Scattering-induced and highly tunable by gate damping-like spin-orbit torque in graphene doubly proximitized by two-dimensional magnet Cr2Ge2Te6 and monolayer

Klaus Zollner

¹

,

Marko D. Petrović

²

,

Kapildeb Dolui

³

et al.

Abstract

Graphene sandwiched between semiconducting monolayers of ferromagnet Cr 2 Ge 2 Te 6 and transition-metal dichalcogenide WS 2 acquires both spin-orbit (SO) coupling, of valley-Zeeman and Rashba types, and exchange coupling. Using first principles combined with quantum transport calculations, we predict that such doubly proximitized graphene within van der Waals heterostructure will exhibit SO torque driven by unpolarized charge current. This system lacks spin Hall current which is putatively considered as necessary for the efficient damping-like (DL) SO torque that plays a key role in magnetization switching. Instead, it demonstrates how a DL SO torque component can be generated solely by skew scattering off spin-independent potential barrier or impurities in purely two-dimensional electronic transport due to the presence of proximity SO coupling and its spin texture tilted out of plane. This leads to current-driven nonequilibrium spin density emerging in all spatial directions, whose cross product with proximity magnetization yields DL SO torque, unlike the ballistic regime with no scatterers in which only field-like (FL) SO torque appears. In contrast to SO torque on conventional metallic ferromagnets in contact with three-dimensional SO-coupled materials, the ratio of FL and DL components of SO torque can be tuned by more than an order of magnitude via combined top and back gates.

Engineering Proximity Exchange by Twisting: Reversal of Ferromagnetic and Emergence of Antiferromagnetic Dirac Bands in Graphene/Cr$_2$Ge$_2$Te$_6$

“…2(a), we show the global band structure for the graphene/CGT heterostructure for a twist angle of 30 • ; the results for other angles and effects of interlayer charge transfer are summarized in the SM [84]. In agreement with recent calculations [39,70], we find the Dirac cone located at the Fermi level and close to the conduction band edge of the CGT.…”

“…Magnetism in graphene can be induced by proximity exchange coupling with a ferro-or antiferromagnet. Of particular interest are magnetic insulators (semiconductors) such as Cr 2 Ge 2 Te 6 [39,58,70] (CGT) or CrI 3 [40,49,71,72], which can modulate the band structure of graphene (or another nonmagnetic material) without significant charge transfer and without contributing additional transport channels. Proximity exchange effects in graphene can be observed by quantum anomalous Hall effect [73], magnetoresistance [74], or nonlocal spin transport experiments [75].…”

“…Proximity exchange effects in graphene can be observed by quantum anomalous Hall effect [73], magnetoresistance [74], or nonlocal spin transport experiments [75]. Joined with strong SOC in exso-tic heterostructures [76] proximity exchange can also induce spin-orbit torque [70,[77][78][79].…”

Magnetoelectric torque and edge currents in spin-orbit coupled graphene nanoribbons

“…The controllability of the RSOC suggests that this transverse susceptibility serves as a gate-voltage-induced magnetoelectric torque on the magnetization without the need of a bias voltage, contrary to the current-induced spin-orbit torque. 54,[57][58][59][60][61] While this torque averages to zero for a homogeneously spin polarized system, well designed local variations in the magnetization can yield a net torque signal available to practical purpose. We further investigate the pattern of equilibrium spin currents in nanoribbons, especially concerning the symmetry of flow directions between the two edges, e.g.…”

Quantum interference tuning of spin-orbit coupling in twisted van der Waals trilayers

“…Thus Eq. ( 1) is valid not only for graphene/TMDC heterostructures, but for a wide range of twisted heterostructures consisting of hexagonal layers, such as heterostructures of graphene with semiconductor [53,54], ferromagnetic [55], and topological insulator [56,57] structures. This general nature of the effect is one of the main motivations for our work.…”