Controlling Knot Topology in Magnetic Hopfions via Spin-orbit Torque

TL;DR

This paper demonstrates that spin-orbit torque can dynamically control the topology of magnetic hopfions by manipulating their Hopf number, enabling topological transitions and potential applications in memory devices.

Contribution

It introduces a method to control hopfion topology using spin-orbit torque, including the splitting of high-Hopf-number hopfions into lower ones, which was not previously achievable.

Findings

SOT induces splitting of high-H hopfions into lower-H ones.

Hierarchy of instabilities governs topological transitions.

Effective tension model explains hopfion dynamics.

Abstract

Knots, characterized by topological invariants called the Hopf number $H$, arise from the intertwining of strings and exhibit diverse configurations. The knot structures have recently been observed in condensed matters, as examplified by a magnetic hopfion, sparking interest in controlling their topology. Here, we show that spin-orbit torque (SOT) enables dynamic manipulation of the Hopf number of magnetic hopfions. We investigate the SOT-driven evolution of hopfions, revealing the splitting of a high-$H$ hopfion into multiple lower-$H$ ones, a process that can be quantified by an effective tension picture. Comparative analysis across different $H$ uncovers a hierarchy of instabilities that dictates these dynamical topological transitions. These findings establish SOT as a powerful tool for controlling hopfion topology, paving the way for potential applications in topological memory devices.