Magnetism and magnetocaloric properties of Co$_{1-x}$Mn$_x$Cr$_2$O$_4$

Abstract: Co$_{1-x}$Mn$_x$Cr$_2$O$_4$ crystallizes as a normal spinel in the cubic $Fd \overline{3}m$ space group, and the end members have been reported to display a region of collinear ferrimagnetism as well as a low-temperature spin-spiral state with variable coherence lengths from 3 nm to 10 nm in polycrystalline samples. Here, we present the synthesis of the entire solid solution, and data showing that the ferrimagnetic ordering temperature as well as the spin-spiral lock-in temperature are tunable with the Co/Mn ratio. The peak magnetocaloric entropy change was determined to be $\Delta S_M$ = -5.63 J kg$^{-1}$ K$^{-1}$ in an applied magnetic field change of $\Delta H$ = 0 T to 5 T for the Mn end-member at the ferrimagnetic ordering temperature. Using density functional theory (DFT), we explore the shortcomings of the magnetic deformation proxy to identify trends in $\Delta S_M$ across composition in this spinel system, and explore future extensions of theory to address these discrepancies.