Magnetic Properties of Cubic Laves Phase Transition-metal Compounds

Electronic structures of d-electrons in the cubic Laves phase transition-metal compounds are calculated in the tight-binding approximation. By making use of the calculated density-of-states curves, various magnetic properties of these compounds are calculated and compared with experiment. The magnetic properties of the intermetallic compounds with the C15-type Laves phase structure have so far been studied intensively. Especially, the transition metal compounds AB2, where the A atom is a 3d, 4d or 5d transition-element and the B atom is Mn, Fe, Co or Ni, show many interesting magnetic properties. The observed magnetic state of these compounds at low temperature is shown in table I by P, F and AF for paramagnetic, ferromagnetic and antiferromagnetic states, respectively. Table I. Magnetic states of the transition-metal compounds AB2 with the C15-type Laves phase structure. AF, F and P denote the antiferromagnetisrn, ferromagnetism and paramagnetism, respectively. The cornpounds shown by do not have the CIS-type structure. The magnetic state of these compounds is mainly determined by the kind of the B atom. As shown in table I, all Fe compounds (AFe2) are ferromagnetic and all Co and Ni compounds (ACo2 and ANi2) are paramagnetic. However, due to the difference between the elements of A atom, there are some differences between their magnetic properties. For instance, all ACo2 are paramagnetic but the temperature dependence of the paramagnetic susceptibility in SCCO~, YCo2 and LuCO~ is very different from those in TiCo2, ZrCo2 and HfCoa. Thus, the A atom seems to play also a part of the role in the magnetic properties of AB2. The present authors [I-41 have recently calculated the electronic structures of d-electrons in these compounds by making use of the tight-binding approximation. The obtained results in a series of their papers are summarised in this paper and compared with experiment. In the numerical calculations of the density-of-states (DOS) curves for d-electrons in AB2, the hopping integrals defined by Slater and Koster are estimated in the Andersen-Jepsen-Pettifor formalism. Details of the method are given in [I]. This method is very simple and actually very useful for the calculation of the electronic structure in d-electron system with such a complex lattice structure as the Laves phase one. The calculated results of the DOS for some transition-metal compounds with the C15type structure are similar to those obtained in the self-consistent band calculations. This is because the contribution of d-states to the DOS is dominant near the Fermi level EF in these compounds. The characteristic of the shape of the DOS for AB2 with C15-type Laves phase structure is the existence of the two sharp peaks around EF [I-31. These two peaks of the DOS are mainly composed of the local DOS of the B atom. The shapes of the DOS and the positions of EF for ScCo2, YCOZ and LuCo2 are very similar to each other. For TiCo2, ZrCo2 and HfCo2, they are also very similar to each other but different from those for SCCO~, YCo2 and LuCo2. The strengths of tkie hybridisation between the d-states of A and Co atoms are not so different from each other when the numbers of d-electrons on the A atom are the same. Therefore, the shapes of the DOS and the position of EF for ACo2 are very similar to each other when the A atom belongs to the same group. In TiCoz, ZrCoz and HfCo2, the strength of the hybridisation is much stronger than that in ScCo2, YCo2 and LuCo2 and the positions of EF in the former compounds lie in the higher energy side than those in the latter compounds. Various kinds of temperature dependence of the paramagnetic susceptibility x (T) were observed in the present system. For YMn2, ScCo2,YCo2 and LuCoz, x (T) shows a maximum above the room temperature. For the ferromagnetic compounds YFe2 and ZeFe2, x (T) obeys the Curie-Weiss law. On the other hand, x (T) for TiCoa, ZrCo2 and HfCoa obeys the modified Curie-Weiss law, that is, x (T) behaves like the sum of a large temperature independent term and a CurieWeiss term. