# Inherited and flatband-induced ordering in twisted graphene bilayers

## TL;DR

This study explores how slight twisting in bilayer graphene influences magnetic ordering, revealing inherited antiferromagnetic tendencies and potential for flat-band-induced ferromagnetism, bridging behaviors between untwisted and twisted systems.

## Contribution

It demonstrates that magnetic ordering in twisted bilayer graphene interpolates between untwisted configurations and can be enhanced or altered by doping, highlighting the role of flat bands in magnetic phases.

## Key findings

- Ordering tendencies interpolate between AA and AB stacking at intermediate temperatures.
- At low temperatures, twisting enhances magnetic ordering tendencies.
- Doping can induce a transition to flat-band-induced ferromagnetic phases.

## Abstract

The nature of the insulating and superconducting states in twisted bilayer graphene systems is intensely debated. While many works seek for explanations in the few flat bands near the Fermi level, theory and a number of experiments suggest that nontwisted bilayer graphene systems do exhibit - or are at least close to - an ordered, insulating ground state related to antiferromagnetic ordering. Here we investigate in which ways this magnetic ordering scenario is affected by the slight twisting between the layers. We find that at charge neutrality the ordering tendencies of twisted systems interpolate between those of untwisted AA and AB stacked bilayers at intermediate temperatures, while at lower temperatures of the order of typical flat-band dispersion energies, the ordering tendencies are even enhanced for the twisted systems. The preferred order at charge neutrality still exhibits an antiferromagnetic spin arrangement, with ordered moments alternating on the carbon-carbon bonds, with an enveloping variation on the moir\'e scale. This ordering can be understood as inherited from the untwisted systems. However, even in the RPA analysis, the possible low-energy behaviors are quite versatile, and slight doping of one or more electrons per moir\'e cell can take the system into a, potentially flat-band induced, ferromagnetic phase.