Anisotropic Band-Split Magnetism in Magnetostrictive CoFe${}_2$O${}_4$

Single crystal spinel CoFe${}_2$O${}_4$ exhibits the largest room-temperature saturation magnetostriction among non-rare-earth compounds and a high Curie temperature ($T_c\sim 780$ K), properties that are critical to a wide range of industrial and medical applications. Neutron spectroscopy reveals a large band splitting ($\sim$ 60 meV) between two ferrimagnetic magnon branches, which is driven by site mixing between Co${}^{2+}$ and Fe${}^{3+}$ cations, and a significantly weaker magnetocrystalline anisotropy ($\sim$ 3 meV). Central to this behavior is the competition between extremely large mismatched molecular fields on the tetrahedral $A$-site and octahedral $B$-site sublattices and the single-ion anisotropy on the $B$-site. This creates a strong energetic anisotropy that locks the magnetic moment within each structural domain in place. As a result of these differing energy scales, switching structural domains is energetically favored over a global spin reorientation under applied magnetic fields, and this is what amplifies the magnetostrictive nature of CoFe${}_2$O${}_4$.