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  • Featured in Physics
  • Letter
  • Open Access

Controlling knot topology in magnetic hopfions via spin-orbit torque

Shoya Kasai1,*, Shun Okumura1,2,3,4, and Yukitoshi Motome1,†

  • *Contact author: kasai@aion.t.u-tokyo.ac.jp
  • †Contact author: motome@ap.t.u-tokyo.ac.jp
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APS Open Sci. 1, L000007 – Published 29 April, 2026

DOI: https://doi.org/10.1103/ngvg-h27j

Abstract

Knots formed by the intertwining of strings have attracted broad interest across various scientific disciplines owing to their rich topology. This concept has recently gained increasing importance in condensed matter physics, as exemplified by a magnetic hopfion labeled by a topological invariant called the Hopf number H. 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 not only indicate potential applications of hopfions in SOT-driven multilevel memory devices, but also provide a paradigm for the dynamical control of knot topology.

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synopsis

Hopfions at the Breaking Point

Published 29 April, 2026

Simulations show that knot-like magnetic structures called hopfions can be pulled apart—a capability that could be harnessed for spintronic memory devices.

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See Also

Nonequilibrium dynamics of magnetic hopfions driven by spin-orbit torque

Shoya Kasai, Shun Okumura, and Yukitoshi Motome
Phys. Rev. B 113, 134445 (2026)

Article Text

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Outline

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APS Open Sci. 1, L000007– Published 29 April, 2026
Vol. 1
  • Received 28 November 2025
  • Accepted 26 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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