Theory of proximity-induced exchange coupling in graphene on hBN/(Co, Ni)

TL;DR

This paper investigates how cobalt and nickel induce exchange coupling in graphene through hBN layers, revealing giant effects near resonant d levels and the potential for electrical control of spin polarization.

Contribution

It provides first-principles calculations of proximity exchange in graphene/hBN/Co(Ni) heterostructures and introduces phenomenological models to describe the observed effects.

Findings

Proximity exchange decreases with additional hBN layers but can be giant near resonant d levels.

External electric fields can reverse the sign of exchange coupling, enabling electrical control.

Nickel induces weaker proximity effects compared to cobalt.

Abstract

We perform systematic first-principles calculations of the proximity exchange coupling, induced by cobalt (Co) and nickel (Ni) in graphene, via a few (up to three) layers of hexagonal boron nitride (hBN). We find that the induced spin splitting of the graphene bands is of the order of 10 meV for a monolayer of hBN, decreasing in magnitude but alternating in sign by adding each new insulating layer. We find that the proximity exchange can be giant if there is a resonant $d$ level of the transition metal close to the Dirac point. Our calculations suggest that this effect could be present in Co heterostructures, in which a $d$ level strongly hybridizes with the valence-band orbitals of graphene. Since this hybridization is spin dependent, the proximity spin splitting is unusually large, about 10 meV even for two layers of hBN. An external electric field can change the offset of the graphene and transition-metal orbitals and can lead to a reversal of the sign of the exchange parameter. This we predict to happen for the case of two monolayers of hBN, enabling electrical control of proximity spin polarization (but also spin injection) in graphene/hBN/Co structures. Nickel-based heterostructures show weaker proximity effects than cobalt heterostructures. We introduce two phenomenological models to describe the first-principles data. The minimal model comprises the graphene (effective) $p_z$ orbitals and can be used to study transport in graphene with proximity exchange, while the $p_z$-$d$ model also includes hybridization with $d$ orbitals, which is important to capture the giant proximity exchange. Crucial to both models is the pseudospin-dependent exchange coupling, needed to describe the different spin splittings of the valence and conduction bands.