Strong intervalley correlation induced a magnetic order transition in monolayer $\text{MoS}_{2}$

TL;DR

This paper models monolayer MoS2 considering intravalley and intervalley electron interactions, revealing a magnetic order transition driven by strong intervalley correlation, with implications for domain formation and phase transitions.

Contribution

It introduces a self-consistent mean-field model for monolayer MoS2 that captures magnetic order transitions induced by intervalley correlations, a novel insight into its magnetic properties.

Findings

Zero net magnetization at zero magnetic field due to domain structure.

First order phase transitions between different ground states with changing chemical potential.

Correlation-driven magnetic order transition consistent with experimental observations.

Abstract

In this work, we study a model for monolayer molybdenum disulfide with including the intravalley and intervalley electron-electron interaction. We solve the model at a self-consistent mean-field level and get three solutions $L_{0}$, $L_{+}$ and $L_{-}$. As for $L_{0}$, the spin polarizations are opposite at $\textbf{K}$ and $\textbf{K}^{\prime}$ valley and the total magnetization is zero. $L_{\pm}$ describe 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 $\mathbf{B}$, but a global ferromagnetic ground state for a nonzero $\mathbf{B}$. We estimate the size of domains as several nanometers. As the increase of the chemical potential, the ground state changes between $L_{0}$ and $L_{\pm}$, 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 $\it{et}$ $\it{al.}$, Phys. Rev. Lett. ${\bf 124}$, 187602 (2020)].