A Landau‐Lifshitz‐Gilbert‐Type equation and torsion effects on the dynamics of magnetization

Abstract

Based on the non‐relativistic regime of electrons described by a Dirac equation coupled to a torsion pseudo‐vector, we study the dynamics of magnetization and how it may be affected by the presence of this (background) torsion field. The latter describes some anisotropy of the bulk and it may be accounted for in two ways: by means of a minimal coupling in a covariant derivative endowed with spin connection and a gauge magnetic field; in addition, through a non‐minimal interaction term with the spin density. We show, within this framework, that it is possible to attain a version of the Landau‐Lifshitz equation in presence of the torsion background where its effects are included, re‐enforcing that torsion corresponds to a geometric anisotropy with relevant unfolds on the spin coupling mechanism. We also conclude that the torsion terms can open up two important landscapes in the magnetization dynamics: one of them, related with a damping effect; the other, related with the screw dislocation that gives us a global effect like a sharped‐helix damping. The whole effort here is then to pursue an investigation of torsion in connection with the precession dynamics of the magnetization. image