Magnetoelectric coupling mechanism in metal-organics [CH3NH3][Co(HCOO)3]: Dzyaloshinsky-Moriya role

The multiferroic properties of metal-organic framework [CH₃NH₃][Co(HCOO)₃] have been experimentally found and studied for a long time. As for the direct correlation between magnetic and electric orders, it is still absent in theory. In this letter, we propose a new spin model with Dzyaloshinsky-Moriya interaction to strictly confirm the experimental findings by quantum Green's function method. The spontaneous electric polarization P is related with long-range spin ordering. The magnetization M slowly decreases to zero with increasing temperature T (T_c = 20 K), regardless of magnetic field B. Meanwhile, we also find that magnetization M as a function of magnetic field B demonstrates a linear relationship at fixed temperature T. The calculated polarization ΔP ($\Delta P_{\max }\text{equals}\text{to}$ 0.08588 $\mu C/m^2$) is found in experiments.