Antiferromagnetic to Ferrimagnetic Phase Transition and Possible Phase Coexistence in Polar Magnets (Fe${}_{1-x}$Mn${}_x$)${}_2$Mo${}_3$O${}_8$

In the present work, magnetic properties of single crystal (Fe${}_{1-x}$Mn${}_x$)${}_2$Mo${}_3$O${}_8$ ($0<x<1$) have been studied by performing extensive measurements. A detailed magnetic phase diagram is built up, in which antiferromagnetic state dominates for $x<0.25$ and ferrimagnetic phase arises for $x>0.3$. Meanwhile, sizeable electric polarization of spin origin is commonly observed in all samples, no matter what the magnetic state is. For the samples hosting a ferrimagnetic state, square-like magnetic hysteresis loops are revealed, while the remnant magnetization and coercive field can be tuned drastically by simply varying the Mn-content or temperature. Possible coexistence of the antiferromagnetic and ferrimagnetic phases is proposed to be responsible for the remarkable modulation of magnetic properties in the samples.