Field Derivative Torque (FDT)

• Field Derivative Torque (FDT) is a concept describing distinct torque forms, such as the field-like torque in spin-transfer studies and a relativistic term in ultrafast THz magnetism.
• In spin-transfer and spin–orbit torque experiments, FDT typically refers to a component proportional to m×p that acts as an effective magnetic field, contrasting with the damping-like term.
• In ultrafast THz magnetism, FDT denotes a relativistic, spin–orbit-driven torque proportional to the time derivative of the applied magnetic field, influencing rapid magnetization dynamics.

Searching arXiv for recent and foundational papers on field-derivative torque / field-like torque. Field Derivative Torque (FDT) denotes different torque structures in different research literatures. In spin-transfer and spin–orbit-torque studies, FDT is conventionally synonymous with the field-like torque (FLT), the component proportional to $\mathbf{m}\times\mathbf{p}$ or $\mathbf{m}\times\boldsymbol{\sigma}$ that acts as an effective field along a reference polarization direction [(Taniguchi et al., 2014); (Arun et al., 2021); (Abert et al., 2016)]. In ultrafast THz magnetism, by contrast, FDT denotes a relativistic torque proportional to the time derivative of the applied magnetic field, typically entering the Landau–Lifshitz–Gilbert equation as a correction to the effective field proportional to $\partial_t \mathbf{B}_{\rm THz}$ (Mondal et al., 2019, Dutta et al., 2024, Dutta et al., 2024). The coexistence of these usages is a central feature of the term.

1. Terminological scope and principal definitions

The literature covered here uses the same acronym for distinct torque symmetries and dynamical mechanisms. In magnetic tunnel junctions, spin-torque oscillators, and spin-Hall nano-oscillators, FDT is identified with the field-like torque, often written as the component proportional to $\mathbf{m}\times\mathbf{p}$ or $\mathbf{m}\times\boldsymbol{\sigma}$, in contrast to the damping-like Slonczewski term $\mathbf{m}\times(\mathbf{p}\times\mathbf{m})$ or $$\mathbf{m}\times(\mathbf{m}\times\boldsymbol{\sigma})$$ [(Taniguchi et al., 2014); (Arun et al., 2021)]. In THz-driven antiferromagnets and ferrimagnets, FDT is a relativistic spin–orbit-driven term that couples the magnetization to the temporal slope of the applied field and therefore vanishes for time-independent fields (Mondal et al., 2019, Dutta et al., 2024). A further, conceptually distinct usage appears in Weng’s complex-octonion framework, where FDT refers to the torque-derivative vector $N_1$ that arises from the octonion force equation (Weng, 2020).

Context	Torque form	Representative papers
Spin-transfer / spin–orbit torque	$\tau_{\rm FL}\propto \mathbf{m}\times\mathbf{p}$ or $\mathbf{m}\times\boldsymbol{\sigma}$	[1401.