Order parameter dynamics in Mn$_3$Sn driven by DC and pulsed spin-orbit torques

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.