Density Functional Study of the magnetic structure on spin frustrated MnSb$_{2}$S$_{4 }$ and Sr$_{2}$MOsO$_{6}$ (M = Cu, Ni)

We explored the electronic structures of two spin-frustrated magnetic systems monoclinic MnSb$_{2}$S$_{4}$ and Sr$_{2}$MOsO$_{6}$ (M = Cu, Ni) on the basis of first principles DFT calculations. The spin exchanges of MnSb$_{2}$S$_{4}$ are frustrated within each MnS$_{4}$ chain and between adjacent MnS$_{4}$ chains, which explains the observed helical spin order of MnSb$_{2}$S$_{4}$. We predict that MnSb$_{2}$S$_{4}$ is multiferroic with ferroelectric polarization of $\sim $14 $\mu $C/m$^{2}$ along the chain direction, and a field-induced reversal of the ferroelectric polarization occurs by reversing the direction of the helical spin rotation. The ordered double perovskites Sr$_{2}$MOsO$_{6}$ (M = Cu, Ni), reported to be half-metallic, are found to be magnetic insulators. The magnetic structures of Sr$_{2}$MOsO$_{6}$ were probed by evaluating their spin exchanges.