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We analyze magnetic phases of monolayers of transition metal dichalcogenidesthat are two-valley materials with electron-electron interactions. The exchangeinter-valley scattering makes two-valley systems less stable to the spinfluctuations but more stable to the valley fluctuations. We predict a firstorder ferromagnetic phase transition governed by the non-analytic and negativecubic term in the free energy that results in a large spontaneous spinmagnetization. Finite spin-orbit interaction leads to the out-of-plane Isingorder of the ferromagnetic phase. Our theoretical prediction is consistent withthe recent experiment on electron-doped monolayers of MoS$_2$ reported by Roch$\textit{et al.}$ [1]. The proposed first order phase transition can also betested by measuring the linear magnetic field dependence of the spinsusceptibility in the paramagnetic phase which is a direct consequence of thenon-analyticity of the free energy.

Exchange Intervalley Scattering And Magnetic Phase Diagram Of Transition Metal Dichalcogenide Monolayers