3 [5]. This compound has a magnetic structure that is characterized by a collinear arrangement of the Cr magnetic moments along the c-axis from TC down to 3 K and a spin reorientation at very low temperature with a canting angle, away from the c-axis, y of 32(6)1 at 1.7 K. In order to study the influence of the magnetic ordering of both the rare-earth and chromium sublattices on the complex magnetic behaviour observed at low temperature, we report here the magnetic structure of NdCrGe3 (TC ¼122 K) as determined by neutron powder diffraction.
2. Experimental methods The NdCrGe3 sample was synthesized by arc melting, starting from stoichiometric amounts of high-purity elements (99.9% or better). The resulting ingot was annealed at 800 1C for 20 days and then water quenched. More experimental details about the preparation of this sample can be found in Ref. [3]. Neutron powder diffraction measurements were carried out on the Echidna high-resolution powder diffractometer at the OPAL reactor in ˚ Sydney, Australia, with a neutron wavelength l of 2.4395(5) A. The patterns were refined using the FullProf/WinPlotr suite [6,7]. Some weak diffraction peaks corresponding to a l/2 contamination of 0.3% were observed in the neutron diffraction patterns and were included in the refinements.
0304-8853/$ - see front matter Crown Copyright & 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.08.028
136
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
3. Results 3.1. Paramagnetic state (T ¼150 K) The neutron diffraction pattern recorded in the paramagnetic state (T¼ 150 K) confirms the BaNiO3-type structure (P63/mmc) of NdCrGe3 (Fig. 3). The Nd atoms occupy the 2d site (1/3, 2/3, 3/4), the Cr atoms occupy the 2a site (0, 0, 0) and the Ge atoms occupy the 6h site (x, 2x, 1/4). A detailed description of this crystal structure can be found in Ref. [3]. The refined parameters are presented in Table 1. Small amounts of NdGe2 (ThSi2-type, I41/amd) ( o2 wt%) and unreacted Ge (diamond-type, Fd-3 m) ( o1 wt%) were detected in the sample. The ferromagnetic ordering of NdGe2 at very low temperature (TC ¼3.6 K) [8,9] was taken into account during the refinement of the NdCrGe3 magnetic structure.
3.2. Magnetic state (below TC ¼122 K) The neutron diffraction patterns recorded in the magnetic state show magnetic contributions only at nuclear peak positions, confirming the ferromagnetic order of this compound [3]. The absence of extra magnetic reflections down to 1.8 K also indicates
Fig. 1. Crystallographic structure of the hexagonal perovskite-type RTX3 compounds.
a collinear arrangement of the Cr and Nd sublattices over the entire magnetically ordered regime. In the magnetic state (i.e. below TC ¼122 K), the 101, 110, 211, 300 and 212 reflections clearly show increased intensity (Fig. 4) compared to the respective nuclear contributions, while the 100, 200, 112, 210 and 103 reflections have no significant magnetic contributions (an example is shown in Fig. 4 with the 103 reflection). Due to the (0, 0, 0) and (0, 0, 1/2) positions of the Cr atoms in the unit cell, ferromagnetic order of the Cr sublattice does not contribute to the magnetic intensity of those hkl peaks with l ¼2nþ1. Thus, the observation of a magnetic contribution to the 101 and 211 diffraction peaks allows us to conclude that magnetic ordering of the Nd sublattice is present at 50 K and lower temperatures, while the absence of magnetic contributions to these reflections at T¼100 K (Fig. 4) indicates magnetic ordering of the Cr sublattice only. Magnetic ordering of both the Cr and Nd sublattices below 50 K in NdCrGe3 is in apparent contradiction with the weak effective magnetic moment value of 1.8 mB/f.u. determined by macroscopic magnetic measurements [3], which is relatively close to that determined for the non-magnetic rare-earth compound LaCrGe3 (i.e. meff ¼1.4 mB/f.u. [3]), suggesting magnetic order of the Cr sublattice only. However, the saturated magnetization value of NdCrGe3 is three times higher than that of LaCrGe3 (2.64 mB/f.u. and 0.90 mB/f.u., respectively [3]) and supports the magnetic order of the Nd sublattice at low temperature.
3.2.1. Low temperature magnetic state (from T ¼50 K down to T¼1.8 K) The neutron diffraction patterns recorded between 50 K and 1.8 K (i.e. where both the Cr and Nd sublattices are magnetically ordered) can be well refined with either an axial (y ¼01) or a planar (y ¼901) magnetic order. Simulations performed using an (a,b)-planar orientation of both the Cr and Nd magnetic moments indicate strong magnetic contributions to the 110, 211 and 300 reflections, while for a c-axial orientation of the magnetic moments, a stronger magnetic contribution is expected for the 101 and 102 reflections. Thus, considering the ratio of the intensities of the 101 and 110 peaks, we suggest an axial orientation of both the Cr and Nd magnetic moments. This hypothesis is supported by the fact that planar magnetic order would yield a significant magnetic contribution to the 103 reflection whereas axial order produces a negligible contribution, as observed in the experimental patterns (Fig. 4). Moreover, refinements performed for both planar and axial orientations of the magnetic moments show significantly better magnetic
Fig. 2. Field-cooled (fc) and zero-field-cooled (zfc) dc magnetic susceptibility (inset, inverse susceptibility plot) and isothermal magnetization at various temperatures of powdered NdCrGe3. From Ref. [3].
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
137
Fig. 3. Observed and calculated neutron diffraction patterns of NdCrGe3 in the paramagnetic state (T¼ 150 K). Diffraction peaks distinguished by the symbol n correspond to a weak l/2 contamination.
