Kjetil M. D. Hals

Spin–orbit torques in action

The spin–orbit interaction can generate torques that act on the magnetization of a ferromagnet. Here we examine recent experimental insights into spin–orbit torques, which have generated competing explanations and differing opinions over their potential application in memory devices.

Phenomenology of Current-Induced Dynamics in Antiferromagnets

We derive a phenomenological theory of current-induced staggered magnetization dynamics in antiferromagnets. The theory captures the reactive and dissipative current-induced torques and the conventional effects of magnetic fields and damping. A Walker ansatz describes the dc current-induced domain-wall motion when there is no dissipation. If magnetic damping and dissipative torques are included, the Walker ansatz remains robust when the domain wall moves slowly. As in ferromagnets, the domain-wall velocity is proportional to the ratio between the dissipative torque and the magnetization damping. In addition, a current-driven antiferromagnetic domain wall acquires a net magnetic moment.

Scattering theory of charge-current?induced magnetization dynamics

In ferromagnets, charge currents can excite magnons via the spin-orbit coupling. We develop a novel and general scattering theory of charge-current–induced macrospin magnetization torques in normal metal|ferromagnet|normal metal layers. We apply the formalism to a dirty GaAs|(Ga,Mn)As|GaAs system. By computing the charge-current–induced magnetization torques and solving the Landau-Lifshitz-Gilbert equation, we find magnetization switching for current densities as low as 5×106 A/cm2. Our results are in agreement with a recent experimental observation of charge-current–induced magnetization switching in (Ga, Mn)As.

Intrinsic coupling between current and domain wall motion in (Ga,Mn)As.

We consider current-induced domain wall motion and, the reciprocal process, moving domain wall-induced current. The associated Onsager coefficients are expressed in terms of scattering matrices. Uncommonly, in (Ga,Mn)As, the effective Gilbert damping coefficient alphaw and the effective out-of-plane spin-transfer torque parameter betaw are dominated by spin-orbit interaction in combination with scattering off the domain wall, and not scattering off extrinsic impurities. Numerical calculations give alphaw approximately 0.01 and betaw approximately 1 in dirty (Ga,Mn)As. The extraordinarily large betaw parameter allows experimental detection of current or voltage induced by domain wall motion in (Ga,Mn)As.

Magnonic charge pumping via spin-orbit coupling.

The interplay between spin, charge and orbital degrees of freedom has led to the development of spintronic devices such as spin-torque oscillators and spin-transfer torque magnetic random-access memories. In this development, spin pumping represents a convenient way to electrically detect magnetization dynamics. The effect originates from direct conversion of low-energy quantized spin waves in the magnet, known as magnons, into a flow of spins from the precessing magnet to adjacent leads. In this case, a secondary spin-charge conversion element, such as heavy metals with large spin Hall angle or multilayer layouts, is required to convert the spin current into a charge signal. Here, we report the experimental observation of charge pumping in which a precessing ferromagnet pumps a charge current, demonstrating direct conversion of magnons into high-frequency currents via the relativistic spin-orbit interaction. The generated electric current, unlike spin currents generated by spin-pumping, can be directly detected without the need of any additional spin-charge conversion mechanism. The charge-pumping phenomenon is generic and gives a deeper understanding of its reciprocal effect, the spin orbit torque, which is currently attracting interest for their potential in manipulating magnetic information.

Spin-orbit torques and anisotropic magnetization damping in skyrmion crystals

The length scale of the magnetization gradients in chiral magnets is determined by the relativistic Dzyaloshinskii-Moriya interaction. Thus, even conventional spin-transfer torques are controlled by the relativistic spin-orbit coupling in these systems, and additional relativistic corrections to the current-induced torques and magnetization damping become important for a complete understanding of the current-driven magnetization dynamics. We theoretically study the effects of reactive and dissipative homogeneous spin-orbit torques and anisotropic damping on the current-driven skyrmion dynamics in cubic chiral magnets. Our results demonstrate that spin-orbit torques play a significant role in the current-induced skyrmion velocity. The dissipative spin-orbit torque generates a relativistic Magnus force on the skyrmions, whereas the reactive spin-orbit torque yields a correction to both the drift velocity along the current direction and the transverse velocity associated with the Magnus force. The spin-orbit torque corrections to the velocity scale linearly with the skyrmion size, which is inversely proportional to the spin-orbit coupling. Consequently, the reactive spin-orbit torque correction can be the same order of magnitude as the nonrelativistic contribution. More importantly, the dissipative spin-orbit torque can be the dominant force that causes a deflected motion of the skyrmions if the torque exhibits a linear or quadratic relationship with the spin-orbit coupling. In addition, we demonstrate that the skyrmion velocity is determined by anisotropic magnetization damping parameters governed by the skyrmion size.

Phenomenology of current-induced spin-orbit torques

Currents induce magnetization torques via spin-transfer when the spin angular momentum is conserved or via relativistic spin-orbit coupling. Beyond simple models, the relationship between material properties and spin-orbit torques is not known. Here, we present a novel phenomenology of current-induced torques that is valid for any strength of intrinsic spin-orbit coupling. In

Gilbert damping in noncollinear ferromagnets

\rm Pt|Co|AlO_x

New Boundary-Driven Twist States in Systems with Broken Spatial Inversion Symmetry

, we demonstrate that the domain walls move in response to a novel relativistic dissipative torque that is dependent on the domain wall structure and that can be controlled via the Dzyaloshinskii-Moriya interaction. Unlike the non-relativistic spin-transfer torque, the new torque can, together with the spin-Hall effect in the Pt-layer, move domain walls by means of electric currents parallel to the walls.

Spin-orbit torques for current parallel and perpendicular to a domain wall

The precession and damping of a collinear magnetization displaced from its equilibrium are well described by the Landau-Lifshitz-Gilbert equation. The theoretical and experimental complexity of noncollinear magnetizations is such that it is not known how the damping is modified by the noncollinearity. We use first-principles scattering theory to investigate transverse domain walls (DWs) of the important ferromagnetic alloy Ni80Fe20 and show that the damping depends not only on the magnetization texture but also on the specific dynamic modes of Bloch and Néel DWs in ways that were not theoretically predicted. Even in the highly disordered Ni80Fe20 alloy, the damping is found to be remarkably nonlocal.