Quantifying angular dependence of spin-orbit torques in Ta/CoFeB/MgO trilayers with perpendicular magnetic anisotropy

Abstract

The spin-orbit interactions in heavy-metal/ferromagnet heterostructures have attracted considerable attention because they provide an efficient way to manipulate the magnetization with strong current-driven spin-orbit torques (SOTs) via the spin Hall effect in the heavy metal or Rashba effect due to the symmetry breaking at the interface. Theoretical calculations predict no dependence of the SOTs on the out-of-plane angle of magnetization due to spin Hall effect, but Rashba effect induces a nontrivial angular dependence of SOTs. Quantitative measurements with adiabatic harmonic Hall technique have observed the angular dependence in Ta/CoFeB/MgO or $\mathrm{Pt}/\mathrm{Co}/\mathrm{Al}{\mathrm{O}}_{\mathrm{x}}$ with perpendicular magnetic anisotropy. However, this method is complicated because the signal consists of both anomalous and planar Hall contributions. In addition, the fitting of the measurement data is sensitive to the fitting parameters, particularly to the perpendicular anisotropy, in a certain angle region (40--70\ifmmode^\circ\else\textdegree\fi{}). To avoid this uncertainty, we have developed a scheme to quantify the angular dependence of SOTs based on the magneto-optic Kerr effect with field calibration. Without fitting procedures, we precisely determine the SOTs and their angle dependence on the magnetization orientation. We observe a strong angular dependence that is different from the previous experimental observations. Based on this strong dependence, we conclude that a Rashba effect at the same interface, that is responsible for the perpendicular magnetic anisotropy, is the dominant mechanism for the current-driven SOTs in this system.