Quantum-confined charge transfer that enhances magnetic anisotropy in lanthanum M-type hexaferrites

Iron-based hexaferrites are critical-element-free permanent magnet components of magnetic devices. Of particular interest is electron-doped M-type hexaferrite i.e., LaFe$_{12}$O$_{19}$ (LaM) in which extra electrons introduced by lanthanum substitution of barium/strontium play a key role in uplifting the magnetocrystalline anisotropy. We investigate the electronic structure of lanthanum hexaferrite using a \textit{localized} density functional theory which reproduces semiconducting behavior and identifies the origin of the very large magnetocrystalline anisotropy. Localized charge transfer from lanthanum to the iron at the crystal's $2a$ site produces a narrow $3d_{z^2}$ valence band strongly locking the magnetization along the $c$ axis. The calculated uniaxial magnetic anisotropy energies from fully self-consistent calculations are nearly double the single-shot values, and agree well with available experiments. The chemical similarity of lanthanum to other rare earths suggests that LaM can host for other rare earths possessing non-trivial $4f$ electronic states for, \textit{e.g.,} microwave-optical quantum transduction.