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19888128 C8 288 JOURNAL DE PHYSIQUE It is noted that there is a relation between the type of the temperature variation of x(T) and the shape of the DOS around EF [I, 21. For ScCoz, YCo2 and LuCo2, where the position of EF lies just above a sharp peak of the DOS, x (T) shows a maximum. For YFez and ZeFe2, where the position of EF lies just on the sharp peak of the DOS, x (T) obeys the Curie-Weiss law. On the other hand, for TiCo2, ZrCoz and HfCoz, where EF lies on the broad peak of the DOS, x (T) obeys the modified Curie-Weiss law. By taking into account the effect of spin fluctuations in the classical Gaussian statistics [5], the temperature dependence of x (T) is calculated by using the calculated DOS. In the present calculation, there exist four adjustable parameters; the temperature insensitive orbital susceptibility x,, the molecular field coefficient a, the exchange stiffness constant A and the cut-off wavevector of spin fluctuations 9,. Some of them can be estimated from other experimental data; the value of xc can be estimated from the Knight shift measurements, the value of A can be obtained by the observed spin wave stiffness constant. The value of CY can be estimated from the exchange splitting between the up and down spin bands. The values of parameters which cannot be estimated from other experiments are determined so as to get a good agreement between the calculated and observed results of x (T) at high temperature. A good agreement between the calculated and observed results of x (T) for all compounds listed in table I is obtained by the reasonable choice of the values of the parameters as shown in the original papers [I-31. The electronic structures of d-electrons in the ferromagnetic compounds AFe2 (A = Y, Zr, Lu and Hf) have been calculated in the Hartree-Fock approximation. The calculated value of the local magnetic m e ment on the A atom is small and negative 131, that is, the local moment on A atom is in the opposite direction to that on Fe atom. This is due to the difference between the hybridisations of d-states on A and Fe atoms in the up and down spin bands. The negative local moments on A atom in AFez have not been observed so far. Givord et al. 161 have mea. sured the local moment mFe on Fe atoms in LuFez by means of the polarised neutron diffraction. The observed value of mFe is very close to our, estimated one but the negative magnetic moment localised on Lu atom has not been observed. Gignoux et al. [7] have measured the magnetisation density induced in LuCo2 under the applied magnetic field. They have found the localised induced moments on Co atoms and the additional diffuse density of the negative magnetic moment. But the negative induced moment is not localised on Lu atom. d n the other hand, Durnelow et al. [8] and Shimizu [9] have pointed out the existence of the negative local moment on Y, Zr and Lu atoms from the observed results of the hyperfine fields. In the present paper, we surnmarised the calculated results of the various magnetic properties for the transition metal compounds with the C15-type Laves phase structure. It has been shown that the observed magnetic properties are explained by the shape of the DOS around EF. Not only the results discussed in this paper but also many other magnetic properties were calculated by using the DOS calculated in the tight-binding approximation. For instance, the effect of the excess Co atom in the non-stoichiometric Co rich compounds [2], the high-field spin susceptibility in AFe2 [3], the itinerant electron metamagnetism of ACo2 [4], the antiferromagnetic state of YMn2 [lo], the concentration dependences of the magnetic moments and low temperature specific heat coefficients and the temperature dependence of x (T) in the ternary comp&ds Y (Fe, Co), and Zr (Fe, C O ) ~ [ll] were discussed. These magnetic properties can also be understood in terms of the shape of the DOS around EF. For more quantitative discussion, fully self-consistent band calculations including s and p electrons should be carried out, but the essential points in the magnetic properties for the present system with 3d-transition elements Mn, Fe, Co and Ni can be understood in terms of the shape of the DOS around EF. [l] Yamada, H., Inoue, J., Terao, K., Kanda, S. and Shimizu, M., J. Phys. F 14 (1984) 1943. [2] Yamada, H., Inoue, J. and Shimizu, M., J. Phys. F 15 (1985) 169; J. Magn. Magn. Mater. 54-57 (1986)'961. [3] Yamada, H. and Shimizu, M., J. Phys. F 16 (1986) 1039. [4] Yamada, H. and Shimizu, M., J. Phys. F 15 (1985) L175. Yamada, H., Tohyama, T. and Shimizu, M., ibid. 17 (1987) L163. [5] Shimizu, M., Rep. Prog. Phys. 44 (1981) 329. [6] Givord, D., Gregory, A. R. and Schweizer, J., J. Magn. Magn. Mater. 15-18 (1980) 293. [7] Gignoux, D., Givord, F., Koehler, W. C. and Moon, R. M., J. Magn. Magn. Mater. 5 (1977) 172. [8] Dumelow, T., Riedi, P. C., Mohn, P., Schwarz, K. and Yamada, Y., J. Magn. Magn. Mater. 54-57 (1986) 1081. [9] Shimizu, K., J. Magn. Magn. Mater. 70 (1987) 178. [lo] Yamada, H. and Shimizu, M., J. Phys. F 17 (1987) 2249. [ll] Yamada, H., Tohyama, T. and Shimizu, M., J. Magn. Magn. Mater. 66 (1987) 409, 413.