JOURNAL OF APPLIED PHYSICS 109, 07E152 (2011)
Magnetic properties and exchange interactions in TbNi52xMx (M5Co and Fe) compounds: Ab initio calculations A. V. Lukoyanov,1 Arabinda Haldar,2 A. Das,3 Ajaya K. Nayak,2 K. G. Suresh,2,a) and A. K. Nigam4 1
Institute of Metal Physics, Russian Academy of Sciences–Ural Division, 620041 Yekaterinburg, Russia Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India 3 Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India 4 Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India 2
(Presented 16 November 2010; received 21 September 2010; accepted 3 January 2011; published online 8 April 2011) In order to investigate magnetic structure and the mechanism of the Curie temperature (TC) enhancement in TbNi4Co and TbNi4Fe compounds in comparison with TbNi5, electronic structure calculations were performed within the LSDA þ U method (local spin density approximation with Hubbard U-correction). Magnetic moments for Ni, Fe, and Tb ions resulted from the LSDA þ U calculations for TbNi5 and TbNi4Fe compounds were found to be in very good agreement with the ones refined from the neutron data. Experimental magnetization measurements demonstrate a substantial increase of TC in TbNi4Co (TC 60 K) and especially in TbNi4Fe (TC 280 K) in comparison with TbNi5 (TC 23 K) that correlates with the growth of the exchange–interaction C 2011 American Institute of Physics. parameter in the 3d sublattice calculated in the present work. V [doi:10.1063/1.3563083] I. INTRODUCTION
The RNi5 (R ¼ rare earth) series of materials are well known for their application in hydrogen storage. Many of the anomalous properties of this series stem from the fact that Ni is almost nonmagnetic throughout this series. The properties of TbNi5 are highly influenced by the presence of large magnetocrystalline anisotropy.1 Substitution with certain nonmagnetic elements at Ni sublattice has been investigated in the past.2,3 Here we have studied the effect of substituting Co and Fe at the Ni site. In our earlier work we have reported the magnetic and the neutron diffraction studies of these compounds.4 It was observed that the Ni sublattice gets partially polarized with substitution of these elements. Large enhancement of the ordering temperature, especially in the case of Fe substitution, suggests an increase in the net 3d–3d and 4f–3d exchange interactions. In order to understand this effect in more detail, we have calculated the exchange interaction parameters and magnetic properties using LSDA þ U method without accounting for spin–orbit coupling. In this paper, we discuss the consistency of the calculated results with experimental observations. II. RESULTS AND DISCUSSION
The compounds investigated are TbNi5, TbNi4Co, and TbNi4Fe. Magnetization data have shown that TbNi5 has a low Curie temperature (TC ¼ 23 K), which is strongly enhanced in TbNi4Co (TC 60 K) and TbNi4Fe (TC 280 K) compounds. This clearly reflects the enhanced 3d–3d direct exchange in the substituted compounds. From the neutron diffraction data, the Ni sublattice is found to carry an insignificant moment (< 0.2 lB) in the parent compound. a)
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With the available experimental resolution of the neutron data, we could not incorporate any moment on the Co site in the refinement. However, the Fe site has been found to carry a considerable moment (2.3 lB). It can be mentioned here that Fe preferentially occupies a 3g site, whereas Co is equally distributed in the 2c and 3g sites. In order to investigate the mechanism of the TC growth in TbNi4Co and TbNi4Fe compounds, electronic structure calculations were performed within the LSDA þ U method (local spin density approximation with Hubbard U-correction) in TBLMTO-ASA package (TB—tight binding, LMTO—linear muffin-tin orbitals, and ASA—atomic spheres approximation)5 for the experimental lattice parameters.4 Strong electron correlations in the 4f shell of Tb were taken into account by the values of direct U ¼ 5.4 eV and exchange J ¼ 0.7 eV Coulomb interaction parameters calculated within a constrain LDA method.6 Spin–orbit coupling was not included in these calculations. Exchange–interaction parameters (LEIP) were estimated according to Ref. 7 for the 3d-metal sublattices only. In the calculations for TbNi4Co and TbNi4Fe compounds one Ni atom