# Induced exchange and spin-orbit effects by proximity in graphene on Ni and Co

## TL;DR

This paper models how proximity to Ni and Co substrates induces exchange and spin-orbit effects in graphene, revealing mechanisms for giant exchange splittings and Rashba coupling consistent with experiments.

## Contribution

It provides an analytical tight-binding framework to understand proximity-induced magnetic and spin-orbit effects in graphene on Ni and Co substrates, highlighting the physical origins of observed phenomena.

## Key findings

- Giant exchange splittings in graphene due to proximity effects.
- Robust Rashba spin-orbit coupling transferred to graphene.
- Conditions for preserving Dirac cones in spin-polarized bands.

## Abstract

The induced-proximity effects of nearly commensurate lattice structure of a graphene layer on Ni(111) and Co(0001) substrates in the AC stacking configuration are addressed through an analytical tight-binding approach within the Slater-Koster method. A minimal Hamiltonian is constructed by considering the hybridizations of the magnetic $3d$-orbitals of Ni(Co) atoms with the $p_z$-orbitals of graphene, in addition to the atomic spin-orbit coupling and the magnetization of the Ni(Co) atoms. A low-energy effective Hamiltonian for graphene/Ni(Co) describing the perturbed $\pi$-bands in the vicinity of the Dirac points is derived which enable us to get further insight on the physical nature of the induced-effective couplings to the graphene layer. It is shown that a magneto-spin-orbit type effect may emerge through two competing mechanisms simultaneously present, namely the proximity induced exchange and Rashba spin-orbit interaction. Such effects results in giant exchange splittings and robust Rashba spin-orbit coupling transferred to the graphene layer in agreement with recent density functional theory calculations and experimental observations. We further analyze the physical conditions for the appearance of intact Dirac cones in the minority spin bands as observed by recent photoemission measurements with spin resolution.