Dirac imprints on the $g$-factor anisotropy in graphene

TL;DR

This paper experimentally measures the anisotropic $g$-factor in graphene, revealing the effects of spin-valley-orbit coupling and providing fundamental parameters for atomic structure models.

Contribution

It presents the first experimental determination of the $g$-tensor anisotropy in graphene using resistively-detected ESR and theoretical analysis of spin-orbit coupling effects.

Findings

Measured $g$-factor anisotropy along three axes

Identified intrinsic and extrinsic spin-orbit coupling contributions

Extracted fundamental atomic parameter for $^{12}$C

Abstract

Dirac electrons in graphene are to lowest order spin 1/2 particles, owing to the orbital symmetries at the Fermi level. However, anisotropic corrections in the $g$-factor appear due to the intricate spin-valley-orbit coupling of chiral electrons. We resolve experimentally the $g$-factor along the three orthogonal directions in a large-scale graphene sample. We employ a Hall bar structure with an external magnetic field of arbitrary direction, and extract the effective $g$-tensor via resistively-detected electron spin resonance. We employ a theoretical perturbative approach to identify the intrinsic and extrinsic spin orbit coupling and obtain a fundamental parameter inherent to the atomic structure of $^{12}$C, commonly used in ab-initio models.