Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Binding a hopfion in a chiral magnet nanodisk

Journal Article · · Physical Review. B
 [1];  [2];  [3]
  1. Univ. of California, Riverside, CA (United States); Chinese Academy of Sciences (CAS), Beijing (China)
  2. Univ. of California, Riverside, CA (United States)
  3. Univ. of New Hampshire, Durham, NH (United States)
Hopfions are three-dimensional (3D) topological textures characterized by the integer Hopf invariant $$Q_H$$. In this article, we present the realization of a zero-field, stable hopfion spin texture in a magnetic system consisting of a chiral magnet nanodisk sandwiched by two films with perpendicular magnetic anisotropy. The preimages of the spin texture and numerical calculations of $$Q_H$$ show that the hopfion has $$Q_H$$ = 1. Furthermore, another nontrivial state that includes a monopole-antimonopole pair (MAP) is also stabilized in this system. By applying an external magnetic field, hopfion and MAP states with the same polarization can be switched between each other. The topological transition between the hopfion and the MAP state involves a creation (annihilation) of the MAP and twist of the preimages. Our work paves the way to study nontrivial 3D topological spin textures and stimulates more investigations in the field of 3D spintronics.
Research Organization:
Energy Frontier Research Centers (EFRC) (United States). Spins and Heat in Nanoscale Electronic Systems (SHINES); Univ. of California, Riverside, CA (United States); Univ. of New Hampshire, Durham, NH (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Grant/Contract Number:
SC0012670; SC0016424
OSTI ID:
1566681
Alternate ID(s):
OSTI ID: 1483724
Journal Information:
Physical Review. B, Journal Name: Physical Review. B Journal Issue: 17 Vol. 98; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (47)

�ber die Abbildungen der dreidimensionalen Sph�re auf die Kugelfl�che journal December 1931
A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics journal January 1958
A unified field theory of mesons and baryons journal March 1962
The stability of vortex-like structures in uniaxial ferromagnets journal April 1999
Method for finding mechanism and activation energy of magnetic transitions, applied to skyrmion and antivortex annihilation journal November 2015
Topological Solitons book January 2010
Stable knot-like structures in classical field theory journal May 1997
Spontaneous skyrmion ground states in magnetic metals journal August 2006
Three-dimensional magnetization structures revealed with X-ray vector nanotomography journal July 2017
Three-dimensional nanomagnetism journal June 2017
Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals journal January 2015
Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids journal December 2009
Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids journal December 2016
Skyrmions on the track journal March 2013
Isolated optical vortex knots journal January 2010
Creation and dynamics of knotted vortices journal March 2013
Tying quantum knots journal January 2016
How superfluid vortex knots untie journal March 2016
Thermal stability and topological protection of skyrmions in nanotracks journal June 2017
Ground state search, hysteretic behaviour and reversal mechanism of skyrmionic textures in confined helimagnetic nanostructures journal November 2015
Target-skyrmions and skyrmion clusters in nanowires of chiral magnets journal January 2014
The design and verification of MuMax3 journal October 2014
Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals journal January 2018
An Expression of Hopf's Invariant as an Integral journal May 1947
Solitons, links and knots
  • Battye, Richard A.; Sutcliffe, Paul M.
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 455, Issue 1992 https://doi.org/10.1098/rspa.1999.0502
journal December 1999
Anisotropic Superexchange Interaction and Weak Ferromagnetism journal October 1960
Vortex rings in ferromagnets: Numerical simulations of the time-dependent three-dimensional Landau-Lifshitz equation journal November 2007
Knots in a Spinor Bose-Einstein Condensate journal May 2008
Topological Surface States in Three-Dimensional Magnetic Insulators journal October 2008
Skyrmion Knots in Frustrated Magnets journal June 2017
Direct Imaging of a Zero-Field Target Skyrmion and Its Polarity Switch in a Chiral Magnetic Nanodisk journal November 2017
Linking Numbers, Spin, and Statistics of Solitons journal December 1983
Knots as Stable Soliton Solutions in a Three-Dimensional Classical Field Theory journal November 1998
Propagating Magnetic Vortex Rings in Ferromagnets journal February 1999
Spin Transfer Torques in MnSi at Ultralow Current Densities journal December 2010
Stationary precession topological solitons with nonzero Hopf invariant in a uniaxial ferromagnet journal October 2008
Topological solitons journal December 2012
Magnetic vortex with skyrmionic core in a thin nanodisk of chiral magnets journal February 2013
Three-dimensional nanomagnetism text January 2017
Knots in a Spinor Bose-Einstein Condensate text January 2008
Stationary Precession Topological Solitons with Nonzero Hopf Invariant in a Uniaxial Ferromagnet text January 2008
Spin Transfer Torques in MnSi at Ultra-low Current Densities text January 2010
Magnetic Vortex with Skyrmionic Core in Thin Nanodisk of the Chiral Magnets text January 2012
Method for finding mechanism and activation energy of magnetic transitions, applied to skyrmion and antivortex annihilation text January 2015
How superfluid vortex knots untie text January 2015
Skyrmion knots in frustrated magnets text January 2017
Solitons, Links and Knots text January 1998

Cited By (6)

Spin, Orbital, Weyl and Other Glasses in Topological Superfluids journal December 2018
Generation and stability of structurally imprinted target skyrmions in magnetic multilayers journal September 2019
Launching a new dimension with 3D magnetic nanostructures journal January 2020
Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications journal January 2020
Spirit : Multifunctional framework for atomistic spin simulations journal June 2019
Current-Driven Dynamics of Magnetic Hopfions journal September 2019

Similar Records

Exact hopfion vortices in a 3D Heisenberg ferromagnet
Journal Article · Tue Jun 20 20:00:00 EDT 2023 · Physics Letters. A · OSTI ID:2318950

Interface‐Induced Stability of Nontrivial Topological Spin Textures: Unveiling Room‐Temperature Hopfions and Skyrmions
Journal Article · Sun Aug 17 20:00:00 EDT 2025 · Advanced Materials · OSTI ID:2584458

Three-Dimensional Dynamics of a Magnetic Hopfion Driven by Spin Transfer Torque
Journal Article · Wed Mar 25 20:00:00 EDT 2020 · Physical Review Letters · OSTI ID:1631266