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