MAGNETIC PROPERTIES OF Ni- AND Co-ALLOYS CALCULATED BY KKR-CPA-LSD METHOD

-Electronic structure of fcc Ni-M (M = Ti, V, Cr, Mn, Fe, Co, Cu) and Cc-M (M = Cr, Mn, Fe) are calculated with KKR-CPA, in which the lattice constant as well as the charge and spin densities are determined self-consistently. The calculation well explains the observed magnetic properties of these alloys. Alloys among 3d transition metals show vari2 ety of magnetic properties. Alfhough many theoretical studies on these alloys have been made, there are still few realistic calculations. Accordingly most experiments have been compared with the calculations based on the tight-binding model combined with the coherent 5 potential approximation (CPA) and the Hartree-Fock approximation (TB-CPA-HFA) [I]. Although the b b sic understanding of the magnetic properties of these Z systems is reached with a help of such model calcula8 tions they axe certainly not enough for more detailed information like, e.g. cohesive properties. The purpose of the present paper is to discuss the magnetic properties of ferromagnetic Ni and Co based fcc al0 loys (Ni-Ti, V, Cr, Mn, Fe, Co, Cu and Co-Cr, Mn, Fe Co NIV N i Fe) in the light of realistic calculation based on the 26 27 28 ELECTRONSIATOM Korringa-Kohn-Rostoker coherent potential approximation (KKR-CPA) [2, 31. Fig. 1. Calculated magnetization of Ni and Co based KKR-CPA is one of the best alloy versions of the alloys USaverage number of electrons per atom. g fador usual KKR band structure calculation. Use of a fast is "Ot KKR-CPA procedure [4] makes a full self-consistent, i.e. both in charge (and spin) densities and in the coherent t-matrix, calculation practicable with reason2 able computational time. In the following, the density functional theory in the local spin-density approximation (LSD) with exchangtxorrelation potential by von Barth and Hedin 5 [5] is used to remain in line with obtained successful 5 description of dilute alloys [6, 71. The lattice constant m is directly determined in each concentration by energy 9 1 minimization. Core states are rigorously included; 3 the Brillouin zone integration is performed with 500 5 independent kpoints. The h a l convergence attains 10'~~/atorn stability of the total energy, guaranteeing good accuracy for calculated quantities. See references (Refs. [4, 81) for computational details. 0 Figure 1 shows the calculated magnetization of these Fe Co NIV Ni alloys, which reproduces well the trend of the exper26 27 28 imental data shown in figure 2. The local magnetic ELECTRONS /ATOM moments of Ti, V and Cr of Ni based alloys and those Fig. 2. Experimental values of the magnetization of Ni of Cr and Mn of Co based alloys couple antiparallel and Co based alloys us. average number of electrons. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988804 C8 24 JOURNAL DE PHYSIQUE to the bulk magnetization whereas they couple parallel for other cases. For CeMn a state with parallel moment is also obtained. First we focus on Ni-Fe and Ni-Mn. Both systems undergo the ferro-tenonmagnetic transition which follows after initial increase of magnetization, with increasing Fe or Mn concentration. For Ni-Fe'the calculation predicts a first-order transition in contrast to the experiments where a smoother transition is observed. In addition, the choice of the exchangecorrelation p e tential affects the critical concentration considerably for Ni-Fe. The mechanism underlying the magnetic instability of Ni-Fe has been discussed by many authors [9]. The discrepancy of the calculation from experiment may arise from the following possibilities: (i) LSD may not take account well of the renormalization of the ground state due to the electron-magnon scattering discussed, for instance, by Igarashi [lo]; (ii) the possibility of more-than-one magnetic states of Fe atoms, e.g. one with magnetic moment parallel and another antiparallel one, may require an extension of the present treatment; (iii) since the magnetic instability occurs near the boundary where the fcc phase is no more available, the experimental condition is much complicated i.e. it is not guaranteed that the calculation should suitably simulate the experimental situation. In conclusion, more detailed comparisons with experiments are desirable to judge if the present theory is applicable to Ni-Fe or if any modification accounting for various effects not yet included is necessary. For the Ni-Mn system, the calculated ferro-tononmagnetic transition is of second order, which seemingly explains the observed behavior satisfactorily. However, a discrepancy shows up if the calculated equilibrium lattice constants are compared with experimental ones (Fig. 3). The calculated lattice constant reaches maximum around 10 atom. % of Mn and then rapidly decreases. The experimental one, on the other hand, monotonously increases with increasing Mn. I I 0 10 20 30 ATOM.% Mn Fig. 3. Concentration dependence of the calculated lattice constant of Ni-Mn (0 ) is compared with experiments (A). -5 The reason of this discrepancy lies in the fact that 0 THEORY Ni-Mn A EXPERIMENT Mn atoms retain their magnetic moment even in the paramagnetic state. More realistic treatment is, there5 3.6 a Irn Z 8 fore, to take account of the coexistence of more thah a single magnetic states for each component atom, as is pointed out by Jo years ago [ll]. He calculated such a situation by use of TB-CPA-HFA to explain the NMR data which clearly show the existence of two Mn magnetic states in Ni-Mn. Incidentally we notice that the self-consistent determination of the lattice constant is essential in these calculations. For instance, if a fixed lattice constant suitable for pure Ni is used, the calculation predicts a smooth transition for Ni-Fe, instead of a first order one. Finally we turn our attention to other systems. It certainly is true that CPA is less justifiable for the strongly perturbed systems like Ni-Ti, V, Cr and CoCr. The reasonable agreement with experiments for these alloys, however, implies that the average properties nevertheless are moderately accounted for by CPA even in such cases. For weakly perturbed systems (NiCo, Ni-Cu, Co-Fe) the present treatment seems satisfactory as naturally is expected. Further discussion will appear in future publications. In summary, we successfully calculated Ni and Co based ferromagnetic alloys by KKR-CPA-LSD, which confirms the applicability of the present theory to wide range of the transition metal alloys. For Ni-Fe and NiMn, however, some extension of the theory may be required. [I] Hasegawa, H. and Kanamori, J., J. Phys. Soc. Jpn 31 (1971) 382; 33 (1972) 1599; 33 (1972) 1607. [2] Shiba, H., Prog. Thwr. Phys. 46 (1971) 77. [3] Soven, P., Phys. Rev. B 2 (1970) 4715. [4] Akai, H., Physica B 86-88 (1977) 539; Akai, H. and Kanamori, J., J. Phys. Soc. Jpn 51 (1982) 1176. [5] Von Barth, U. and Hedin, L., J. Phys. C 5 (1972) 1629. [6] Akai, M., Akai, H. and Kanamori, J., J. Phys. Soc. Jpn 54 (1985) 4246; 54 (1985) 4257; 56 (1987) 1064. [q see e.g. Dederichs, P. H., Akai, H., Bliigel, S., Stefanou, N. and Zeller, R., Proc. of the NATO Advanced Study Institute on "Alloy Phase Stability" (Malme, Crete) 1987, in press. [8] Akai, H., to be published. [9] Kanam'ori, J. and Jo, T., Electron Correlation and Magnetism in Narrow-Band Systems, Ed. T. Moriya (Springer) 1981, p. 109. [lo] Jgarashi, J., Electron Correlation and Magnetism in Narrow-Band Systems, Ed. T. Moriya (Springer) 1981, p. 115. [ll] Jo, T., J. Phys. Soc. Jpn. 48 (1980) 1482.