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

Abstract

Graphene, being essentially a surface, can borrow some properties of an insulating substrate (such as exchange or spin-orbit couplings) while still preserving a great degree of autonomy of its electronic structure. Such derived properties are commonly labeled as proximity. Here 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.

Electrically tunable exchange splitting in bilayer graphene on monolayer Cr2X2Te6 with X = Ge, Si, and Sn

“…One prominent example is graphene, which experiences strong proximity spin-orbit coupling (SOC) effects when placed on transition-metal dichalcogenides [1,2], and a giant field-effect SOC when bilayer graphene (BLG) is used [3]. Typical experimental structures like graphene/hBN/ferromagnet, showing very efficient spin injection [4][5][6][7][8], also feature significant proximity exchange [9,10]. These heterostructures are presently used in optospintronic devices [1,11,12] and also for spin transport [4][5][6][7][8] in graphene spintronics [13].…”

Quantum Anomalous Hall Effects in Graphene from Proximity-Induced Uniform and Staggered Spin-Orbit and Exchange Coupling

“…What if exchange coupling were also staggered, realizing proximity antiferromagnetic graphene? Thus far only uniform (ferromagnetic) exchange coupling was considered in the proximity effect of graphene [33][34][35][36][37][38][39][40][41][42][43][44]. Fortunately, there are now suitable candidates, layered semiconducting Ising antiferromagnets, which could serve as substrate for graphene and induce staggered exchange.…”

Giant proximity exchange and valley splitting in transition metal dichalcogenide/ hBN /(Co, Ni) heterostructures

“…For the FM we take three monolayers of hcp Co or fcc (111) Ni. The hBN is placed above the FM, such that the nitrogen sits above the topmost Co/Ni atom, and the boron above the fcc-position above the FM slab, as found by previous studies 19 . The TMDC is placed such above the hBN/FM slab, that a transition metal atom (Mo, W) sits above a nitrogen atom.…”

“…Currently, state of the art spin transport geometries are based on hBN encapsulated graphene 10,12,14,15 , where spins are injected by FMs, with giant mobilities up to 10 6 cm 2 /Vs [16][17][18] and spin lifetimes exceeding 10 ns 10 . The insulating hBN is ideal to reduce the contact resistance to the FM and helps to preserve the linear dispersion of graphene, which is desired for spin transport 19 . Also oxide insulators are used, such as MgO and SiO 2 , resulting in less efficient spin injection 14 .…”