Enhancement of magnetic anisotropy via the Kondo effect

Magnetocrystalline anisotropy is important for permanent magnets, and as a tuning parameter for correlated and topological phases. Here, we discuss the complex effects that Kondo screening has on the magnetic anisotropy, especially at intermediate temperatures above the Kondo temperature. We explore these effects in a simplified J = 3/2 Anderson impurity model with a finite crystal field splitting, which can be solved using numerical renormalization group (NRG). The magnetic susceptibility shows that large magnetic anisotropies can remain even with significant mixed valence, and features anisotropic Kondo temperatures, with screening visible in the in- and out-of- plane susceptibilities at different temperatures. We show how the impurity spectral function can be used to extract the renormalized, temperature dependent crystal field splitting, which generically shows an enhancement at intermediate temperatures, which suggests a small amount of mixed valence may even be beneficial for magnetocrystalline anisotropy.