Higher-order magnetic anisotropy in soft-hard magnetic materials

We have computationally studied the properties of higher-order magnetic anisotropy constants in an L10/A1-FePt core-shell system which is characterized by a strong second-order two-ion Fe-Pt anisotropy component. We show that the core-shell structure induces an unexpected fourth-order anisotropy constant K2, the magnitude of which varies nonmonotonically with the core-size ratio R reaching a peak at R≈0.50. Furthermore, we find that K2 scales with the normalized magnetization by (M/Ms)2.2 at temperatures below the Curie temperature, a remarkable deviation from the established Callen-Callen theory which instead predicts a scaling exponent of 10. We construct an analytic model which demonstrates K2 arises from the canting of the core and shell magnetization, and successfully reproduces and justifies the scaling exponent obtained from numerical simulation.