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Lattice instability of cubic Laves-phase intermetallics of Y with 3d transition-metal elements
ELSEVIER
Physica B 237-238 (1997) 355-356
Lattice instability of cubic Laves-phase intermetallics of Y with 3d transition-metal elements K. Terao*, H. Yamada The Faculty of Science, Shinshu University, 1-1 Asahi 3-chome, Matsumoto 390. Japan
Abstract
Electronic structures for YT2 with the cubic Laves-phase structure, where T = Cr, Mn, Fe, Co and Ni, are calculated by means of the LMTO-ASA as a function of volume and isochoric tetragonal distortion. The total energy calculated for cubic lattice shows a minimum near the observed volume. However, the cubic lattices for T = Cr, Mn and Fe are shown to be instable with respect to the tetragonal distortion, while they are stable for T = Co and Ni. Keywords: Electronic structure; Laves phase; Lattice instability
Cubic Laves-phase intermetallic compounds of Y with 3d transition-metal elements are very interesting for investigations on magnetic behaviors of 3d elements in these compounds. Y atom makes the cubic Laves-phase structure YT2 with T = Mn, Fe, Co and Ni, while YCr2 with this structure does not exist [1]. YMn2 is near the boundary of this structure and shows complicated antiferromagnetism [2]. At the Nrel point, it shows a very large change in volume and also considerable tetragonal distortion of lattice [3]. It is recently shown on the Heisenberg model [4] that the tetragonal lattice distortion may play an important role in appearing of the complicated YMn2-type spin configuration, but these intermetallics should be analysed on the itinerant electron model. In this paper, the electronic structure for YT2 in the paramagnetic state is calculated at 641 k-points in the irreducible ~ Brillouin zone as a function of isochoric tetragonal distortion, by making use of the LMTO-ASA method with the exchange-correlation potential by von Barth and Hedin [5]. The convergence is achieved so that the mean square of moments * Corresponding author. 0921-4526/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PH S0921-4526(97)00224-X
for the occupied partial density of states is less than 10 -6. A basis set of functions with angular momenta upto ~ = 3 on all sites is adopted. We have calculated the volume dependence of the total energy and obtained a minimum near the observed values of volume for the present compounds as shown in Fig. l ( a ) - ( d ) . With respect to the ratio of c/a due to the isochoric tetragonal distortion, however, the energy shows a maximum at cubic lattice ( c / a - - 1 ) for YCr2, YMn2 and YFe2, indicating an instability of the cubic structure into a tetragonal one. For YCo2 and YNi2, the energy shows the minimum at c/a = 1, and the cubic lattices are stable. In the former cases, the obtained minimum of the energy with respect to volume for cubic lattice is, in fact, the saddle point as shown in Fig. l(a) and (b). Although we have shown that the cubic structure is stabilized with increasing 3d electrons of T in YT2 in qualitative agreement with experimental facts, the calculated results show that YCo2 is at the boundary for the stability of cubic lattice, being different from the experimental results. The discrepancy will be due to the ASA or approximate treatment of exchangecorrelation potential. However, it is pointed out here
K. Terao, H. Yamada/ Physica B 237 238 (1997) 355-356
356
(c)
(a) 1.1
1.1
1
1
c/a
c/a
0.9
0.9 6.9
7,1 lattice parameter
6.7
7.3
6.9 lattice parameter
7.1
(d)
(b) 1.1
1.1
1
1
c/a
c/a
0.9
0.9 6.8
7 lattice parameter
7.2
6.8
7 lattice parameter
7.2
Fig. 1. Calculated contour lines of the total energy for YMn2 (a), YFe2 (b), YCo2 (c) and YNi2 (d). The contour lines are at intervals of 2 mRy. The ordinate represents the c/a ratio. The lattice parameter of the conventional cubic cell (c/a = 1) is shown at the abscissa in/~. The calculated result for YCr2 is very similar to that for YMn2.
that YCr2 with the cubic Laves-phase structure does not exist by the lattice instability due to a certain property of the electronic structure. Moreover, it may be pointed out that a large tetragonal strain observed in antiferromagnetic YMn2 is not simply attributed only to the usual spontaneous magnetostriction. It may be interpreted as that, even in paramagnetic state, the cubic YMn2 is near the tetragonal instability, and that the distortion due to the tetragonal instability is brought about by the magnetic ordering.
References [1] K.H.J. Buschow, Rep. Prog. Phys. 40 (1977) 1179. [2] Y. Nakamura, M. Shiga and S. Kawano, Physica B 120 (1983) 212. [3] I.Yu. Gaydukova and A. Markosyan, Phys. Met. Metall. 54 (1982) 168. ~ [4] K. Terao, J. Phys. Soc, Japan 65 (1996) 1413. [5] U. von Barth and L. Hedin, J. Phys. C: Solid State Phys. 5 (1972) 1629.