Table 1 Results from the refinements of the neutron diffraction patterns of NdCrGe3 collected at different temperatures. 150 K
100 K
100 K
50 K
50 K
30 K
30 K
10 K
10 K
4.2 K
4.2 K
1.8 K
1.8 K
˚ a (A)
6.103(1)
6.098(1)
6.098(1)
6.095(1)
6.095(1)
6.094(1)
6.094(1)
6.094(1)
6.094(1)
6.095(1)
6.095(1)
6.094(1)
6.094(1)
˚ c (A) xGe y (1) mNd (mB) mCr (mB) mTot (mB) RBragg Rf Rmagn Rwp Rexp
5.678(1)
5.684(1)
5.684(1)
5.685(1)
5.685(1)
5.685(1)
5.685(1)
5.684(1)
5.684(1)
5.684(1)
5.684(1)
5.684(1)
5.684(1)
0.193(1) – – – – 7.25 10.6 – 7.07 4.61 2.36
0.193(1) 0 0.88(6) 1.15(5) 2.03(11) 7.39 10.8 17.8 7.07 4.67 2.29
0.193(1) 90 0.79(7) 1.40(7) 2.19(14) 7.50 11.0 19.5 7.14 4.67 2.34
0.193(1) 0 1.47(4) 1.43(4) 2.90(8) 6.18 9.56 13.0 6.84 4.64 2.17
0.193(1) 90 1.29(5) 1.60(6) 2.89(11) 7.05 10.3 21.8 7.28 4.64 2.46
0.193(1) 0 1.92(4) 1.49(5) 3.41(9) 6.02 9.90 8.98 7.13 4.64 2.36
0.193(1) 90 1.74(5) 1.65(7) 3.39(12) 7.28 10.8 21.4 7.83 4.64 2.85
0.193(1) 0 2.27(4) 1.50(6) 3.77(10) 5.70 8.48 10.7 7.01 4.66 2.27
0.193(1) 90 2.05(5) 1.63(7) 3.68(12) 7.15 9.71 23.9 8.04 4.66 2.98
0.194(1) 0 2.25(4) 1.51(5) 3.76(9) 6.74 9.59 9.69 6.31 3.18 3.94
0.194(1) 90 2.04(4) 1.78(6) 3.82(10) 7.83 10.7 22.8 7.23 3.18 5.18
0.194(1) 0 2.25(4) 1.56(5) 3.81(9) 6.09 8.17 8.07 6.17 3.24 3.62
0.193(1) 90 2.05(4) 1.80(6) 3.85(10) 7.20 9.21 20.8 7.14 3.24 4.86
w2
Fig. 4. Thermal evolution of the 101, 110, 211, 300, 212 and 103 diffraction peaks.
138
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
R-factors and w2 fit factors for the axial orientation compared to the planar orientation (Table 1). For example, the refinement of the neutron pattern recorded at 1.8 K yields Rmagn ¼8.07 and w2 ¼3.62 for an axial orientation, and Rmagn ¼20.8 and w2 ¼4.86 for a planar orientation. Thus, our results indicate an axial orientation of both the Cr and Nd magnetic moments, which is consistent with the previously reported work on the Cr sublattice in LaCrGe3 [5] and the magnetic space group theory. Indeed, the only magnetic space group within {P63/mmc} that allows ferromagnetic order at both the 2d (Nd) and 2a (Cr) sites is P63/mm’c’ with the magnetic moments oriented along the c-axis. At 1.8 K, the best refinement (Fig. 5) is obtained with an axial orientation and refined values of the magnetic moments of 2.25(4) mB and 1.56(5) mB for Nd and Cr, respectively, leading to a total magnetic moment of 3.81(9) mB (Table 1). This value is higher than the saturated magnetic moment determined by macroscopic magnetic measurements at 2 K (i.e. 2.64 mB/f.u.) [3]. The difference between these two values can be attributed to the measurement of the magnetic properties on powdered sample, leading to a lower magnetic moment value than that expected for a single-crystal measurement with the magnetic field oriented along the c-axis. The magnetic structure of NdCrGe3, refined at 1.8 K, is shown in Fig. 6.
Fig. 6. The axial ferromagnetic structure of NdCrGe3 at 1.8 K.
The strong similarity of the neutron patterns (Fig. 5) and the thermal evolution of both the Nd and Cr magnetic moments refined from 1.8 K up to 50 K (Table 1) suggest no spin reorientation at low temperature for this compound. However, a weak spin reorientation of the Cr sublattice, such as observed for LaCrGe3 [5] cannot be excluded since the magnetic contribution to the diffraction peaks would be very weak for a canting angle y away from the c-axis of o301. 3.2.2. Intermediate temperature magnetic state (T¼ 100 K) At 100 K, the absence of magnetic contributions to the hkl reflections with l ¼2n þ1 (examples shown in Fig. 4 with the 101 and 211 diffraction peaks) suggests magnetic order of the Cr sublattice only. However, the neutron diffraction pattern cannot be perfectly refined taking into account magnetic moments only on the Cr sublattice; a good refinement can be obtained with magnetic moments on both the Cr and Nd atoms (Table 1). The refinements performed using both planar and axial orientations of the magnetic moments lead to slightly better magnetic R-factor and w2 fit factor for an axial orientation (Rmagn ¼17.8 and w2 ¼2.29) compared to a planar orientation (Rmagn ¼19.5 and w2 ¼2.34). The magnetic behaviour of the RCrGe3 system suggests that a spin reorientation is more likely to occur at very low temperature, allowing one to deduce an axial orientation of the magnetic moments at 100 K, as observed at lower temperature. At 100 K, the best refinement (with an angle y of 01, Fig. 5) leads to the refined values of the magnetic moments of 1.15(5) mB for the Cr atoms and 0.88(6) mB for the Nd atoms, yielding a total magnetic moment of 2.03(11) mB (Table 1).
