Instantons in chiral magnets
Abstract
In this work, we exhaustively construct instanton solutions and elucidate their properties in one-dimensional antiferromagnetic chiral magnets based on the $$\textit{O}(3)$$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips called merons) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.
- Authors:
-
[1];
[4]
- Keio University, Kanagawa (Japan); RIKEN, Saitama (Japan); Univ. of Illinois, Chicago, IL (United States)
- Keio University, Kanagawa (Japan)
- Akita University (Japan); Keio University, Kanagawa (Japan); RIKEN, Saitama (Japan)
- Keio University, Kanagawa (Japan); RIKEN, Saitama (Japan)
- Publication Date:
- Research Org.:
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Org.:
- Japan Society for the Promotion of Science (JSPS); Ministry of Education, Culture, Sports, Science and Technology (MEXT); USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1800024
- Alternate Identifier(s):
- OSTI ID: 1605969
- Grant/Contract Number:
- FG02-01ER41195; S1511006; 18H01217; 18K03627; 19K03817; 16H03984; 15H05855; FG0201ER41195
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 101; Journal Issue: 10; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics
Citation Formats
Hongo, Masaru, Fujimori, Toshiaki, Misumi, Tatsuhiro, Nitta, Muneto, and Sakai, Norisuke. Instantons in chiral magnets. United States: N. p., 2020.
Web. doi:10.1103/physrevb.101.104417.
Hongo, Masaru, Fujimori, Toshiaki, Misumi, Tatsuhiro, Nitta, Muneto, & Sakai, Norisuke. Instantons in chiral magnets. United States. https://doi.org/10.1103/physrevb.101.104417
Hongo, Masaru, Fujimori, Toshiaki, Misumi, Tatsuhiro, Nitta, Muneto, and Sakai, Norisuke. Mon .
"Instantons in chiral magnets". United States. https://doi.org/10.1103/physrevb.101.104417. https://www.osti.gov/servlets/purl/1800024.
@article{osti_1800024,
title = {Instantons in chiral magnets},
author = {Hongo, Masaru and Fujimori, Toshiaki and Misumi, Tatsuhiro and Nitta, Muneto and Sakai, Norisuke},
abstractNote = {In this work, we exhaustively construct instanton solutions and elucidate their properties in one-dimensional antiferromagnetic chiral magnets based on the $\textit{O}(3)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips called merons) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.},
doi = {10.1103/physrevb.101.104417},
journal = {Physical Review B},
number = 10,
volume = 101,
place = {United States},
year = {Mon Mar 23 00:00:00 EDT 2020},
month = {Mon Mar 23 00:00:00 EDT 2020}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 11 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Symmetry Breaking through Bell-Jackiw Anomalies
journal, July 1976
- 't Hooft, G.
- Physical Review Letters, Vol. 37, Issue 1
Field Theories of Condensed Matter Physics
book, January 2013
- Fradkin, Eduardo
- Cambridge University Press
A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics
journal, January 1958
- Dzyaloshinsky, I.
- Journal of Physics and Chemistry of Solids, Vol. 4, Issue 4
Vacuum Periodicity in a Yang-Mills Quantum Theory
journal, July 1976
- Jackiw, R.; Rebbi, C.
- Physical Review Letters, Vol. 37, Issue 3
Critical phenomena of emergent magnetic monopoles in a chiral magnet
journal, May 2016
- Kanazawa, N.; Nii, Y.; Zhang, X. -X.
- Nature Communications, Vol. 7, Issue 1
Moriya’s anisotropic superexchange interaction, frustration, and Dzyaloshinsky’s weak ferromagnetism
journal, August 1992
- Shekhtman, L.; Entin-Wohlman, O.; Aharony, Amnon
- Physical Review Letters, Vol. 69, Issue 5
Thermodynamically stable magnetic vortex states in magnetic crystals
journal, December 1994
- Bogdanov, A.; Hubert, A.
- Journal of Magnetism and Magnetic Materials, Vol. 138, Issue 3
Instantons in QCD
journal, April 1998
- Schäfer, T.; Shuryak, E. V.
- Reviews of Modern Physics, Vol. 70, Issue 2
Nonreciprocal Magnons and Symmetry-Breaking in the Noncentrosymmetric Antiferromagnet
journal, July 2017
- Gitgeatpong, G.; Zhao, Y.; Piyawongwatthana, P.
- Physical Review Letters, Vol. 119, Issue 4
Instantons in the Higgs phase
journal, July 2005
- Eto, Minoru; Isozumi, Youichi; Nitta, Muneto
- Physical Review D, Vol. 72, Issue 2
Non-Abelian vortices on a cylinder: Duality between vortices and walls
journal, April 2006
- Eto, Minoru; Fujimori, Toshiaki; Isozumi, Youichi
- Physical Review D, Vol. 73, Issue 8
Towards an Effective Theory of Skyrmion Crystals
journal, February 2019
- Timofeev, V. E.; Sorokin, A. O.; Aristov, D. N.
