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We present a density functional theory study of the carrier-density andstrain 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 metaltrichalcogenides. Our {\em ab initio} calculations show that this class ofcompounds includes wide and narrow gap semiconductors and metals andhalf-metals, and that most of these compounds are magnetic. Althoughantiferromagnetic order is most common, ferromagnetism is predicted inMSiSe$_3$ 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 thesecompounds CrGeTe$_3$ and VSnTe$_3$ are ferromagnetic semiconductors. Ourcalculations suggest that the competition between antiferromagnetic andferromagnetic order can be substantially altered by strain engineering, and inthe semiconductor case also by gating. The associated critical temperatures canbe substantially enhanced by means of carrier doping and strains.

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