4. Discussion
Fig. 5. Observed and calculated neutron diffraction patterns of NdCrGe3 at 100 K, 50 K and 1.8 K. Diffraction peaks distinguished by the symbol n correspond to a weak l/2 contamination.
Neutron powder diffraction measurements confirm the ferromagnetic order of the Cr and Nd sublattices in NdCrGe3, as determined previously by macroscopic magnetic measurements [3]. The ferromagnetic coupling of the Cr and Nd magnetic moments is in agreement with the usual sign of the R–T magnetic coupling generally found in intermetallic compounds involving transition metals and light rare-earths [10–12]. The magnetic structure of NdCrGe3 is characterized by a collinear arrangement of both the Cr and Nd sublattices along the c-axis, similar to that found in isotypic LaCrGe3 [5]. However, a spin reorientation of the Cr sublattice occurs at very low temperature (TE3 K) in LaCrGe3 whereas NdCrGe3 shows an axial orientation of the magnetic moments over the entire magnetically ordered temperature range studied here. The values of the refined Cr and Nd magnetic moments at 1.8 K are 1.56(5) mB and 2.25(4) mB, respectively. The value of the Cr magnetic moment is higher in NdCrGe3 than in LaCrGe3 at the
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
Fig. 7. Thermal variation of the refined Cr and Nd magnetic moments of NdCrGe3 (dashed curves are just a guide for eyes).
same temperature (i.e. 1.31(4) mB at 1.7 K). This difference of E0.25 mB is unlikely to be the result of differences in the Cr–Cr bond lengths and more likely reflects the magnetic ordering of the Nd sublattice inducing an increase in the Cr magnetic moment. The magnetic ordering of the Nd sublattice and significant Nd–Cr magnetic interactions can also explain the absence of a spin reorientation of the Cr sublattice at very low temperature. The Nd magnetic moment refined at 1.8 K is smaller than that expected for the Nd3 þ free ion (3.27 mB), most likely indicating crystal electric field effects. At higher temperatures, the refinements of the neutron diffraction patterns show different thermal evolutions for the Cr and the Nd sublattices in NdCrGe3. Indeed, the thermal variation of the refined Cr and Nd magnetic moments, shown in Fig. 7, suggests a magnetic ordering of the Cr sublattice below TC, while the Nd sublattice seems to be magnetically ordered below a temperature of around 70 K. This latter temperature is deduced from the extrapolation of the thermal variation of the Nd magnetic moment value from 1.8 K up to 50 K, and coincides with the temperature of the divergence of the zero-field-cooled (ZFC) and field-cooled (FC) susceptibility curves previously published [3] and shown in Fig. 2. Above the Nd magnetic ordering temperature, the weak Nd magnetic moment of 0.88(6) mB refined at 100 K can be explained by non-negligible Nd–Cr magnetic interactions, inducing a polarization of the Nd sublattice by the magnetically ordered Cr sublattice, as already observed in the ferrimagnetic R6Mn23 compounds [13,14]. This conclusion is also supported by the variation of the Curie temperature for RCrGe3 involving a 4 f element (R¼Ce, Pr, Nd, Sm), which tends to be maximum for the R atom having the highest de Gennes factor (gJ 1)2J(Jþ1) [15], showing that the R-Cr magnetic interactions are important in these compounds. Previous macroscopic magnetic measurements performed on powdered NdCrGe3 [3] have shown complex magnetic behaviour at low temperature, in particular a divergence of the susceptibility between the ZFC and FC measurements below TE70 K (i.e. the magnetic ordering temperature of the Nd sublattice), and a metamagnetic transition with strong hysteresis at 2 K (Fig. 2), suggesting a possible spin reorientation at low temperature. However, the collinear ferromagnetic structure from TC down to 1.8 K, determined by neutron powder diffraction, rules out a spin reorientation in NdCrGe3. Thus, the divergence between the FC and ZFC susceptibility curves indicates strong magnetocrystalline anisotropy, which may be a consequence of domain walls dynamics. Indeed, in ZFC mode and small applied magnetic fields, domain wall movement can be blocked, leading to weak magnetic susceptibility at low temperature. On the contrary, in FC mode the
139
magnetic field applied in the paramagnetic state down to the lower temperature orients the magnetic domains in the same direction, leading to higher magnetic susceptibility compared to that measured in ZFC mode. At higher temperatures, the thermal activation of the domain wall motion explains the reduction of the susceptibility divergence between the ZFC and the FC curves observed at higher temperature in the macroscopic magnetic measurements (Fig. 2). The metamagnetic transition with a strong hysteresis observed in the isothermal magnetization curve at 2 K (Fig. 2) does not contradict the ferromagnetic structure determined by neutron powder diffraction and can also be explained by domain wall dynamics. Indeed, the measurement performed in ZFC mode leads to a domain wall blocking and therefore a weak magnetic susceptibility at low applied magnetic field. For applied magnetic fields higher than the threshold magnetic field (m0H4Ht), all magnetic domains are aligned in the same direction, leading to the metamagnetic transition. The magnetic domains remain aligned when the applied magnetic field decreases, leading to magnetic hysteresis and the remanent magnetization. The thermal activation of the domain wall motion also explains the reduction of these magnetic phenomena observed on the macroscopic magnetic curves at higher temperature (Fig. 2). The divergence of the susceptibility between the ZFC and FC measurements could also result from the coexistence of both ferro- and antiferromagnetic interactions (with a predominance of ferromagnetic interactions deduced from the paramagnetic Curie temperature yp of 134 K [3]) or a spin-glass behaviour [16–19]. However, saturation of the magnetization for relatively low applied magnetic field (m0Ho5T) (Fig. 2) does not support the existence of antiferromagnetic interactions or magnetic moment disorder in NdCrGe3 at low temperatures.
