Quantitative characterization of spin-orbit torques in Pt/Co/Pt/Co/Ta/BTO heterostructures due to the magnetization azimuthal angle dependence

Substantial understanding of spin-orbit interactions in heavy- metal (HM)/ferromagnet ( FM) heterostructures is crucial in developing spin-orbit torque (SOT) spintronics devices utilizing spin Hall and Rashba effects. Though the study of SOT effective field dependence on the out- of- plane magnetization angle has been relatively extensive, the understanding of in- plane magnetization angle dependence remains unknown. Here, we analytically propose a method to compute the SOT effective fields as a function of the in- plane magnetization angle using the harmonic Hall technique in perpendicular magnetic anisotropy (PMA) structures. Two different samples with PMA, a Pt/Co/Pt/Co/Ta/BaTiO3 (BTO) test sample and a Pt/Co/Pt/Co/Ta reference sample, are studied using the derived formula. Our measurements reveal that only the dampinglike field of the test sample with a BTO capping layer exhibits an in- plane magnetization angle dependence, while no angular dependence is found in the reference sample. The presence of the BTO layer in the test sample, which gives rise to a Rashba effect at the interface, is ascribed as the source of the angular dependence of the dampinglike field.