- JETP Letters, Vol. 109, Issue 3
O(3) Nonlinear Model and the Topological Distinction between Integer- and Half-Integer-Spin Antiferromagnets in Two Dimensions
journal, August 1988
- Haldane, F. D. M.
- Physical Review Letters, Vol. 61, Issue 8
Topological properties and dynamics of magnetic skyrmions
journal, December 2013
- Nagaosa, Naoto; Tokura, Yoshinori
- Nature Nanotechnology, Vol. 8, Issue 12
Controlling the Dzyaloshinskii-Moriya interaction to alter the chiral link between structure and magnetism for
journal, May 2015
- Siegfried, S. -A.; Altynbaev, E. V.; Chubova, N. M.
- Physical Review B, Vol. 91, Issue 18
Two soluble models of an antiferromagnetic chain
journal, December 1961
- Lieb, Elliott; Schultz, Theodore; Mattis, Daniel
- Annals of Physics, Vol. 16, Issue 3
Single-band Hubbard model with spin-orbit coupling
journal, December 1983
- Kaplan, T. A.
- Zeitschrift f�r Physik B Condensed Matter, Vol. 49, Issue 4
Nonperturbative contributions from complexified solutions in models
journal, November 2016
- Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro
- Physical Review D, Vol. 94, Issue 10
Chiral Magnetic Soliton Lattice on a Chiral Helimagnet
journal, March 2012
- Togawa, Y.; Koyama, T.; Takayanagi, K.
- Physical Review Letters, Vol. 108, Issue 10
Resurgence in sine-Gordon quantum mechanics: exact agreement between multi-instantons and uniform WKB
journal, September 2015
- Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
- Journal of High Energy Physics, Vol. 2015, Issue 9
Conformal symmetry of trapped Bose-Einstein condensates and massive Nambu-Goldstone modes
journal, November 2017
- Ohashi, Keisuke; Fujimori, Toshiaki; Nitta, Muneto
- Physical Review A, Vol. 96, Issue 5
Decomposing instantons in two dimensions
journal, April 2012
- Nitta, Muneto; Vinci, Walter
- Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 17
Formation of incommensurate long-range magnetic order in the Dzyaloshinskii-Moriya antiferromagnet studied by neutron diffraction
journal, October 2017
- Mühlbauer, S.; Brandl, G.; Månsson, M.
- Physical Review B, Vol. 96, Issue 13
Skyrmion lattice in a two-dimensional chiral magnet
journal, September 2010
- Han, Jung Hoon; Zang, Jiadong; Yang, Zhihua
- Physical Review B, Vol. 82, Issue 9
Exact Classical Solution for the 't Hooft Monopole and the Julia-Zee Dyon
journal, September 1975
- Prasad, M. K.; Sommerfield, Charles M.
- Physical Review Letters, Vol. 35, Issue 12
Real-space observation of a two-dimensional skyrmion crystal
journal, June 2010
- Yu, X. Z.; Onose, Y.; Kanazawa, N.
- Nature, Vol. 465, Issue 7300
Magnetic structures and reorientation transitions in noncentrosymmetric uniaxial antiferromagnets
journal, December 2002
- Bogdanov, A. N.; Rößler, U. K.; Wolf, M.
- Physical Review B, Vol. 66, Issue 21
Solitons in the Higgs phase: the moduli matrix approach
journal, June 2006
- Eto, Minoru; Isozumi, Youichi; Nitta, Muneto
- Journal of Physics A: Mathematical and General, Vol. 39, Issue 26
Nonlinear Field Theory of Large-Spin Heisenberg Antiferromagnets: Semiclassically Quantized Solitons of the One-Dimensional Easy-Axis Néel State
journal, April 1983
- Haldane, F. D. M.
- Physical Review Letters, Vol. 50, Issue 15
The structure of the gauge theory vacuum
journal, August 1976
- Callan, C. G.; Dashen, R. F.; Gross, D. J.
- Physics Letters B, Vol. 63, Issue 3
Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
journal, March 2015
- Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
- Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 3
Skyrmion Lattice in a Chiral Magnet
journal, February 2009
- Muhlbauer, S.; Binz, B.; Jonietz, F.
- Science, Vol. 323, Issue 5916
Symmetry, Structure, and Dynamics of Monoaxial Chiral Magnets
journal, November 2016
- Togawa, Yoshihiko; Kousaka, Yusuke; Inoue, Katsuya
- Journal of the Physical Society of Japan, Vol. 85, Issue 11
Dzyaloshinskii-Moriya domain walls in magnetic nanotubes
journal, February 2016
- Goussev, Arseni; Robbins, J. M.; Slastikov, Valeriy
- Physical Review B, Vol. 93, Issue 5
New Nonperturbative Methods in Quantum Field Theory: From Large- N Orbifold Equivalence to Bions and Resurgence
journal, October 2016
- Dunne, Gerald V.; Ünsal, Mithat
- Annual Review of Nuclear and Particle Science, Vol. 66, Issue 1
Resurgence structure to all orders of multi-bions in deformed SUSY quantum mechanics
journal, August 2017
- Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro
- Progress of Theoretical and Experimental Physics, Vol. 2017, Issue 8
Unwinding of a Skyrmion Lattice by Magnetic Monopoles
journal, May 2013
- Milde, P.; Kohler, D.; Seidel, J.
