Magnetic order transition in monolayer MoS2 induced by strong intervalley correlation

In this paper, we study a model for monolayer molybdenum disulfide, including the intravalley and intervalley electron-electron interaction. We solve the model at a self-consistent mean-field level and get three solutions: L0, L+, and L-. As for L0, the spin polarizations are opposite at K and K' valleys and the total magnetization is zero. L +/- describes two degenerate spin-polarized states, and the directions of polarization are opposite for the states of L+ and L-. Based on these results, the ground state can be deduced to be spin polarized in domains in which their particular states can be randomly described by L+ or L-. Therefore, a zero net magnetization is induced for zero external magnetic field B, but a global ferromagnetic ground state for a nonzero B. We estimate the size of domains as several nanometers. With the increase of the chemical potential, the ground state changes between L0 and L +/-, indicating first-order phase transitions at the borders, which is coincident with the observation of photoluminescence experiments in the absence of the external magnetic field [J. G. Roch, et al., Phys. Rev. Lett.