5. Summary Neutron powder diffraction experiments performed from the paramagnetic state down to 1.8 K confirm the BaNiO3-type structure and the ferromagnetic order of the Nd and Cr sublattices in NdCrGe3. In this compound, both Nd and Cr magnetic moments are oriented along the c-axis over the entire magnetically ordered temperature range. The thermal evolution of the magnetic moments suggests a magnetic ordering temperature around 70 K for the Nd sublattice, while the Cr sublattice is magnetically ordered up to the Curie temperature of 122 K. The weak magnetic moment of 0.88(6) mB refined on the Nd atoms at 100 K can be explained by non-negligible Nd–Cr magnetic interactions, which is supported by the variation of the Curie temperature measured for RCrGe3 compounds. This neutron powder neutron diffraction study shows that the complex macroscopic magnetic results previously published for NdCrGe3 are, in fact, the consequence of strong magnetocrystalline anisotropy effects. Similar conclusions can be extended to the other RCrGe3 compounds involving a 4 f element (R¼ Ce, Pr, Sm).
Acknowledgements Parts of this work were carried out while JMC was a Faculty member of the University of Manitoba, supported by the Canada Research Chairs programme. Financial support for some stages of this work was provided by the Natural Sciences and Engineering Research Council of Canada. The authors would like to thank the reviewer for his comments and suggestions which improved the quality of the paper.
140
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
References [1] P. Manfrinetti, S.K. Dhar, R. Kulkarni, A.V. Morozkin, Solid State Communications 135 (2005) 444–448. [2] H. Bie, A. Mar, Journal of Materials Chemistry 19 (2009) 6225–6230. [3] H. Bie, O.Ya. Zelinska, A.V. Tkachuk, A. Mar, Chemistry of Materials 19 (2007) 4613–4620. [4] P. Villars, K. Cenzual, Pearson’s Crystal Data: Crystal Structure Database for Inorganic compounds, ASM International, Materials Park, Ohio, USA, 2007/8, Release. [5] J.M. Cadogan, P. Lemoine, B.R. Slater, A. Mar, M. Avdeev, Solid State Phenomena, 194 (2013) 71-74. [6] J. Rodriguez-Carvajal, Physica B: Condensed Matter 192 (1993) 55–69. [7] T. Roisnel, J. Rodriguez-Carvajal, Materials Science Forum 378–381 (2001) 118–123. [8] B.T. Matthias, E. Corenzwit, W.H. Zachariasen, Physical Review 112 (1958) 89. [9] K. Sekizawa, Journal of the Physical Society of Japan 21 (1966) 1137–1142. [10] I.A. Campbell, Journal of Physics F: Metal Physics 2 (1972) L47–50.
¨ [11] M.S.S. Brooks, T. Gasche, S. Auluck, L. Nordstrom, L. Severin, J. Trygg, B. Johansson, Journal of Applied Physics 70 (1991) 5972–5976. [12] J.J.M. Franse, R.J. Radwanski, Magnetic porperties of binary rare-earth 3d-transition-metal intermetallic compounds, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, 1993, pp. 307–501, chapter 5. [13] B. Ouladdiaf, J. De´portes, J. Rodriguez-Carvajal, Physica B: Condensed Matter 213–214 (1995) 330–332. [14] P. Lemoine, A. Vernie re, T. Mazet, B. Malaman, Journal of Magnetism and Magnetic Materials 323 (2011) 2690–2695. [15] P.G. de Gennes, Journal of Physics Radium 23 (1962) 510. [16] E.M. Levin, V.K. Pecharsky, K.A. Gschneidner Jr., Journal of Applied Physics 90 (2001) 6255–6262. [17] H. Ahmadvand, H. Salamati, P. Kameli, Journal of Applied Physics 107 (2010) 083913. [18] A. Haldar, K.G. Suresh, A.K. Nigam, Europhysics Letters 91 (2010) 67006. [19] N.K. Singh, D. Paudyal, Ya. Mudryk, V.K. Pecharsky, K.A. Gschneidner Jr., Physical Review B 81 (2010) 184414.
Contents lists available at SciVerse ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Neutron diffraction study of NdCrGe3 P. Lemoine a,n, J.M. Cadogan b, B.R. Slater c, A. Mar c, M. Avdeev d a
Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB, Canada, R3T 2N2 School of Physical, Environmental and Mathematical Sciences, The University of New South Wales, Canberra ACT BC2610, Australia Department of Chemistry, University of Alberta, Edmonton, AB, Canada, T6G 2G2 d Bragg Institute, ANSTO, PMB 1, Menai, NSW 2234, Australia b c
a r t i c l e i n f o
abstract
Article history: Received 18 July 2012 Received in revised form 15 August 2012 Available online 29 August 2012
The hexagonal perovskite (BaNiO3-type) structure of NdCrGe3 and its ferromagnetic order at TC ¼ 122 K have been confirmed by neutron powder diffraction measurements. The magnetic structure is characterized by an axial ferromagnetic arrangement of both the Cr and Nd sublattices below TC. The relatively high Curie temperature of this compound is mainly driven by the magnetic ordering of the Cr sublattice with Nd–Cr magnetic interactions also playing a role. The magnetic ordering of the Nd sublattice, deduced from the thermal variation of the magnetic moments, occurs at around TE 70 K. The absence of a spin reorientation of the Nd and Cr magnetic order allows us to conclude that the complex magnetic behaviour previously observed at low temperatures in macroscopic magnetic measurements is a consequence of strong magnetocrystalline anisotropy effects. Crown Copyright & 2012 Published by Elsevier B.V. All rights reserved.
