Experimental magnetic form factors inCo3V2O8: A combined study ofab initiocalculations, magnetic Compton scattering, and polarized neutron diffraction

Abstract

We present a combination of ab initio calculations, magnetic Compton scattering, and polarized neutron experiments, which elucidate the density distribution of unpaired electrons in the kagome staircase system ${\text{Co}}_{3}{\text{V}}_{2}{\text{O}}_{8}$. Ab initio wave functions were used to calculate the spin densities in real and momentum spaces, which show good agreement with the respective experiments. It has been found that the spin polarized orbitals are equally distributed between the ${t}_{2g}$ and the ${e}_{g}$ levels for the spine $(s)$ Co ions while the ${e}_{g}$ orbitals of the cross-tie $(c)$ Co ions only represent 30% of the atomic spin density. Furthermore, the results reveal that the magnetic moments of the cross-tie Co ions, which are significantly smaller than those of the spine Co ions in the zero-field ferromagnetic structure, do not saturate by applying an external magnetic field of 2 T along the easy axis $a$. In turn, the increasing bulk magnetization, which can be observed by field dependent macroscopic measurements, originates from induced magnetic moments on the O and V sites. The refined individual magnetic moments are $\ensuremath{\mu}({\text{Co}}_{c})=1.54(4){\ensuremath{\mu}}_{B}$, $\ensuremath{\mu}({\text{Co}}_{s})=2.87(3){\ensuremath{\mu}}_{B}$, $\ensuremath{\mu}(\text{V})=0.41(4){\ensuremath{\mu}}_{B}$, $\ensuremath{\mu}(\text{O}1)=0.05(5){\ensuremath{\mu}}_{B}$, $\ensuremath{\mu}(\text{O}2)=0.35(5){\ensuremath{\mu}}_{B}$, and $\ensuremath{\mu}(\text{O}3)=0.36(5){\ensuremath{\mu}}_{B}$ combining to the same macroscopic magnetization value, which was previously only attributed to the Co ions.