Orbital torque: Torque generation by orbital current injection

Abstract

We propose a mechanism of torque generation by injection of an orbital current, which we call orbital torque. In a magnetic bilayer consisting of a nonmagnet (NM) and a ferromagnet (FM), we consider a situation where the spin-orbit coupling (SOC) is present only in the FM. Although the SOC is absent in the NM, the orbital Hall effect can arise in the NM. When the resulting orbital Hall current is injected to the FM, the SOC of the FM converts the orbital angular momentum into spin, which exerts torque to the magnetization of the FM. Remarkably, even for small SOC strength comparable to that of 3d FMs, the orbital torque can be comparable to the spin torque induced by the spin Hall effect of the NM with strong SOC. This provides a way to experimentally probe the OHE and opens a new venue to achieving spin-torque devices based on light elements that exhibit gigantic orbital response. Experimental implications are discussed. * hwl@postech.ac.kr

Intrinsic orbital moment and prediction of a large orbital Hall effect in two-dimensional transition metal dichalcogenides

“…Due to the opposite Berry curvatures at the valley points K and K , these orbital moments flow in opposite directions, leading to a large OHC (≈ 10 4 /e Ω −1 ). The vanishingly small intrinsic SHC in these materials make them particularly suitable for the direct observation of the OHE, which can be measured by detecting the orbital torque generated by the orbital Hall current [5]. Magneto-optical Kerr effect may also be used to detect the orbital moments accumulated at the edges of the sample due to the OHE [23].…”

“…By matrix multiplication, we immediately find that J z,orb α = τ v α and J x,orb α = J y,orb α = 0, which leads to the result(8). The expression for the orbital Berry curvature then follows from Eqs (5). and(8), viz.,…”

“…In fact, the idea of OHE has already been invoked to explain the origin of a large anomalous and spin Hall effect in several materials [1][2][3]. Because of this and the fact that OHE is expected to have a larger magnitude than its spin counterpart, there is a noticeable interest in developing the OHE [4][5][6][7], with an eye towards future "orbitronics" device applications.…”

Magnetization switching driven by current-induced torque from weakly spin-orbit coupled Zr

“…where J o is the effective spin current density in the Zr layer generated by the orbital current injection into the Zr layer [19]. When SOT and OT are comparable, θ SH should contain both contributions.…”

“…The orbital current may be either transformed to the spin current within a nonmagnetic metal (thus providing a mechanism to generate SHE of the nonmagnetic metal), or may be injected to an adjacent FM layer. According to a recent theoretical calculation [19], the injection of the orbital current generates an orbital torque (OT) in the FM layer. Since OT has similar properties to SOT, OT should also achieve CIMS in a perpendicularly magnetized multilayer.…”