in the corresponding position was substituted by one Fe (in the 3g position) or Co (in the 2c or 3g position) atom. The calculated densities of states (DOS) are presented in Fig. 1. In the interval from 5 to 1 eV total DOS mainly consists of Ni (Co and Fe) 3d states; according to the applied U-correction, Tb 4f states are split into occupied at 6 and 2.5 eV and empty states at 2 eV and have small contribution at the Fermi level. For the parent compound TbNi5 the calculations resulted in Tb ion magnetic moment of 6 lB (see Table I), whereas all Ni ions have a small moment 0.2–0.3 lB, perfectly matching the neutron data. For TbNi4Co and TbNi4Fe compounds, the magnetic moment of the Tb ion remains 6 lB, the Ni magnetic moments increase up to 0.4 lB and the moment of
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J. Appl. Phys. 109, 07E152 (2011) TABLE II. Exchange interaction parameters (in meV) in the 3d sublattice of TbNi5, TbNi4Fe, and TbNi4Co from the LSDA þ U calculations. Exchange Ni (2c)–Ni (2c) Ni (2c)–Ni (3g) Ni (3g)–Ni (3g) Ni (2c)–Fe (Co) Ni (3g)–Fe (Co)
TbNi5
TbNi4Fe (3g)
TbNi4Co (3g)
TbNi4Co (2c)
2.1 2.1 2.1 — —
1.1 1.7 2.7 24.8 29.2
1.9 2.2 2.9 12.5 13.4
— 1.2 2.0 7.1 13.8
perature values can be estimated from the calculated LEIP parameters in the 3d sublattice only. However, in the first coordination sphere one finds the largest values of the exchange interaction with the nearest neighbors that determine the order of TC. In this work we are focused on exchange interactions in the 3d subsystem only, as the main effect of the addition of Fe or Co is expected in the Ni–Fe or Ni–Co exchange interactions. But one should also consider the influence of spin–orbit coupling in Tb (not accounted for in this work) on the exchange interactions. This should be an additional investigation beyond the scope of this paper. III. CONCLUSIONS
FIG. 1. (Color online) Total and partial densities of states (DOS) of TbNi5, TbNi4Co, and TbNi4Fe calculated within LSDA þ U. Shaded area shows contributions of Fe or Co 3d states.
the Fe ion is 2.4 lB. These values are in reasonable agreement with neutron diffraction data where Tb has 5.6 lB, Ni at the 2c site has 0.1 lB and Ni þ Fe at the 3g site has 2.3 lB. Although experimentally for the TbNi4Co compound, the magnetic moment was refined only at the Tb ion (as 6 lB) at T ¼ 17 K, the theoretical calculations yield a value of 1 lB for Co. The presence of an Fe or Co ion results not only in the enhanced magnetic moments in the 3d sublattice, but also in the increased exchange–interaction parameters (see Table II). For TbNi5 compound Ni–Ni exchange–interaction parameter was calculated to be 2 meV (24 K), which accounts for the low Curie temperature TC ¼ 23 K. On the other hand, the Fe– Ni exchange interaction parameter in TbNi4Fe is 25–29 meV (288–339 K) and that for Co–Ni is 7–14 meV (82–160 K), which generally agrees with the large TC enhancement (up to TC 280 K) in TbNi4Fe and a moderate value (TC 60 K) in TbNi4Co. In Ref. 8 it was demonstrated that the Curie temTABLE I. Magnetic moments (in lB) of TbNi5, TbNi4Fe (Fe ions in the 3g position), and TbNi4Co (Co ion in 2c or 3g positions) obtained from the LSDA þ U calculations. Ion Tb Ni (2c) Ni (3g) Fe (Co)
TbNi5,
TbNi4Fe (3g)
TbNi4Co (3g)
TbNi4Co (2c)
6.1 0.3 0.2 —
6.0 0.4 0.4 2.4
6.0 0.3 0.3 1.1
6.1 0.3 0.3 1.2
In this work we report the results of theoretical and experimental investigations of magnetic properties and exchange interactions of TbNi5, TbNi4Co, and TbNi4Fe compounds. Magnetic moments for Ni, Fe, and Tb ions calculated from the LSDA þ U method for TbNi5 and TbNi4Fe compounds were found in good agreement with the ones refined from the neutron data. For TbNi4Co moments of Ni and Co were not refined. Experimental magnetization measurements demonstrate substantial increase of the Curie temperature TC in TbNi4Co (TC 60 K) and especially in TbNi4Fe (TC 280K) that correlates with the growth of exchange–interaction parameter in the 3d sublattice calculated using the theoretical model. ACKNOWLEDGMENTS
A.V.L. acknowledges the support of the Russian Foundation for Basic Research (Project Nos. 10-02-00546 and 1002-00046) MK-3376.2011.2. K.G.S. and A.K.N. acknowledge the financial support received from BRNS, DAE, Govt. of India for carrying out this work. 1
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