Vanadium magnetoelectric multipoles inV2O3

Abstract

We establish the contributions made by the vanadium anapole, and other magnetoelectric multipoles, to the electron ground state of ${\mathrm{V}}_2{\mathrm{O}}_3$ in its antiferromagnetic modification. To this end, observations made by resonant x-ray Bragg diffraction are analyzed in terms of a scattering amplitude derived within the atomic model. The amplitude is a coherent sum of $E1\text{−}E2$ and $E2\text{−}E2$ resonance events that is fully compliant with the established chemical $(I2∕a)$ and magnetic space groups. One set of values for the V multipoles are found to give a totally satisfactory account of all data collected at two space-group forbidden Bragg reflections in the two polarization channels ${\sigma }^{\prime }\sigma$ and ${\pi }^{\prime }\sigma$ ($\sigma$ primary polarization, and ${\sigma }^{\prime }$ and ${\pi }^{\prime }$ secondary polarizations). Derived estimates of the V anapole $\left(E1\text{−}E2\right)$ and V octupole $\left(E2\text{−}E2\right)$ are good to within a few percent, and the $E1\text{−}E2$ event alone is shown not to adequately describe the diffraction data.