Quantitative model for anisotropy and reorientation thickness of the magnetic moment in thin epitaxially strained metal films

TL;DR

This paper presents a mathematical model to predict the critical thickness at which magnetic moments in strained epitaxial metal films reorient from in-plane to perpendicular anisotropy, based on energy minimization.

Contribution

It introduces a new quantitative model that predicts reorientation thickness using magnetic anisotropy energies and strain from lattice mismatch, requiring minimal material constants.

Findings

Model accurately predicts reorientation thickness.

Uses strain and anisotropy energies for calculations.

Provides an approximate closed-form expression.

Abstract

A quantitative mathematical model for the critical thickness of strained epitaxial metal films is presented, at which the magnetic moment experiences a reorientation from in-plane to perpendicular magnetic anisotropy. The model is based on the minimum of the magnetic anisotropy energy with respect to the orientation of the magnetic moment of the film. Magnetic anisotropy energies are taken as the sum of shape anisotropy, magnetocrystalline anisotropy and magnetoelastic anisotropy, the two latter ones being present as constant surface and variable volume contributions. Other than anisotropy materials constants, readily available from literature, only information about the strain in the films for the determination of the magnetoelastic anisotropy energy is required. Application of the epitaxial Bain path allows to express the strain in the film in terms of substrate lattice constant and film lattice parameter, and thus to obtain an approximate closed expression for the reorientation thickness in terms of lattice mismatch. The model can predict the critical spin reorientation transition thickness with surprising accuracy.