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Mn$_3$Sn, a metallic antiferromagnet with an anti-chiral 120$^\circ$ spin structure, generates intriguing magneto-transport signatures such as a large anomalous Hall effect, spin-polarized current with novel symmetries, anomalous Nernst effect, and magneto-optic Kerr effect. When grown epitaxially as MgO(110)[001]$\parallel$ Mn$_3$Sn($0\bar{1}\bar{1}0$)[0001], Mn$_3$Sn experiences a uniaxial tensile strain, which changes the bulk six-fold anisotropy landscape to a perpendicular magnetic anisotropy with two stable states. In this work, we investigate the field-assisted spin orbit-torque (SOT)-driven response of the order parameter in single-domain Mn$_3$Sn with uniaxial tensile strain. We find that for a non-zero external magnetic field, the order parameter can be switched between the two stable states if the magnitude of the input current is between two field-dependent critical currents. Below the lower critical current, the order parameter exhibits a stationary state in the vicinity of the initial stable state. On the other hand, above the higher critical current, the order parameter shows oscillatory dynamics which could be tuned from the 100's of megahertz to the gigahertz range. We obtain approximate expressions of the two critical currents and find them to agree very well with the numerical simulations for experimentally relevant magnetic fields. We also obtain unified functional form of the switching time versus the input current for different magnetic fields. Finally, we show that for lower values of Gilbert damping ($\alpha \leq 2\times 10^{-3}$), the critical currents and the final steady states depend significantly on the damping constant. The numerical and analytic results presented in our work can be used by both theorists and experimentalists to understand the SOT-driven order dynamics in PMA Mn$_3$Sn and design future experiments and devices., Comment: 14 pages, 17 figures

We numerically investigate and develop analytic models for both the DC and pulsed spin-orbit-torque (SOT)-driven response of order parameter in single-domain Mn$_3$Sn, which is a metallic antiferromagnet with an anti-chiral 120$^\circ$ spin structure. We show that DC currents above a critical threshold can excite oscillatory dynamics of the order parameter in the gigahertz to terahertz frequency spectrum. Detailed models of the oscillation frequency versus input current are developed and found to be in excellent agreement with the numerical simulations of the dynamics. In the case of pulsed excitation, the magnetization can be switched from one stable state to any of the other five stable states in the Kagome plane by tuning the duration or the amplitude of the current pulse. Precise functional forms of the final switched state versus the input current are derived, offering crucial insights into the switching dynamics of Mn$_3$Sn. The readout of the magnetic state can be carried out via either the anomalous Hall effect, or the recently demonstrated tunneling magnetoresistance in an all-Mn$_3$Sn junction. We also discuss possible disturbance of the magnetic order due to heating that may occur if the sample is subject to large currents. Operating the device in pulsed mode or using low DC currents reduces the peak temperature rise in the sample due to Joule heating. Our predictive modeling and simulation results can be used by both theorists and experimentalists to explore the interplay of SOT and the order dynamics in Mn$_3$Sn, and to further benchmark the device performance., Comment: 13 pages, 13 figures