Influence of domain wall anisotropy on the current-induced hysteresis loop shift for quantification of the Dzyaloshinskii-Moriya interaction

Using several material systems with various magnitudes of the interfacial Dzyaloshinskii-Moriya interaction (DMI), we elucidate a critical influence of domain wall (DW) anisotropy on the current-induced hysteresis loop shift scheme widely employed to determine the magnitude of the Dzyaloshinskii-Moriya effective field (${H}_{\mathrm{DMI}}$). Taking into account the DW anisotropy in the analysis of the hysteresis loop shift, which has not been included in the original model [Phys. Rev. B 93, 144409 (2016)], we show that it provides quantitative agreement of ${H}_{\mathrm{DMI}}$ with that determined from an asymmetric bubble expansion technique for small DMI material systems. For large DMI systems, the DW anisotropy gives rise to nonlinearity in the response of spin-orbit torque efficiency to the in-plane magnetic field, from which ${H}_{\mathrm{DMI}}$ can be determined. The consequence of the directions of DW motion in the Hall device on the current-induced shift of the hysteresis loop is also discussed. The present findings deliver important insights for reliable evaluation of DMI, which are of significance in spintronics with chiral objects.