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

Quantitative characterization of spin-orbit torques in Pt/Co/Pt /Co/Ta/BTO heterostructure on the magnetization azimuthal angle dependence