Antidamping-like (ADL) spin-orbit torques (SOTs) exhibit the efficiency of magnetization switching in recent experiments, especially in topological insulator/ferromagnet (TI/FM) heterostructures where a giant SOT has been reported even at room temperature. While most experiments have confirmed that the giant ADL torque arises from TI surface states via the well-known Edelstein effect, theoretical understanding of the physical origin of ADL SOT is challenging because the ADL SOT from the Edelstein effect is quite weak in linear-response theory. In this paper, in sharp contrast to the existing linear-response theory, we develop a nonlinear Edelstein effect theory as the mechanism of generating a large ADL torque in the nonlinear response regime. We unveil that mixed quantum metrics, defined in the extended parameter space spanned by momentum and magnetization, can contribute an intrinsic ADL SOT via interband coherence mechanisms (injection, shift, and anomalous), and the resulting SOT can exceed the linear one by several orders of magnitude around the Dirac points. This nonlinear ADL SOT provides an alternative explanation of the observed giant SOT in recent experiments, and also offers us a new route to probe quantum metrics.

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• Spin-orbit torque
• Spintronics
• Topological insulators
• Quantum master equation