Spin and valley quantum Hall ferromagnetism in graphene

TL;DR

This paper investigates quantum Hall ferromagnetism in graphene, revealing how Coulomb interactions and Landau level structure lead to various spin and valley ordered states with distinct excitations.

Contribution

It classifies quantum Hall isospin ferromagnetic states in graphene and demonstrates their dependence on Landau level index and underlying symmetry-breaking mechanisms.

Findings

Observation of numerous QHIFM states in graphene

Activation gaps confirm Coulomb interaction origin

Different spin orders in high and zero energy Landau levels

Abstract

In a graphene Landau level (LL), strong Coulomb interactions and the fourfold spin/valley degeneracy lead to an approximate SU(4) isospin symmetry. At partial filling, exchange interactions can spontaneously break this symmetry, manifesting as additional integer quantum Hall plateaus outside the normal sequence. Here we report the observation of a large number of these quantum Hall isospin ferromagnetic (QHIFM) states, which we classify according to their real spin structure using temperature-dependent tilted field magnetotransport. The large measured activation gaps confirm the Coulomb origin of the broken symmetry states, but the order is strongly dependent on LL index. In the high energy LLs, the Zeeman effect is the dominant aligning field, leading to real spin ferromagnets with Skyrmionic excitations at half filling, whereas in the `relativistic' zero energy LL, lattice scale anisotropies drive the system to a spin unpolarized state, likely a charge- or spin-density wave.