# Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene

## TL;DR

This paper develops a microscopic theory for collective excitations in quantum anomalous Hall ferromagnets within twisted bilayer graphene, analyzing spin and valley magnon spectra, stability, and thermal effects.

## Contribution

It introduces a detailed microscopic framework for understanding collective excitations and stability in QAH ferromagnets in twisted bilayer graphene, including magnon spectra and thermal effects.

## Key findings

- Spin magnon and valley magnon spectra calculated.
- QAH ferromagnet stability verified.
- Valley wave mode is gapped, favoring valley polarization.

## Abstract

We present a microscopic theory for collective excitations of quantum anomalous Hall ferromagnets (QAHF) in twisted bilayer graphene. We calculate the spin magnon and valley magnon spectra by solving Bethe-Salpeter equations, and verify the stability of QAHF. We extract the spin stiffness from the gapless spin wave dispersion, and estimate the energy cost of a skyrmion-antiskyrmion pair, which is found to be comparable in energy with the Hartree-Fock gap. The valley wave mode is gapped, implying that the valley polarized state is more favorable compared to the valley coherent state. Using a nonlinear sigma model, we estimate the valley ordering temperature, which is considerably reduced from the mean-field transition temperature due to thermal excitations of valley waves.