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Mn 3 Sn, a metallic antiferromagnet with an anti-chiral 120° 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]∥Mn3Sn(01¯1¯0)[0001], Mn3Sn experiences a uniaxial tensile strain, which changes the bulk sixfold anisotropy to a twofold perpendicular magnetic anisotropy (PMA). Here, we investigate the field-assisted spin–orbit-torque (SOT)-driven dynamics in single-domain Mn3Sn with PMA. We find that for non-zero external magnetic fields, the magnetic octupole moment of Mn3Sn can be switched between the two stable states if the input current is between two field-dependent critical currents. Below the lower critical current, the magnetic octupole moment exhibits a stationary state in the vicinity of the initial stable state. On the other hand, above the higher critical current, the magnetic octupole moment shows oscillatory dynamics which could, in principle, be tuned from the 100s of megahertz to the terahertz range. We obtain approximate analytic expressions of the two critical currents that agree very well with the numerical simulations for experimentally relevant magnetic fields. We also obtain a unified functional form of the switching time vs the input current for different magnetic fields. Finally, we show that for lower values of Gilbert damping (α≲2×10−3), the critical currents and the final steady states depend significantly on α. 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 Mn3Sn and design future experiments and devices. 

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 Mn3Sn, which is a metallic antiferromagnet with an anti-chiral 120° 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 vs 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 vs the input current are derived, offering crucial insights into the switching dynamics of Mn3Sn. 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-Mn3Sn 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 a 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 Mn3Sn and to further benchmark the device performance. 

We present Pasado, a technique for synthesizing precise static analyzers for Automatic Differentiation. Our technique allows one to automatically construct a static analyzer specialized for the Chain Rule, Product Rule, and Quotient Rule computations for Automatic Differentiation in a way that abstracts all of the nonlinear operations of each respective rule simultaneously. By directly synthesizing an abstract transformer for the composite expressions of these 3 most common rules of AD, we are able to obtain significant precision improvement compared to prior works which compose standard abstract transformers together suboptimally. We prove our synthesized static analyzers sound and additionally demonstrate the generality of our approach by instantiating these AD static analyzers with different nonlinear functions, different abstract domains (both intervals and zonotopes) and both forward-mode and reverse-mode AD. We evaluate Pasado on multiple case studies, namely soundly computing bounds on a neural network’s local Lipschitz constant, soundly bounding the sensitivities of financial models, certifying monotonicity, and lastly, bounding sensitivities of the solutions of differential equations from climate science and chemistry for verified ranges of initial conditions and parameters. The local Lipschitz constants computed by Pasado on our largest CNN are up to 2750× more precise compared to the existing state-of-the-art zonotope analysis. The bounds obtained on the sensitivities of the climate, chemical, and financial differential equation solutions are between 1.31 − 2.81× more precise (on average) compared to a state-of-the-art zonotope analysis.