DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Nonlinear soliton confinement in weakly coupled antiferromagnetic spin chains

Abstract

In this work, we analyze the low-energy dynamics of quasi-one-dimensional, large-$$\textit{S}$$ quantum antiferromagnets with easy-axis anisotropy, using a semiclassical nonlinear sigma model. The saddle point approximation leads to a sine-Gordon equation which supports soliton solutions. These correspond to the movement of spatially extended domain walls. Long-range magnetic order is a consequence of a weak interchain coupling. Below the ordering temperature, the coupling to nearby chains leads to an energy cost associated with the separation of two domain walls. From the kink-antikink two-soliton solution, we compute the effective confinement potential. At distances large compared to the size of the solitons the potential is linear, as expected for pointlike domain walls. At small distances the gradual annihilation of the solitons weakens the effective attraction and renders the potential quadratic. From numerically solving the effective one-dimensional Schrödinger equation with this nonlinear confinement potential we compute the soliton bound state spectrum. We apply the theory to CaFe2O4, an anisotropic $$\textit{S}$$ = 5/2 magnet based upon antiferromagnetic zigzag chains. Using inelastic neutron scattering, we are able to resolve seven discrete energy levels for spectra recorded slightly below the Néel temperature $$T_N$$ ≈ 200 K. These modes are well described by our nonlinear confinement model in the regime of large spatially extended solitons.

Authors:
 [1];  [2];  [3]; ORCiD logo [4]; ORCiD logo [4]; ORCiD logo [5]
  1. Univ. of Edinburgh, Scotland (United Kingdom); Science and Technology Facilities Council (STFC), Oxford (United Kingdom). Rutherford Appleton Lab. (RAL)
  2. Univ. of Edinburgh, Scotland (United Kingdom)
  3. Rutgers Univ., Piscataway, NJ (United States)
  4. Science and Technology Facilities Council (STFC), Oxford (United Kingdom). Rutherford Appleton Lab. (RAL)
  5. Science and Technology Facilities Council (STFC), Oxford (United Kingdom). Rutherford Appleton Lab. (RAL); Univ. College London (United Kingdom)
Publication Date:
Research Org.:
Rutgers Univ., Piscataway, NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC); Engineering and Physical Sciences Research Council (EPSRC); Science and Technology Facilities Council (STFC)
OSTI Identifier:
1800461
Grant/Contract Number:  
FG02-07ER46382; EP/P013449/1
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 102; Journal Issue: 2; 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

Lane, H., Stock, C., Cheong, S.-W., Demmel, F., Ewings, R. A., and Krüger, F. Nonlinear soliton confinement in weakly coupled antiferromagnetic spin chains. United States: N. p., 2020. Web. doi:10.1103/physrevb.102.024437.
Lane, H., Stock, C., Cheong, S.-W., Demmel, F., Ewings, R. A., & Krüger, F. Nonlinear soliton confinement in weakly coupled antiferromagnetic spin chains. United States. https://doi.org/10.1103/physrevb.102.024437
Lane, H., Stock, C., Cheong, S.-W., Demmel, F., Ewings, R. A., and Krüger, F. Wed . "Nonlinear soliton confinement in weakly coupled antiferromagnetic spin chains". United States. https://doi.org/10.1103/physrevb.102.024437. https://www.osti.gov/servlets/purl/1800461.
@article{osti_1800461,
title = {Nonlinear soliton confinement in weakly coupled antiferromagnetic spin chains},
author = {Lane, H. and Stock, C. and Cheong, S.-W. and Demmel, F. and Ewings, R. A. and Krüger, F.},
abstractNote = {In this work, we analyze the low-energy dynamics of quasi-one-dimensional, large-$\textit{S}$ quantum antiferromagnets with easy-axis anisotropy, using a semiclassical nonlinear sigma model. The saddle point approximation leads to a sine-Gordon equation which supports soliton solutions. These correspond to the movement of spatially extended domain walls. Long-range magnetic order is a consequence of a weak interchain coupling. Below the ordering temperature, the coupling to nearby chains leads to an energy cost associated with the separation of two domain walls. From the kink-antikink two-soliton solution, we compute the effective confinement potential. At distances large compared to the size of the solitons the potential is linear, as expected for pointlike domain walls. At small distances the gradual annihilation of the solitons weakens the effective attraction and renders the potential quadratic. From numerically solving the effective one-dimensional Schrödinger equation with this nonlinear confinement potential we compute the soliton bound state spectrum. We apply the theory to CaFe2O4, an anisotropic $\textit{S}$ = 5/2 magnet based upon antiferromagnetic zigzag chains. Using inelastic neutron scattering, we are able to resolve seven discrete energy levels for spectra recorded slightly below the Néel temperature $T_N$ ≈ 200 K. These modes are well described by our nonlinear confinement model in the regime of large spatially extended solitons.},
doi = {10.1103/physrevb.102.024437},
journal = {Physical Review. B},
number = 2,
volume = 102,
place = {United States},
year = {Wed Jul 22 00:00:00 EDT 2020},
month = {Wed Jul 22 00:00:00 EDT 2020}
}

