Unusual ferrimagnetism in CaFe2O4

Abstract

Incomplete cancellation of collinear antiparallel spins gives rise to ferrimagnetism. Even if the oppositely polarized spins are owing to the equal number of a single magnetic element having the same valence state, in principle, a ferrimagnetic state can still arise from the crystallographic inequivalence of the host ions. However, experimental identification of such a state as ``ferrimagnetic'' is not straightforward because of the often tiny magnitude expected for $M$ and the requirement for a sophisticated technique to differentiate similar magnetic sites. We report a synchrotron-based resonant x-ray investigation at the Fe ${L}_{2,3}$ edges on an epitaxial film of $\mathrm{Ca}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$, which exhibits two magnetic phases with similar energies. We find that while one phase of $\mathrm{Ca}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$ is antiferromagnetic, the other one is ferrimagnetic with an antiparallel arrangement of an equal number of spins between two distinct crystallographic sites with very similar local coordination environments. Our results further indicate two distinct origins of an overall minute $M$; one is intrinsic, from distinct ${\mathrm{Fe}}^{3+}$ sites, and the other one is extrinsic, arising from defective ${\mathrm{Fe}}^{2+}$ likely forming weakly coupled ferrimagnetic clusters. These two origins are uncorrelated and have very different coercive fields. Hence, this work provides a direct experimental demonstration of ferrimagnetism solely due to crystallographic inequivalence of the ${\mathrm{Fe}}^{3+}$ as the origin of the weak $M$ of $\mathrm{Ca}{\mathrm{Fe}}_{2}{\mathrm{O}}_{4}$.