Second Order Anisotropy in Exchange Spring Systems

Traditionally torque curves are used to measure the anisotropy of magnetic materials, assuming that the magnetization behaves as a single spin. In exchange spring systems-consisting of a soft magnetic layer ferromagnetically coupled to a hard magnetic layer-the magnetization rotates incoherently. We propose an analytic micromagnetic theory of torque curves that takes into account the fact that the magnetization orientation in the soft layer is closer to the external field direction than in the hard layer. The magnetic materials used for both the hard and soft layers have in general only first order anisotropy Ku⁽¹⁾. We observed experimentally a change in the symmetry of the torque curve for exchange spring systems that leads to an apparent second order term Ku⁽²⁾ in the anisotropy energy. The micromagnetic theory is able to fully explain the experimental findings.