Magnetic anisotropy of ferromagnetic metals in low-symmetry systems

TL;DR

This paper derives an analytic formula for perpendicular magnetic anisotropy energy in low-symmetry ferromagnetic metals, highlighting the role of orbital angular momentum and magnetic dipole operators, with applications to multilayer systems.

Contribution

It provides a concrete expression for the spin-flip virtual excitation process term, enhancing understanding of magnetic anisotropy in low-symmetry ferromagnetic systems.

Findings

An explicit formula relates anisotropy energy to orbital and dipole expectation values.

The spin-flip excitation term is significant in atoms with small magnetic moments.

Application examples include Pt monolayers, Co/Pd, Co/Ni multilayers, and Fe(CoB)/MgO bilayers.

Abstract

We have constructed an analytic formula to treat the perpendicular magnetic anisotropy energy in ferromagnetic metals with low symmetry, such as C4V and C3V. We find that the anisotropy energy is proportional to a part of the expectation values of the orbital angular momentum and magnetic dipole operator. Although the result is similar to the model proposed by Laan [J. Phys.: Condens. Matter 10, 3239 (1998)], we have derived a concrete expression for the spin-flip virtual excitation process term, which can be dominant in atoms with small magnetic moments and/or small exchange splitting. Pt monatomic layer with proximity-induced spin polarization grown on Fe is an example of this. Other multilayer systems such as Co/Pd and Co/Ni and bilayer systems such as Fe(CoB)/MgO can be discussed similarly. Moreover, the relation between perpendicular magnetic anisotropy energy and measurable physical parameters is discussed based on X-ray magnetic circular dichroism spectroscopy.