Keywords: Rare-earth intermetallic compound Hexagonal perovskite-type structure Neutron powder diffraction Magnetic structure
1. Introduction Among the RTX3 compounds (R ¼rare earth; T¼transition metal; X ¼p-block element), the ternary germanides RTiGe3 (R¼La–Pr) [1], RVGe3 (R¼ La–Nd) [2] and RCrGe3 (R¼La–Nd, Sm) [3] represent unusual instances of intermetallic phases adopting the hexagonal perovskite structure (BaNiO3-type, P63/mmc). This structure consists of one-dimensional chains of face-sharing TX6 octahedra along the c axis (Fig. 1) linked by triangular X3 clusters and is normally found for chalcogenides and halides [4]. Due to their quasi-one-dimensional structure, the BaNiO3-type intermetallic compounds show interesting magnetic properties which are dependent on the transition metal. For example, CeTiGe3 orders ferromagnetically at low temperature (TC ¼14 K) [1], while the RVGe3 (R¼Ce–Nd) compounds have low temperature antiferromagnetic ordering with TN ranging from 4 K for CeVGe3 to 15 K for PrVGe3 [2]. The magnetic properties of the RCrGe3 compounds are also varied due to the magnetic ordering of both the rare-earth and transition metal sublattices, leading to ferromagnetic order at relatively high temperatures (TC ranges from 66 K for CeCrGe3 to 155 K for SmCrGe3) and complex magnetic behaviours at low temperature [3]. For example, macroscopic magnetic measurements performed on powdered NdCrGe3 show a divergence of the susceptibility between the ZFC and FC measurements below TE70 K and a metamagnetic transition
n
Corresponding author. E-mail addresses: [email protected] (P. Lemoine), [email protected] (J.M. Cadogan).
with strong hysteresis at 2 K (Fig. 2), suggesting a possible spin reorientation at low temperature. The ferromagnetic order of the Cr sublattice was recently confirmed by neutron powder diffraction on LaCrGe3 [5]. This compound has a magnetic structure that is characterized by a collinear arrangement of the Cr magnetic moments along the c-axis from TC down to 3 K and a spin reorientation at very low temperature with a canting angle, away from the c-axis, y of 32(6)1 at 1.7 K. In order to study the influence of the magnetic ordering of both the rare-earth and chromium sublattices on the complex magnetic behaviour observed at low temperature, we report here the magnetic structure of NdCrGe3 (TC ¼122 K) as determined by neutron powder diffraction.
2. Experimental methods The NdCrGe3 sample was synthesized by arc melting, starting from stoichiometric amounts of high-purity elements (99.9% or better). The resulting ingot was annealed at 800 1C for 20 days and then water quenched. More experimental details about the preparation of this sample can be found in Ref. [3]. Neutron powder diffraction measurements were carried out on the Echidna high-resolution powder diffractometer at the OPAL reactor in ˚ Sydney, Australia, with a neutron wavelength l of 2.4395(5) A. The patterns were refined using the FullProf/WinPlotr suite [6,7]. Some weak diffraction peaks corresponding to a l/2 contamination of 0.3% were observed in the neutron diffraction patterns and were included in the refinements.
0304-8853/$ - see front matter Crown Copyright & 2012 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jmmm.2012.08.028
136
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
3. Results 3.1. Paramagnetic state (T ¼150 K) The neutron diffraction pattern recorded in the paramagnetic state (T¼ 150 K) confirms the BaNiO3-type structure (P63/mmc) of NdCrGe3 (Fig. 3). The Nd atoms occupy the 2d site (1/3, 2/3, 3/4), the Cr atoms occupy the 2a site (0, 0, 0) and the Ge atoms occupy the 6h site (x, 2x, 1/4). A detailed description of this crystal structure can be found in Ref. [3]. The refined parameters are presented in Table 1. Small amounts of NdGe2 (ThSi2-type, I41/amd) ( o2 wt%) and unreacted Ge (diamond-type, Fd-3 m) ( o1 wt%) were detected in the sample. The ferromagnetic ordering of NdGe2 at very low temperature (TC ¼3.6 K) [8,9] was taken into account during the refinement of the NdCrGe3 magnetic structure.
3.2. Magnetic state (below TC ¼122 K) The neutron diffraction patterns recorded in the magnetic state show magnetic contributions only at nuclear peak positions, confirming the ferromagnetic order of this compound [3]. The absence of extra magnetic reflections down to 1.8 K also indicates
Fig. 1. Crystallographic structure of the hexagonal perovskite-type RTX3 compounds.
a collinear arrangement of the Cr and Nd sublattices over the entire magnetically ordered regime. In the magnetic state (i.e. below TC ¼122 K), the 101, 110, 211, 300 and 212 reflections clearly show increased intensity (Fig. 4) compared to the respective nuclear contributions, while the 100, 200, 112, 210 and 103 reflections have no significant magnetic contributions (an example is shown in Fig. 4 with the 103 reflection). Due to the (0, 0, 0) and (0, 0, 1/2) positions of the Cr atoms in the unit cell, ferromagnetic order of the Cr sublattice does not contribute to the magnetic intensity of those hkl peaks with l ¼2nþ1. Thus, the observation of a magnetic contribution to the 101 and 211 diffraction peaks allows us to conclude that magnetic ordering of the Nd sublattice is present at 50 K and lower temperatures, while the absence of magnetic contributions to these reflections at T¼100 K (Fig. 4) indicates magnetic ordering of the Cr sublattice only. Magnetic ordering of both the Cr and Nd sublattices below 50 K in NdCrGe3 is in apparent contradiction with the weak effective magnetic moment value of 1.8 mB/f.u. determined by macroscopic magnetic measurements [3], which is relatively close to that determined for the non-magnetic rare-earth compound LaCrGe3 (i.e. meff ¼1.4 mB/f.u. [3]), suggesting magnetic order of the Cr sublattice only. However, the saturated magnetization value of NdCrGe3 is three times higher than that of LaCrGe3 (2.64 mB/f.u. and 0.90 mB/f.u., respectively [3]) and supports the magnetic order of the Nd sublattice at low temperature.