- Science, Vol. 340, Issue 6136
Valence-bond and spin-Peierls ground states of low-dimensional quantum antiferromagnets
journal, April 1989
- Read, N.; Sachdev, Subir
- Physical Review Letters, Vol. 62, Issue 14
Control of Dzyaloshinskii-Moriya interaction in Mn1−xFexGe: a first-principles study
journal, August 2015
- Koretsune, Takashi; Nagaosa, Naoto; Arita, Ryotaro
- Scientific Reports, Vol. 5, Issue 1
Continuity and Resurgence: Towards a continuum definition of the model
journal, January 2013
- Dunne, Gerald V.; Ünsal, Mithat
- Physical Review D, Vol. 87, Issue 2
Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions
journal, July 2011
- Heinze, Stefan; von Bergmann, Kirsten; Menzel, Matthias
- Nature Physics, Vol. 7, Issue 9
Spontaneous skyrmion ground states in magnetic metals
journal, August 2006
- Rößler, U. K.; Bogdanov, A. N.; Pfleiderer, C.
- Nature, Vol. 442, Issue 7104, p. 797-801
Two-dimensional Schrödinger symmetry and three-dimensional breathers and Kelvin-ripple complexes as quasi-massive-Nambu-Goldstone modes
journal, August 2017
- Takahashi, Daisuke A.; Ohashi, Keisuke; Fujimori, Toshiaki
- Physical Review A, Vol. 96, Issue 2
Field-Induced Commensurate-Incommensurate Phase Transition in a Dzyaloshinskii-Moriya Spiral Antiferromagnet
journal, June 1997
- Zheludev, A.; Maslov, S.; Shirane, G.
- Physical Review Letters, Vol. 78, Issue 25
Interfacial control of Dzyaloshinskii-Moriya interaction in heavy metal/ferromagnetic metal thin film heterostructures
journal, November 2016
- Ma, Xin; Yu, Guoqiang; Li, Xiang
- Physical Review B, Vol. 94, Issue 18
Pseudoparticle solutions of the Yang-Mills equations
journal, October 1975
- Belavin, A. A.; Polyakov, A. M.; Schwartz, A. S.
- Physics Letters B, Vol. 59, Issue 1
Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models
journal, February 2019
- Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro
- Journal of High Energy Physics, Vol. 2019, Issue 2
Theory of the Helical Spin Crystal: A Candidate for the Partially Ordered State of MnSi
journal, May 2006
- Binz, B.; Vishwanath, A.; Aji, V.
- Physical Review Letters, Vol. 96, Issue 20
Computation of the quantum effects due to a four-dimensional pseudoparticle
journal, December 1976
- 't Hooft, G.
- Physical Review D, Vol. 14, Issue 12
Oxygen-enabled control of Dzyaloshinskii-Moriya Interaction in ultra-thin magnetic films
journal, April 2016
- Belabbes, Abderrezak; Bihlmayer, Gustav; Blügel, Stefan
- Scientific Reports, Vol. 6, Issue 1
Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model
journal, June 2014
- Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
- Journal of High Energy Physics, Vol. 2014, Issue 6
Intermediate phase in the spiral antiferromagnet
journal, January 2002
- Chovan, J.; Papanicolaou, N.; Komineas, S.
- Physical Review B, Vol. 65, Issue 6
Gauged sigma models and magnetic Skyrmions
journal, January 2019
- Schroers, Bernd
- SciPost Physics, Vol. 7, Issue 3
Easy plane baby Skyrmions
journal, December 2010
- Jäykkä, Juha; Speight, Martin
- Physical Review D, Vol. 82, Issue 12
Magnetic Skyrmions at Critical Coupling
journal, January 2020
- Barton-Singer, Bruno; Ross, Calum; Schroers, Bernd J.
- Communications in Mathematical Physics
Anisotropic Superexchange Interaction and Weak Ferromagnetism
journal, October 1960
- Moriya, Tôru
- Physical Review, Vol. 120, Issue 1
Fractional vortex molecules and vortex polygons in a baby Skyrme model
journal, June 2013
- Kobayashi, Michikazu; Nitta, Muneto
- Physical Review D, Vol. 87, Issue 12
A proof of part of Haldane's conjecture on spin chains
journal, July 1986
- Affleck, Ian; Lieb, Elliott H.
- Letters in Mathematical Physics, Vol. 12, Issue 1
Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model
journal, February 1983
- Haldane, F. D. M.
- Physics Letters A, Vol. 93, Issue 9
Dynamic solitons in antiferromagnets (Review Article)
journal, July 2018
- Galkina, E. G.; Ivanov, B. A.
- Low Temperature Physics, Vol. 44, Issue 7
Exact resurgent trans-series and multibion contributions to all orders
journal, May 2017
- Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro
- Physical Review D, Vol. 95, Issue 10