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

## TL;DR

This paper investigates the magnetic phase transitions in transition metal dichalcogenide monolayers, revealing a first order ferromagnetic transition influenced by exchange intervalley scattering and spin-orbit coupling, consistent with recent experiments.

## Contribution

It introduces a theoretical model predicting a first order ferromagnetic phase transition in monolayer TMDs due to exchange intervalley scattering and spin-orbit effects.

## Key findings

- Prediction of a first order ferromagnetic phase transition.
- Identification of non-analytic cubic terms in free energy.
- Consistency with recent experimental observations on MoS₂ monolayers.

## Abstract

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.