3.2.1. Low temperature magnetic state (from T ¼50 K down to T¼1.8 K) The neutron diffraction patterns recorded between 50 K and 1.8 K (i.e. where both the Cr and Nd sublattices are magnetically ordered) can be well refined with either an axial (y ¼01) or a planar (y ¼901) magnetic order. Simulations performed using an (a,b)-planar orientation of both the Cr and Nd magnetic moments indicate strong magnetic contributions to the 110, 211 and 300 reflections, while for a c-axial orientation of the magnetic moments, a stronger magnetic contribution is expected for the 101 and 102 reflections. Thus, considering the ratio of the intensities of the 101 and 110 peaks, we suggest an axial orientation of both the Cr and Nd magnetic moments. This hypothesis is supported by the fact that planar magnetic order would yield a significant magnetic contribution to the 103 reflection whereas axial order produces a negligible contribution, as observed in the experimental patterns (Fig. 4). Moreover, refinements performed for both planar and axial orientations of the magnetic moments show significantly better magnetic
Fig. 2. Field-cooled (fc) and zero-field-cooled (zfc) dc magnetic susceptibility (inset, inverse susceptibility plot) and isothermal magnetization at various temperatures of powdered NdCrGe3. From Ref. [3].
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
137
Fig. 3. Observed and calculated neutron diffraction patterns of NdCrGe3 in the paramagnetic state (T¼ 150 K). Diffraction peaks distinguished by the symbol n correspond to a weak l/2 contamination.
Table 1 Results from the refinements of the neutron diffraction patterns of NdCrGe3 collected at different temperatures. 150 K
100 K
100 K
50 K
50 K
30 K
30 K
10 K
10 K
4.2 K
4.2 K
1.8 K
1.8 K
˚ a (A)
6.103(1)
6.098(1)
6.098(1)
6.095(1)
6.095(1)
6.094(1)
6.094(1)
6.094(1)
6.094(1)
6.095(1)
6.095(1)
6.094(1)
6.094(1)
˚ c (A) xGe y (1) mNd (mB) mCr (mB) mTot (mB) RBragg Rf Rmagn Rwp Rexp
5.678(1)
5.684(1)
5.684(1)
5.685(1)
5.685(1)
5.685(1)
5.685(1)
5.684(1)
5.684(1)
5.684(1)
5.684(1)
5.684(1)
5.684(1)
0.193(1) – – – – 7.25 10.6 – 7.07 4.61 2.36
0.193(1) 0 0.88(6) 1.15(5) 2.03(11) 7.39 10.8 17.8 7.07 4.67 2.29
0.193(1) 90 0.79(7) 1.40(7) 2.19(14) 7.50 11.0 19.5 7.14 4.67 2.34
0.193(1) 0 1.47(4) 1.43(4) 2.90(8) 6.18 9.56 13.0 6.84 4.64 2.17
0.193(1) 90 1.29(5) 1.60(6) 2.89(11) 7.05 10.3 21.8 7.28 4.64 2.46
0.193(1) 0 1.92(4) 1.49(5) 3.41(9) 6.02 9.90 8.98 7.13 4.64 2.36
0.193(1) 90 1.74(5) 1.65(7) 3.39(12) 7.28 10.8 21.4 7.83 4.64 2.85
0.193(1) 0 2.27(4) 1.50(6) 3.77(10) 5.70 8.48 10.7 7.01 4.66 2.27
0.193(1) 90 2.05(5) 1.63(7) 3.68(12) 7.15 9.71 23.9 8.04 4.66 2.98
0.194(1) 0 2.25(4) 1.51(5) 3.76(9) 6.74 9.59 9.69 6.31 3.18 3.94
0.194(1) 90 2.04(4) 1.78(6) 3.82(10) 7.83 10.7 22.8 7.23 3.18 5.18
0.194(1) 0 2.25(4) 1.56(5) 3.81(9) 6.09 8.17 8.07 6.17 3.24 3.62
0.193(1) 90 2.05(4) 1.80(6) 3.85(10) 7.20 9.21 20.8 7.14 3.24 4.86
w2
Fig. 4. Thermal evolution of the 101, 110, 211, 300, 212 and 103 diffraction peaks.
138
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
R-factors and w2 fit factors for the axial orientation compared to the planar orientation (Table 1). For example, the refinement of the neutron pattern recorded at 1.8 K yields Rmagn ¼8.07 and w2 ¼3.62 for an axial orientation, and Rmagn ¼20.8 and w2 ¼4.86 for a planar orientation. Thus, our results indicate an axial orientation of both the Cr and Nd magnetic moments, which is consistent with the previously reported work on the Cr sublattice in LaCrGe3 [5] and the magnetic space group theory. Indeed, the only magnetic space group within {P63/mmc} that allows ferromagnetic order at both the 2d (Nd) and 2a (Cr) sites is P63/mm’c’ with the magnetic moments oriented along the c-axis. At 1.8 K, the best refinement (Fig. 5) is obtained with an axial orientation and refined values of the magnetic moments of 2.25(4) mB and 1.56(5) mB for Nd and Cr, respectively, leading to a total magnetic moment of 3.81(9) mB (Table 1). This value is higher than the saturated magnetic moment determined by macroscopic magnetic measurements at 2 K (i.e. 2.64 mB/f.u.) [3]. The difference between these two values can be attributed to the measurement of the magnetic properties on powdered sample, leading to a lower magnetic moment value than that expected for a single-crystal measurement with the magnetic field oriented along the c-axis. The magnetic structure of NdCrGe3, refined at 1.8 K, is shown in Fig. 6.
Fig. 6. The axial ferromagnetic structure of NdCrGe3 at 1.8 K.
