Accurate measurement of the in-plane magnetic anisotropy energy function [formula omitted] in ultrathin films by magneto-optics

Abstract

We present a sensitive and precise determination of an arbitrary thin film magnetic anisotropy energy E a (or E a / M S if the saturation magnetization M S is not known) versus in-plane polar angle θ by means of initial inverse susceptibility and torque measurements under constant transverse bias field H B . In this method coined TBIISTtwo magnetic fields H L and H B are applied in the plane of the film along directions defined by θ and θ - ( π / 2 ) , respectively, and m L the magnetization component in units of M S is measured versus H L around m L = 0 . This readily provides two quantities χ - 1 = ( ∂ H L / ∂ m L ) ( m L = 0 ) the initial inverse susceptibility and Δ H = H L ( m L = 0 ) the field offset or torque at m L = 0 , shown to be respectively related to the second ( 1 / M S ) ( ∂ 2 E a / ∂ θ 2 ) ( θ - ( π / 2 ) ) and first ( 1 / M S ) ( ∂ E a / ∂ θ ) ( θ - π / 2 ) derivatives of E a . This, in turn, yields two determinations of E a ( θ ) from χ - 1 ( θ ) and Δ H ( θ ) , respectively. Fourier analysis then easily resolves various contributions of different symmetries to the magnetic anisotropy. The magnetization m L ( H L ) is measured with a conventional magneto-optical Kerr experiment in longitudinal geometry with respect to H L and higher-order (nonlinear in m L ) contributions as well as polar or other contributions to the Kerr signal are carefully determined and corrected in order to obtain the desirable accuracy or even simply meaningful results. Typical acquisition times including all corrections are about a few minutes per angle θ . The power of the method is demonstrated on typical examples of epitaxial Fe layers on Si(0 0 1) and Si(1 1 1) substrates. For instance, it is shown that extremely small contributions up to the 12th order in-spin to the cubic magnetocrystalline anisotropy of iron are readily detected.