---
title: Field Derivative Torque (FDT)
url: https://www.emergentmind.com/topics/field-derivative-torque-fdt
type: topic
---

# Field Derivative Torque (FDT)

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 [1401.8088; 2103.10037; 1612.00194]. 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 $\partial_t \mathbf{B}_{\rm THz}$ [1904.11768; 2408.05510; 2409.08541]. 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 $\mathbf{m}\times(\mathbf{m}\times\boldsymbol{\sigma})$ [1401.8088; 2103.10037]. 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 [1904.11768; 2409.08541]. 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 [2005.04000].

| 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.

Source: https://www.emergentmind.com/topics/field-derivative-torque-fdt