Permanent current from non-commutative spin algebra

TL;DR

This paper demonstrates that non-commutative spin algebra induces a spontaneous electric current in a nano-scale ring with three ferromagnets, linking spin chirality to observable electrical effects.

Contribution

It reveals a novel mechanism where non-commutative spin algebra causes spontaneous currents, explaining the chirality-driven anomalous Hall effect.

Findings

Spontaneous current arises from non-commutative spin algebra.

Current is proportional to magnetization vector chirality.

Provides a natural explanation for the anomalous Hall effect.

Abstract

We show that a spontaneous electric current is induced in a nano-scale conducting ring just by putting three ferromagnets. The current is a direct consequence of the non-commutativity of the spin algebra, and is proportional to the non-coplanarity (chirality) of the magnetization vectors. The spontaneous current gives a natural explanation to the chirality-driven anomalous Hall effect.