Physica B 237-238 (1997) 355-356
Lattice instability of cubic Laves-phase intermetallics of Y with 3d transition-metal elements K. Terao*, H. Yamada The Faculty of Science, Shinshu University, 1-1 Asahi 3-chome, Matsumoto 390. Japan
Abstract
Electronic structures for YT2 with the cubic Laves-phase structure, where T = Cr, Mn, Fe, Co and Ni, are calculated by means of the LMTO-ASA as a function of volume and isochoric tetragonal distortion. The total energy calculated for cubic lattice shows a minimum near the observed volume. However, the cubic lattices for T = Cr, Mn and Fe are shown to be instable with respect to the tetragonal distortion, while they are stable for T = Co and Ni. Keywords: Electronic structure; Laves phase; Lattice instability
Cubic Laves-phase intermetallic compounds of Y with 3d transition-metal elements are very interesting for investigations on magnetic behaviors of 3d elements in these compounds. Y atom makes the cubic Laves-phase structure YT2 with T = Mn, Fe, Co and Ni, while YCr2 with this structure does not exist [1]. YMn2 is near the boundary of this structure and shows complicated antiferromagnetism [2]. At the Nrel point, it shows a very large change in volume and also considerable tetragonal distortion of lattice [3]. It is recently shown on the Heisenberg model [4] that the tetragonal lattice distortion may play an important role in appearing of the complicated YMn2-type spin configuration, but these intermetallics should be analysed on the itinerant electron model. In this paper, the electronic structure for YT2 in the paramagnetic state is calculated at 641 k-points in the irreducible ~ Brillouin zone as a function of isochoric tetragonal distortion, by making use of the LMTO-ASA method with the exchange-correlation potential by von Barth and Hedin [5]. The convergence is achieved so that the mean square of moments * Corresponding author. 0921-4526/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved PH S0921-4526(97)00224-X
for the occupied partial density of states is less than 10 -6. A basis set of functions with angular momenta upto ~ = 3 on all sites is adopted. We have calculated the volume dependence of the total energy and obtained a minimum near the observed values of volume for the present compounds as shown in Fig. l ( a ) - ( d ) . With respect to the ratio of c/a due to the isochoric tetragonal distortion, however, the energy shows a maximum at cubic lattice ( c / a - - 1 ) for YCr2, YMn2 and YFe2, indicating an instability of the cubic structure into a tetragonal one. For YCo2 and YNi2, the energy shows the minimum at c/a = 1, and the cubic lattices are stable. In the former cases, the obtained minimum of the energy with respect to volume for cubic lattice is, in fact, the saddle point as shown in Fig. l(a) and (b). Although we have shown that the cubic structure is stabilized with increasing 3d electrons of T in YT2 in qualitative agreement with experimental facts, the calculated results show that YCo2 is at the boundary for the stability of cubic lattice, being different from the experimental results. The discrepancy will be due to the ASA or approximate treatment of exchangecorrelation potential. However, it is pointed out here
K. Terao, H. Yamada/ Physica B 237 238 (1997) 355-356
356
(c)
(a) 1.1
1.1
1
1
c/a
c/a
0.9
0.9 6.9
7,1 lattice parameter
6.7
7.3
6.9 lattice parameter
7.1
(d)
(b) 1.1
1.1
1
1
c/a
c/a
0.9
0.9 6.8
7 lattice parameter
7.2
6.8
7 lattice parameter
7.2
Fig. 1. Calculated contour lines of the total energy for YMn2 (a), YFe2 (b), YCo2 (c) and YNi2 (d). The contour lines are at intervals of 2 mRy. The ordinate represents the c/a ratio. The lattice parameter of the conventional cubic cell (c/a = 1) is shown at the abscissa in/~. The calculated result for YCr2 is very similar to that for YMn2.
that YCr2 with the cubic Laves-phase structure does not exist by the lattice instability due to a certain property of the electronic structure. Moreover, it may be pointed out that a large tetragonal strain observed in antiferromagnetic YMn2 is not simply attributed only to the usual spontaneous magnetostriction. It may be interpreted as that, even in paramagnetic state, the cubic YMn2 is near the tetragonal instability, and that the distortion due to the tetragonal instability is brought about by the magnetic ordering.
References [1] K.H.J. Buschow, Rep. Prog. Phys. 40 (1977) 1179. [2] Y. Nakamura, M. Shiga and S. Kawano, Physica B 120 (1983) 212. [3] I.Yu. Gaydukova and A. Markosyan, Phys. Met. Metall. 54 (1982) 168. ~ [4] K. Terao, J. Phys. Soc, Japan 65 (1996) 1413. [5] U. von Barth and L. Hedin, J. Phys. C: Solid State Phys. 5 (1972) 1629.