Calculation of uniaxial magnetic anisotropy energy of tetragonal and trigonal Fe, Co, and Ni

Abstract

The magnetic anisotropy energy (MAE) of Fe, Co, and Ni is presented for tetragonal and trigonal structures along two paths of structural distortion connecting the bcc and the fcc structure. The MAE was calculated from first principles with the full-potential linear muffin-tin orbital method and the force theorem. As is expected from symmetry considerations, the MAE increases by orders of magnitude when the cubic symmetry is broken. For tetragonal structures of Co and Ni a regular behavior of the MAE is observed, i.e., only the symmetry dictated nodes at the cubic structures appear along this path of distortion. In the case of tetragonal Fe, additional reorientations of the easy axis occur that are attributed to a topological change of the Fermi surface upon distortion. For the trigonal structures of all three elements the strain dependence of the MAE is more complicated, with additional reorientations of the easy axis and an unexpectedly large MAE for certain distortions of Ni, and a strongly nonlinear behavior for trigonal structures of Co close to fcc. Furthermore, the linear magnetoelastic coupling coefficients are calculated from the MAE at small distortions from the cubic equilibrium structure of the three elements. Two different Brillouin-zone integration techniques were used to calculate the MAE. Since the Gaussian broadening method smears out details of the Fermi surface, it results in a different MAE as compared to the tetrahedron method in some cases.