Higher-order magnetic anisotropy in soft-hard magnetic materials

We have computationally studied the properties of higher-order magnetic anisotropy constants in an $L{1}_{0}/A1\text{\ensuremath{-}}\mathrm{FePt}$ core-shell system which is characterized by a strong second-order two-ion Fe-Pt component. show that structure induces unexpected fourth-order constant ${K}_{2}$, magnitude varies nonmonotonically with core-size ratio $R$ reaching peak at $R\ensuremath{\approx}0.50$. Furthermore, we find ${K}_{2}$ scales normalized magnetization ${(M/{M}_{s})}^{2.2}$ temperatures below Curie temperature, remarkable deviation from established Callen-Callen theory instead predicts scaling exponent 10. construct analytic model demonstrates arises canting core and shell magnetization, successfully reproduces justifies obtained numerical simulation.