Anatomy of large perpendicular magnetic anisotropy in free-standing Co/Ni (1 1 1) multilayer

Abstract We investigated the magnetic anisotropy energy (MAE) in the free-standing Co/Ni (111) multilayer as both Ni thickness dependence ( t Ni =1-4MLs) and number of multilayer repetition times (N=1-3) by means of a first-principles electronic structure calculation based on spin density functional theory. We included both contributions to the MAE from magnetocrystalline anisotropy energy (MCAE) originating from spin-orbit coupling and shape magnetic anisotropy energy (SMAE) originating from spin dipole-dipole interaction. The MCAE part was evaluated from both methods of total energy (TE) and grand-canonical force theorem (GCFT). The SMAE part was calculated by using a spin density approach (SDA). All MCAE values from the TE are well reproduced by those from the GCFT method. In N=1, the total MAE (MCAE+SMAE) for t Ni showed a perpendicular MAE (PMAE) with a maximum value of 1.67 mJ/ m 2 at t Ni =2MLs. The PMAE increases with increasing N. The series of t Ni =3MLs showed a linear behavior as N dependence with an increasing ratio of 0.68 mJ/ m 2 , which is in good agreement with experimental measurement. By using the GCFT, we evaluated the atom-resolved and k -resolved MCAEs. The atom-resolved MCAE indicates that the Co/Ni interface is the main origin of PMAE. The PMAE is mainly located at Γ ¯ - K ¯ line in the two dimensional Brillouin zone. This is attributed to large components of the d-orbitals extending along the multilayer plane on Co and Ni near the Fermi energy. We also calculated the SMAE using a discrete approach (DA) and found that there is a reduction of SMAE part in the SDA, compared to the DA. This reduction originates from a prolate quadrupole component of spin density distribution. The present comprehensive study may provide a better understanding of magnetic properties in Co/Ni multilayers as widely used in spintronic devices.