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 $E1\text{\ensuremath{-}}E2$ and $E2\text{\ensuremath{-}}E2$ 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 ${\ensuremath{\sigma}}^{\ensuremath{'}}\ensuremath{\sigma}$ and ${\ensuremath{\pi}}^{\ensuremath{'}}\ensuremath{\sigma}$ ($\ensuremath{\sigma}$ primary polarization, and ${\ensuremath{\sigma}}^{\ensuremath{'}}$ and ${\ensuremath{\pi}}^{\ensuremath{'}}$ secondary polarizations). Derived estimates of the V anapole $(E1\text{\ensuremath{-}}E2)$ and V octupole $(E2\text{\ensuremath{-}}E2)$ are good to within a few percent, and the $E1\text{\ensuremath{-}}E2$ event alone is shown not to adequately describe the diffraction data.