The First-principles Calculations On Magnetocrystalline Anisotropy In RCo₅ Alloy

Under the density functional theory and using the full potential line augmented plane wave (FLAPW) method we calculate the magnetocrystalline anisotropy energy (MAE) of YCo₅, SmCo₅ and NdCo₅. The LDA+U method is used for the exchange correlation energy of Sm and Nd. Accroding to the force theorem, we calculate MAE by summing the eigenvalues of the occupied states for system in different magnetization directions, and the difference of these sums corresponding to the MAE:ΔE=ΣE_i^axis-ΣE_i^plane .We get the MAE of YCo₅,SmCo₅ and NdCo₅ are-2.2meV/f.u.,-17.27 meV/f.u. and 33.79meV/f.u., which match well with experiments in values and directions. Further study on NdCo₅ proves that there aretwo easy axis in basal plane of NdCos, [110] and [110]. By distorting of a axis and caxis (extend or contract) and change c/a ratio but holding the volume of the cell, we find that MAE get reduced. When extending the c axis more than 6.8%, we find the magnetocrystalline anisotropy turns to along c axis. Analyzing the electronic density of states and the differentia in spin densities of atoms we conclude that the spatial distribution of 4f electron and the 4f-3d coupling are controlling factors to MAE of NdCo₅. From study the atomic magnetic moments of NdCo₅, we find distortion of crystal lattice will mainly affect the orbital moments due to changing of the crystalline field of rare-earth atom and affect MAE by spin-orbit coupling. Comparatively, the variations of spin moments in the process of the distortion are very small. We then replace the Co atoms by Fe atoms in NdCo₅, from the calculation we find that the substitution of Fe can increase the magnetic moment and improve MAE evidently, which will be instructive in improving the property of the materials used inmicrowave fields. For NdCo₂Fe₃,ΔE_[110]=12.13meV/f.u.ΔE_[110] = 2.59meV/f.u.The modification could be attributed to the difference in number and orbital distribution of 3d electron of Co and Fe. And the distortion of crystal lattice bringing by substitution will influence the distribution of 4f thus affect the MAE also.