Ferromagnetism in Magic-angle Twisted Bilayer Graphene: A Monte Carlo Study

TL;DR

This study uses Monte Carlo simulations of Ising models on various lattices to explore ferromagnetism in magic-angle twisted bilayer graphene, revealing phase transition temperatures and hysteresis consistent with experiments.

Contribution

It provides a theoretical Monte Carlo analysis of ferromagnetism in twisted bilayer graphene using different lattice models, matching experimental findings.

Findings

Identified phase transition temperatures for different lattice fillings.

Observed strong hysteresis below 0.5 K indicating ferromagnetism.

Results align with experimental observations of ferromagnetic behavior.

Abstract

Ferromagnetism emerges when the Moire superlattice formed by stacking two graphene monolayers in a magic twist angle are filled with integer number electrons. This work investigates the ferromagnetism based on the Ising models for a triangular lattice at one-quarter filling, a square lattice at half filling and a Kagome lattice at three-quarters filling of electrons. The temperature dependent heat capacity, magnetic susceptibility, energy and magnetization curves are calculated at zero magnetic field with a Monte Carlo method, leading to derive the phase transition temperatures, T_c=0.76, 1.33 and 4.75 K, respectively. Magnetization curves at finite magnetic field show strong hysteresis at temperature below 0.5 K for all the fillings considered, indicating the ferromagnetism of the system; the results are in agreement with experimental observations.