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Register a new userFirst Principles Study of Angular Dependence of Spin-Orbit Torque in Pt/Co and Pd/Co Bilayers
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Spin-orbit torque (SOT) induced by spin Hall and interfacial effects in heavy metal(HM)/ferromagnetic(FM) bilayers has recently been employed to switch the magnetization direction using in-plane current injection. In this paper, using the Keldysh Greens function approach and first principles electronic structure calculations we determine the Field-Like (FL) and Damping-Like (DL) components of the SOT for the HM/Co (HM = Pt, Pd) bilayers. Our approach yields the angular dependence of both the FL- and DL-SOT on the magnetization direction without assuming a priori their angular form. Decomposition of the SOT into the Fermi sea and Fermi surface contributions reveals that the SOT is dominated by the latter. Due to the large lattice mismatch between the Co and the HM we have also determined the effect of tensile biaxial strain on both the FL- and DL-SOT components. The calculated dependence of FL- and DL-SOT on the HM thickness is overall in good agreement with experiment. The dependence of the SOT with the position of the Fermi level suggests that the DL-SOT dominated by the Spin Hall effect of the bulk HM.
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Current-induced torques in ultrathin Co/Pt bilayers were investigated using an electrically driven FMR technique. The angle dependence of the resonances, detected by a rectification effect as a voltage, were analysed to determine the symmetries and relative magnitudes of the spin-orbit torques. Both anti-damping (Slonczewski) and field-like torques were observed. As the ferromagnet thickness was reduced from 3 to 1 nm, the sign of the field-like torque reversed. This observation is consistent with the emergence of a Rashba spin orbit torque in ultra-thin bilayers.
The manipulation of the magnetization by spin-orbit torques (SOTs) has recently been extensively studied due to its potential for efficiently writing information in magnetic memories. Particular attention is paid to non-centrosymmetric systems with space inversion asymmetry, where SOTs emerge even in single-layer materials. The half-metallic half-Heusler PtMnSb is an interesting candidate for studies of this intrinsic SOT. Here, we report on the growth and epitaxial properties of PtMnSb thin films and PtMnSb/Pt bilayers deposited on MgO(001) substrates by dc magnetron co-sputtering at high temperature in ultra-high vacuum. The film properties were investigated by x-ray diffraction, x-ray reflectivity, atomic force microscopy, and electron microscopy. Thin PtMnSb films present a monocrystalline C1b phase with (001) orientation, coexisting at increasing thickness with a polycrystalline phase with (111) texture. Films thinner than about 5 nm grow in islands, whereas thicker films grow layer-by-layer, forming a perfect MgO/PtMnSb interface. The thin PtMnSb/Pt bilayers also show island growth and a defective transition zone, while thicker films grow layer-by-layer and Pt grows epitaxially on the half-Heusler compound without significant interdiffusion.
The magnetic properties of (111)-oriented Rh/Co/Pt and Pd/Co/Pt multilayers are investigated by first-principles calculations. We focus on the interlayer exchange coupling, and identify thicknesses and composition where a typical ferromagnet or a synthetic antiferromagnet across the spacer layer is formed. All systems under investigation show a collinear magnetic intralayer order, but the Dzyaloshinskii-Moriya interaction (DMI) is rather strong for Pd-based systems, so that single magnetic skyrmions can be expected. In general, we find a strong sensitivity of the magnetic parameters (especially the DMI) in Rh-based systems, but Pd-based multilayers are less sensitive to structural details.
We have studied the spin Hall magnetoresistance (SMR), the magnetoresistance within the plane transverse to the current flow, of Pt/Co bilayers. We find that the SMR increases with increasing Co thickness: the effective spin Hall angle for bilayers with thick Co exceeds the reported values of Pt when a conventional drift-diffusion model is used. An extended model including spin transport within the Co layer cannot account for the large SMR. To identify its origin, contributions from other sources are studied. For most bilayers, the SMR increases with decreasing temperature and increasing magnetic field, indicating that magnon-related effects in the Co layer play little role. Without the Pt layer, we do not observe the large SMR found for the Pt/Co bilayers with thick Co. Implementing the effect of the so-called interface magnetoresistance and the textured induced anisotropic scattering cannot account for the Co thickness dependent SMR. Since the large SMR is present for W/Co but its magnitude reduces in W/CoFeB, we infer its origin is associated with a particular property of Co.
We have studied the spin orbit torque (SOT) in Pt/Co/Ir multilayers with 3 repeats of the unit structure. As the system exhibits oscillatory interlayer exchange coupling (IEC) with varying Ir layer thickness, we compare the SOT of films when the Co layers are coupled ferromagnetically and antiferromagnetically. SOT is evaluated using current induced shift of the anomalous Hall resistance hysteresis loops. A relatively thick Pt layer, serving as a seed layer to the multilayer, is used to generate spin current via the spin Hall effect. In the absence of antiferromagnetic coupling, the SOT is constant against the applied current density and the corresponding spin torque efficiency (i.e. the effective spin Hall angle) is $sim$0.09, in agreement with previous reports. In contrast, for films with antiferromagnetic coupling, the SOT increases with the applied current density and eventually saturates. The SOT at saturation is a factor of $sim$15 larger than that without the antiferromagnetic coupling. The spin torque efficiency is $sim$5 times larger if we assume the net total magnetization is reduced by a factor of 3 due to the antiferromagnetic coupling. Model calculations based on the Landau Lifshitz Gilbert equation show that the presence of antiferromagnetic coupling can increase the SOT but the degree of enhancement is limited, in this case, to a factor of 1.2-1.4. We thus consider there are other sources of SOT, possibly at the interfaces, which may account for the highly efficient SOT in the uncompensated synthetic anti-ferromagnet (SAF) multilayers.
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