Transverse Bias Inverse Initial Susceptibility and Torque

We use a sensitive and precise determination of an arbitrary thin film magnetic anisotropy energy Ea (or Ea/MS if the saturation magnetization MS is not known) versus in-plane polar angle θ by means of initial inverse susceptibility and torque measurements under constant transverse bias field HB.

In this method coined TBIIST two magnetic fields HL and HB are applied in the plane of the film along directions defined by θ and θ-(π/2), respectively, and mL the magnetization component in units of MS is measured versus HL around mL=0.

This readily provides two quantities χ-1=(∂HL/∂mL)(mL=0) the initial inverse susceptibility and ΔH=HL(mL=0) the field offset or torque at mL=0, shown to be respectively related to the second (1/MS)(∂2Ea/∂θ2)(θ-(π/2)) and first (1/MS)(∂Ea/∂θ)(θ-π/2) derivatives of Ea.

This, in turn, yields two determinations of Ea(θ) from χ-1(θ) and ΔH(θ), respectively. Fourier analysis then easily resolves various contributions of different symmetries to the magnetic anisotropy. The magnetization mL(HL) is measured with a conventional magneto-optical Kerr experiment in longitudinal geometry with respect to HL and higher-order (nonlinear in mL) 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.