Evolution of spin wave excitations with Co-doping in the spinel MnV$_2$O$_4$

Spin waves were measured at several levels of Co-doping in the spinel system MnV$_2$O$_4$ by inelastic neutron scattering and analyzed with first-principles-guided spin models. Co-doping creates a rich phase diagram encompassing the transition from localized- to itinerant-electron regimes. Increasing Co concentration weakens the single-ion anisotropy and increases both the magnitude and isotropy of the nearest-neighbor exchange interactions. First principles calculations emphasize the the distinctly different microscopic origins of the two-in-two-out magnetic structure at the Mn-rich and Co-rich limits.