Non-collinear magnetism in monolayer and magic-angle twisted bilayer graphene

Résumé :

Recent studies of twisted bilayer graphene (or other 2D materials) have been stimulated by the discovery of correlations between electronic flatband states due to a moiré pattern [1]. It is shown experimentally and theoretically that the filling of the flat bands affects their correlation and magnetic properties significantly.
On the other hand, the effect of doping on a simple graphene layer is still unclear. Indeed, its half-filled case is well known [2], but unlike other lattices [3] its magnetic properties beyond half filling are mostly unexplored, except at 1/4 doping [4] i.e when the Fermi energy is set inside of a Van Hove singularity associated to a flatband.
In this talk, I will first present our analysis of graphene magnetism using a combination of the Hubbard model and Hartree-Fock Mean Field Theory (MFT). We work at density values around 1/4 doping (average number of electrons per site Ne=0.75) as it puts the system right into one of the Van Hove singularities found in graphene’s density of states, giving rise to interesting magnetic properties. We present an interaction-density phase diagram and its associated magnetic orders, described by their band structure and spin structure factor [5].
I will then talk about magic-angle twisted bilayer graphene, to which we applied the same MFT method. While still a work in progress, I will present the current results we obtained on a Moiré lattice for various values of interaction and flat-band filling, revealing exotic spin textures such as an antiferromagnetic triangular order on the Moiré scale.
[1] Y. Cao et al., Nature 556, 43 (2018); Nature 556, 80 (2018).
[2] M. Raczkowski et al., Phys. Rev. B 101, 125103 (2020), and Refs. therein.
[3] R. Scholle et al., Phys. Rev. B 108, 035139 (2023)
[4] S. Jiang, A. Mesaros, Y. Ran, Phys. Rev. X 4, 031040 (2014)
[5] M. Lucas, A. Ralko, A. Honecker, G. Trambly de Laissardière, arXiv:2511.22714 (2025)

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Contact : andrew.fefferman@neel.cnrs.fr