Deterministic, field-free switching of perpendicular magnetization is a key requirement for scalable and energy-efficient spintronic memory. Recent experiments have demonstrated threefold rotational ($3m$) symmetry-driven spin-orbit torque (SOT) switching in epitaxial (111)-oriented ${\mathrm{Tm}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (TmIG)/Pt bilayers, where the deterministic switching is intrinsically governed by the magnetocrystalline anisotropy (MCA) of TmIG. In this study, we employ micromagnetic simulations to investigate the role of the interfacial Dzyaloshinskii-Moriya interaction (DMI) on the switching behavior, which is governed by the same $3m$ crystal symmetry. We find that the DMI substantially reduces the effective anisotropy energy barrier by stabilizing a canted magnetization state, while simultaneously amplifying the symmetry-guided effective magnetic field arising from the intrinsic $3m$ MCA. This synergy between the DMI and the underlying crystal symmetry significantly accelerates the deterministic SOT switching process, resulting in an approximately 40% reduction in the magnetization switching relaxation time, with a distinct maximum reduction observed at an optimal DMI strength. These findings reveal a unique synergistic acceleration mechanism between the DMI and the $3m$ crystal symmetry, extending beyond the conventional symmetry-breaking role typically attributed to a DMI.

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• Dzyaloshinskii-Moriya interaction
• Magnetism
• Spin-orbit torque
• Spintronics