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Capturing the non-collinear magnetic ground state of the spinel vanadatesAV$_2$O$_4$ (A= Mn, Fe and Co) remains an outstanding challenge forstate-of-the-art ab-initio methods. We demonstrate that both the non-collinearspin texture, as well as the magnitude of local moments, are captured by asingle value of the on-site Hubbard $U$ of 2.7~eV in conjunction with the localspin density approximation (LSDA+$U$), provided the source term (i.e., magneticmonopole term) is removed from the exchange-correlation magnetic field ${\bfB}_{XC}$. We further demonstrate that the magnetic monopole structure in ${\bfB}_{XC}$ is highly sensitive to the value of $U$, to the extent that theinterplay between on-site localization and local moment magnitude isqualitatively different depending on whether the source term is removed or not.This suggests that in treating strongly correlated magnetic materials withinthe LSDA+$U$ formalism, subtraction of the unphysical magnetic monopole termfrom the exchange-correlation magnetic field is essential to correctly treatthe magnetic ground state.

A complete description of the magnetic ground state in spinel vanadates