Carrier and strain tunable intrinsic magnetism in two-dimensional MAX$_3$ transition metal chalcogenides

We present a density functional theory study of the carrier-density and strain dependence of magnetic order in two-dimensional (2D) MAX$_3$ (M= V, Cr, Mn, Fe, Co, Ni; A= Si, Ge, Sn, and X= S, Se, Te) transition metal trichalcogenides. Our {\em ab initio} calculations show that this class of compounds includes wide and narrow gap semiconductors and metals and half-metals, and that most of these compounds are magnetic. Although antiferromagnetic order is most common, ferromagnetism is predicted in MSiSe$_3$ for M= Mn, Ni, in MSiTe$_3$ for M= V, Ni, in MnGeSe$_3$, in MGeTe$_3$ for M=Cr, Mn, Ni, in FeSnS$_3$, and in MSnTe$_3$ for M= V, Mn, Fe. Among these compounds CrGeTe$_3$ and VSnTe$_3$ are ferromagnetic semiconductors. Our calculations suggest that the competition between antiferromagnetic and ferromagnetic order can be substantially altered by strain engineering, and in the semiconductor case also by gating. The associated critical temperatures can be substantially enhanced by means of carrier doping and strains.