Recent demonstrations of magnetization switching induced by in-plane current injection in heavy metal/ferromagnetic heterostructures have drawn increasing attention to spin torques based on orbital-to-spin momentum transfer. The symmetry, magnitude and origin of spin-orbit torques (SOTs), however, remain a matter of debate. Here we report on the three-dimensional vector measurement of SOTs in AlOx/Co/Pt and MgO/CoFeB/Ta trilayers using harmonic analysis of the anomalous and planar Hall effects. We provide a general scheme to measure the amplitude and direction of SOTs as a function of the magnetization direction. Based on space and time inversion symmetry arguments, we demonstrate that heavy metal/ferromagnetic layers allow for two different SOTs having odd and even behaviour with respect to magnetization reversal. Such torques include strongly anisotropic field-like and spin transfer-like components, which depend on the type of heavy metal layer and annealing treatment. These results call for SOT models that go beyond the spin Hall and Rashba effects investigated thus far.

Spin-orbit torques induced by spin Hall and interfacial effects in heavy metal/ferromagnetic bilayers allow for a switching geometry based on in-plane current injection. Using this geometry, we demonstrate deterministic magnetization reversal by current pulses ranging from 180~ps to ms in Pt/Co/AlOx dots with lateral dimensions of 90~nm. We characterize the switching probability and critical current $I_c$ as function of pulse length, amplitude, and external field. Our data evidence two distinct regimes: a short-time intrinsic regime, where $I_c$ scales linearly with the inverse of the pulse length, and a long-time thermally assisted regime where $I_c$ varies weakly. Both regimes are consistent with magnetization reversal proceeding by nucleation and fast propagation of domains. We find that $I_c$ is a factor 3-4 smaller compared to a single domain model and that the incubation time is negligibly small, which is a hallmark feature of spin-orbit torques

Magnetoresistive effects are usually invariant on inversion of the magnetization direction. In non-centrosymmetric conductors, however, nonlinear resistive terms can give rise to a current dependence that is quadratic in the applied voltage and linear in the magnetization. Here we demonstrate that such conditions are realized in simple bilayer metal films where the spin-orbit interaction and spin-dependent scattering couple the current-induced spin accumulation to the electrical conductivity. We show that the longitudinal resistance of Ta|Co and Pt|Co bilayers changes when reversing the polarity of the current or the sign of the magnetization. This unidirectional magnetoresistance scales linearly with current density and has opposite sign in Ta and Pt, which we associate with the modification of the interface scattering potential induced by the spin Hall effect in these materials. Our results suggest a route to control the resistance and detect magnetization switching in spintronic devices using a two-terminal geometry, which applies also to heterostructures including topological insulators.T he effects of the magnetization on the electric conductivity of metals have been studied for a long time 1 , providing understanding of fundamental phenomena associated with electron transport and magnetism as well as a multitude of applications in sensor technology. The anisotropic magnetoresistance (AMR)-the change of the resistance of a material on rotation of the magnetization-is a prominent manifestation of spin-orbit coupling and spin-dependent conductivity in bulk ferromagnets 2,3 . In thin-film heterostructures, the additional possibility of orienting the magnetization of stacked ferromagnetic layers parallel or antiparallel to each other gives rise to the celebrated giant magnetoresistance (GMR) effect 4,5 , which has played a major role in all modern developments of spintronics. Together with the early spin-injection experiments 6,7 , the study of GMR revealed how non-equilibrium spin accumulation at the interface between ferromagnetic (FM) and normal metal (NM) conductors governs the propagation of spin currents 8-11 and, ultimately, the conductivity of multilayer systems 10,12 .Recently, it has been shown that significant spin accumulation at a FM/NM interface can be achieved using a current-in-plane (CIP) geometry owing to the spin Hall effect (SHE) in the NM (ref. 13). When the FM is a metal and NM is a heavy element such as Pt or Ta, the spin accumulation is strong enough to induce magnetization reversal of nanometre-thick FM layers at current densities of the order of j = 10 7 -10 8 A cm −2 (refs 14-16). When the FM is an insulator, such as yttrium iron garnet, the SHE causes an unusual magnetoresistance associated with the back-flow of a spin current into the NM when the spin accumulation μ s ∼ (j ×ẑ) is aligned with the magnetization of the FM, which increases the conductivity of the NM due to the inverse SHE (refs 17-20). This so-called spin Hall magnetoresistance (SMR) is characterized by R y < R z ≈ R x ...

We present harmonic transverse voltage measurements of current-induced thermoelectric and spin-orbit torque (SOT) effects in ferromagnet/normal metal bilayers, in which thermal gradients produced by Joule heating and SOT coexist and give rise to ac transverse signals with comparable symmetry and magnitude. Based on the symmetry and field-dependence of the transverse resistance, we develop a consistent method to separate thermoelectric and SOT measurements. By addressing first ferromagnet/light metal bilayers with negligible spin-orbit coupling, we show that in-plane current injection induces a vertical thermal gradient whose sign and magnitude are determined by the resistivity difference and stacking order of the magnetic and nonmagnetic layers.We then study ferromagnet/heavy metal bilayers with strong spin-orbit coupling, showing that second harmonic thermoelectric contributions to the transverse voltage may lead to a significant overestimation of the antidamping SOT. We find that thermoelectric effects are very strong in Ta(6nm)/Co(2.5nm) and negligible in Pt(6nm)/Co(2.5nm) bilayers. After including these effects in the analysis of the transverse voltage, we find that the antidamping SOTs in these bilayers, after normalization to the magnetization volume, are comparable to those found in thinner Co layers with perpendicular magnetization, whereas the field-like SOTs are about an order of magnitude smaller.

Electrical currents at the surface or edge of a topological insulator are intrinsically spin-polarized. We show that such surface/edge currents can be used to switch the orientation of a molecular magnet weakly coupled to the surface or edge of a topological insulator. For the edge of a two-dimensional topological insulator as well as for the surface of a three-dimensional topological insulator the application of a well-chosen surface/edge current can lead to a complete polarization of the molecule if the molecule's magnetic anisotropy axis is appropriately aligned with the current direction. For a generic orientation of the molecule a nonzero but incomplete polarization is obtained. We calculate the probability distribution of the magnetic states and the switching rates as a function of the applied current.