Exchange scattering and magnetic phase diagram of transition metal dichalcogenide monolayers

We analyze magnetic phases of monolayers of transition metal dichalcogenides that are two-valley materials with electron-electron interactions. The exchange intervalley 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 nonanalytic 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 the electron-doped monolayers of MoS2 reported by Roch et al. [Nat. Nanotechnol. 14, 432 (2019)]. 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 nonanalyticity of the free energy.