The strong similarity of the neutron patterns (Fig. 5) and the thermal evolution of both the Nd and Cr magnetic moments refined from 1.8 K up to 50 K (Table 1) suggest no spin reorientation at low temperature for this compound. However, a weak spin reorientation of the Cr sublattice, such as observed for LaCrGe3 [5] cannot be excluded since the magnetic contribution to the diffraction peaks would be very weak for a canting angle y away from the c-axis of o301. 3.2.2. Intermediate temperature magnetic state (T¼ 100 K) At 100 K, the absence of magnetic contributions to the hkl reflections with l ¼2n þ1 (examples shown in Fig. 4 with the 101 and 211 diffraction peaks) suggests magnetic order of the Cr sublattice only. However, the neutron diffraction pattern cannot be perfectly refined taking into account magnetic moments only on the Cr sublattice; a good refinement can be obtained with magnetic moments on both the Cr and Nd atoms (Table 1). The refinements performed using both planar and axial orientations of the magnetic moments lead to slightly better magnetic R-factor and w2 fit factor for an axial orientation (Rmagn ¼17.8 and w2 ¼2.29) compared to a planar orientation (Rmagn ¼19.5 and w2 ¼2.34). The magnetic behaviour of the RCrGe3 system suggests that a spin reorientation is more likely to occur at very low temperature, allowing one to deduce an axial orientation of the magnetic moments at 100 K, as observed at lower temperature. At 100 K, the best refinement (with an angle y of 01, Fig. 5) leads to the refined values of the magnetic moments of 1.15(5) mB for the Cr atoms and 0.88(6) mB for the Nd atoms, yielding a total magnetic moment of 2.03(11) mB (Table 1).
4. Discussion
Fig. 5. Observed and calculated neutron diffraction patterns of NdCrGe3 at 100 K, 50 K and 1.8 K. Diffraction peaks distinguished by the symbol n correspond to a weak l/2 contamination.
Neutron powder diffraction measurements confirm the ferromagnetic order of the Cr and Nd sublattices in NdCrGe3, as determined previously by macroscopic magnetic measurements [3]. The ferromagnetic coupling of the Cr and Nd magnetic moments is in agreement with the usual sign of the R–T magnetic coupling generally found in intermetallic compounds involving transition metals and light rare-earths [10–12]. The magnetic structure of NdCrGe3 is characterized by a collinear arrangement of both the Cr and Nd sublattices along the c-axis, similar to that found in isotypic LaCrGe3 [5]. However, a spin reorientation of the Cr sublattice occurs at very low temperature (TE3 K) in LaCrGe3 whereas NdCrGe3 shows an axial orientation of the magnetic moments over the entire magnetically ordered temperature range studied here. The values of the refined Cr and Nd magnetic moments at 1.8 K are 1.56(5) mB and 2.25(4) mB, respectively. The value of the Cr magnetic moment is higher in NdCrGe3 than in LaCrGe3 at the
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
Fig. 7. Thermal variation of the refined Cr and Nd magnetic moments of NdCrGe3 (dashed curves are just a guide for eyes).
same temperature (i.e. 1.31(4) mB at 1.7 K). This difference of E0.25 mB is unlikely to be the result of differences in the Cr–Cr bond lengths and more likely reflects the magnetic ordering of the Nd sublattice inducing an increase in the Cr magnetic moment. The magnetic ordering of the Nd sublattice and significant Nd–Cr magnetic interactions can also explain the absence of a spin reorientation of the Cr sublattice at very low temperature. The Nd magnetic moment refined at 1.8 K is smaller than that expected for the Nd3 þ free ion (3.27 mB), most likely indicating crystal electric field effects. At higher temperatures, the refinements of the neutron diffraction patterns show different thermal evolutions for the Cr and the Nd sublattices in NdCrGe3. Indeed, the thermal variation of the refined Cr and Nd magnetic moments, shown in Fig. 7, suggests a magnetic ordering of the Cr sublattice below TC, while the Nd sublattice seems to be magnetically ordered below a temperature of around 70 K. This latter temperature is deduced from the extrapolation of the thermal variation of the Nd magnetic moment value from 1.8 K up to 50 K, and coincides with the temperature of the divergence of the zero-field-cooled (ZFC) and field-cooled (FC) susceptibility curves previously published [3] and shown in Fig. 2. Above the Nd magnetic ordering temperature, the weak Nd magnetic moment of 0.88(6) mB refined at 100 K can be explained by non-negligible Nd–Cr magnetic interactions, inducing a polarization of the Nd sublattice by the magnetically ordered Cr sublattice, as already observed in the ferrimagnetic R6Mn23 compounds [13,14]. This conclusion is also supported by the variation of the Curie temperature for RCrGe3 involving a 4 f element (R¼Ce, Pr, Nd, Sm), which tends to be maximum for the R atom having the highest de Gennes factor (gJ 1)2J(Jþ1) [15], showing that the R-Cr magnetic interactions are important in these compounds. Previous macroscopic magnetic measurements performed on powdered NdCrGe3 [3] have shown complex magnetic behaviour at low temperature, in particular a divergence of the susceptibility between the ZFC and FC measurements below TE70 K (i.e. the magnetic ordering temperature of the Nd sublattice), and a metamagnetic transition with strong hysteresis at 2 K (Fig. 2), suggesting a possible spin reorientation at low temperature. However, the collinear ferromagnetic structure from TC down to 1.8 K, determined by neutron powder diffraction, rules out a spin reorientation in NdCrGe3. Thus, the divergence between the FC and ZFC susceptibility curves indicates strong magnetocrystalline anisotropy, which may be a consequence of domain walls dynamics. Indeed, in ZFC mode and small applied magnetic fields, domain wall movement can be blocked, leading to weak magnetic susceptibility at low temperature. On the contrary, in FC mode the
139
magnetic field applied in the paramagnetic state down to the lower temperature orients the magnetic domains in the same direction, leading to higher magnetic susceptibility compared to that measured in ZFC mode. At higher temperatures, the thermal activation of the domain wall motion explains the reduction of the susceptibility divergence between the ZFC and the FC curves observed at higher temperature in the macroscopic magnetic measurements (Fig. 2). The metamagnetic transition with a strong hysteresis observed in the isothermal magnetization curve at 2 K (Fig. 2) does not contradict the ferromagnetic structure determined by neutron powder diffraction and can also be explained by domain wall dynamics. Indeed, the measurement performed in ZFC mode leads to a domain wall blocking and therefore a weak magnetic susceptibility at low applied magnetic field. For applied magnetic fields higher than the threshold magnetic field (m0H4Ht), all magnetic domains are aligned in the same direction, leading to the metamagnetic transition. The magnetic domains remain aligned when the applied magnetic field decreases, leading to magnetic hysteresis and the remanent magnetization. The thermal activation of the domain wall motion also explains the reduction of these magnetic phenomena observed on the macroscopic magnetic curves at higher temperature (Fig. 2). The divergence of the susceptibility between the ZFC and FC measurements could also result from the coexistence of both ferro- and antiferromagnetic interactions (with a predominance of ferromagnetic interactions deduced from the paramagnetic Curie temperature yp of 134 K [3]) or a spin-glass behaviour [16–19]. However, saturation of the magnetization for relatively low applied magnetic field (m0Ho5T) (Fig. 2) does not support the existence of antiferromagnetic interactions or magnetic moment disorder in NdCrGe3 at low temperatures.
5. Summary Neutron powder diffraction experiments performed from the paramagnetic state down to 1.8 K confirm the BaNiO3-type structure and the ferromagnetic order of the Nd and Cr sublattices in NdCrGe3. In this compound, both Nd and Cr magnetic moments are oriented along the c-axis over the entire magnetically ordered temperature range. The thermal evolution of the magnetic moments suggests a magnetic ordering temperature around 70 K for the Nd sublattice, while the Cr sublattice is magnetically ordered up to the Curie temperature of 122 K. The weak magnetic moment of 0.88(6) mB refined on the Nd atoms at 100 K can be explained by non-negligible Nd–Cr magnetic interactions, which is supported by the variation of the Curie temperature measured for RCrGe3 compounds. This neutron powder neutron diffraction study shows that the complex macroscopic magnetic results previously published for NdCrGe3 are, in fact, the consequence of strong magnetocrystalline anisotropy effects. Similar conclusions can be extended to the other RCrGe3 compounds involving a 4 f element (R¼ Ce, Pr, Sm).
Acknowledgements Parts of this work were carried out while JMC was a Faculty member of the University of Manitoba, supported by the Canada Research Chairs programme. Financial support for some stages of this work was provided by the Natural Sciences and Engineering Research Council of Canada. The authors would like to thank the reviewer for his comments and suggestions which improved the quality of the paper.
140
P. Lemoine et al. / Journal of Magnetism and Magnetic Materials 325 (2013) 135–140
References [1] P. Manfrinetti, S.K. Dhar, R. Kulkarni, A.V. Morozkin, Solid State Communications 135 (2005) 444–448. [2] H. Bie, A. Mar, Journal of Materials Chemistry 19 (2009) 6225–6230. [3] H. Bie, O.Ya. Zelinska, A.V. Tkachuk, A. Mar, Chemistry of Materials 19 (2007) 4613–4620. [4] P. Villars, K. Cenzual, Pearson’s Crystal Data: Crystal Structure Database for Inorganic compounds, ASM International, Materials Park, Ohio, USA, 2007/8, Release. [5] J.M. Cadogan, P. Lemoine, B.R. Slater, A. Mar, M. Avdeev, Solid State Phenomena, 194 (2013) 71-74. [6] J. Rodriguez-Carvajal, Physica B: Condensed Matter 192 (1993) 55–69. [7] T. Roisnel, J. Rodriguez-Carvajal, Materials Science Forum 378–381 (2001) 118–123. [8] B.T. Matthias, E. Corenzwit, W.H. Zachariasen, Physical Review 112 (1958) 89. [9] K. Sekizawa, Journal of the Physical Society of Japan 21 (1966) 1137–1142. [10] I.A. Campbell, Journal of Physics F: Metal Physics 2 (1972) L47–50.
¨ [11] M.S.S. Brooks, T. Gasche, S. Auluck, L. Nordstrom, L. Severin, J. Trygg, B. Johansson, Journal of Applied Physics 70 (1991) 5972–5976. [12] J.J.M. Franse, R.J. Radwanski, Magnetic porperties of binary rare-earth 3d-transition-metal intermetallic compounds, in: K.H.J. Buschow (Ed.), Handbook of Magnetic Materials, 1993, pp. 307–501, chapter 5. [13] B. Ouladdiaf, J. De´portes, J. Rodriguez-Carvajal, Physica B: Condensed Matter 213–214 (1995) 330–332. [14] P. Lemoine, A. Vernie re, T. Mazet, B. Malaman, Journal of Magnetism and Magnetic Materials 323 (2011) 2690–2695. [15] P.G. de Gennes, Journal of Physics Radium 23 (1962) 510. [16] E.M. Levin, V.K. Pecharsky, K.A. Gschneidner Jr., Journal of Applied Physics 90 (2001) 6255–6262. [17] H. Ahmadvand, H. Salamati, P. Kameli, Journal of Applied Physics 107 (2010) 083913. [18] A. Haldar, K.G. Suresh, A.K. Nigam, Europhysics Letters 91 (2010) 67006. [19] N.K. Singh, D. Paudyal, Ya. Mudryk, V.K. Pecharsky, K.A. Gschneidner Jr., Physical Review B 81 (2010) 184414.