Works referenced in this record:

Structure and magnetic properties of epitaxial CaFe2O4 thin films
journal, June 2020


Field-induced gap in Cu benzoate and other S = 1 2 antiferromagnetic chains
journal, July 1999


Spinon, soliton, and breather in the spin- 1 2 antiferromagnetic chain compound KCuGaF 6
journal, November 2015


Theory of two-dimensional quantum Heisenberg antiferromagnets with a nearly critical ground state
journal, May 1994


Effect of the Magnetic Field on the des Cloizeaux-Pearson Spin-Wave Spectrum
journal, June 1977

  • Ishimura, N.; Shiba, H.
  • Progress of Theoretical Physics, Vol. 57, Issue 6
  • DOI: 10.1143/PTP.57.1862

Emergence of soliton chirality in a quantum antiferromagnet
journal, November 2005

  • Braun, Hans-Benjamin; Kulda, Jiri; Roessli, Bertrand
  • Nature Physics, Vol. 1, Issue 3
  • DOI: 10.1038/nphys152

What is the spin of a spin wave?
journal, October 1981


Magnetic properties of a quasi-one-dimensional S =1/2 antiferromagnet: Copper benzoate
journal, February 1996


The two-spinon transverse structure factor of the gapped Heisenberg antiferromagnetic chain
journal, August 2008

  • Caux, Jean-Sébastien; Mossel, Jorn; Castillo, Isaac Pérez
  • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2008, Issue 08
  • DOI: 10.1088/1742-5468/2008/08/P08006

Longitudinal and Transverse Zeeman Ladders in the Ising-Like Chain Antiferromagnet BaCo 2 V 2 O 8
journal, January 2015


Sine-Gordon kink-antikink generation on spatially periodic potentials
journal, April 1992


The structure of calcium ferrite
journal, April 1957


Quantum spin dynamics of the antiferromagnetic linear chain in zero and nonzero magnetic field
journal, August 1981


The sine-Gordon equation, Tchebyshev nets, and harmonic maps
journal, June 1986


The OSIRIS diffractometer and polarisation-analysis backscattering spectrometer
journal, December 2002

  • Andersen, K. H.; Mart�n y. Marero, D.; Barlow, M. J.
  • Applied Physics A: Materials Science & Processing, Vol. 74, Issue 0
  • DOI: 10.1007/s003390201804

Two-spinon dynamic structure factor of the one-dimensional s= Heisenberg antiferromagnet
journal, May 1997

  • Karbach, Michael; Müller, Gerhard; Bougourzi, A. Hamid
  • Physical Review B, Vol. 55, Issue 18
  • DOI: 10.1103/PhysRevB.55.12510

Unconventional Field-Induced Spin Gap in an S = 1 / 2 Chiral Staggered Chain
journal, February 2019


Superdense Matter: Neutrons or Asymptotically Free Quarks?
journal, May 1975


Remarks on Bloch's Method of Sound Waves applied to Many-Fermion Problems
journal, July 1950


An Exactly Soluble Model of a Many‐Fermion System
journal, September 1963

  • Luttinger, J. M.
  • Journal of Mathematical Physics, Vol. 4, Issue 9
  • DOI: 10.1063/1.1704046

Quantum magnets show their hand
journal, December 2005


Quantum Phase Transitions
book, January 2011


Kink-antikink interactions in the double sine-Gordon equation
journal, March 1986


Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
journal, June 2013

  • Mourigal, Martin; Enderle, Mechthild; Klöpperpieper, Axel
  • Nature Physics, Vol. 9, Issue 7
  • DOI: 10.1038/nphys2652

A model unified field equation
journal, March 1962


Dyon Analogs in Antiferromagnetic Chains
journal, August 1986


Spinon confinement and a sharp longitudinal mode in Yb2Pt2Pb in magnetic fields
journal, March 2019


Bound Spinons in an Antiferromagnetic S = 1 / 2 Chain with a Staggered Field
journal, July 2004


Excitation Hierarchy of the Quantum Sine-Gordon Spin Chain in a Strong Magnetic Field
journal, July 2004


The crystal structure of calcium ferrite and β calcium chromite
journal, December 1956


Disorder and magnetic excitations in CaC r x F e 2 x O 4 ( x = 0 , 0.5 )
journal, January 2020


Spinon confinement in a quasi-one-dimensional anisotropic Heisenberg magnet
journal, August 2017


Electronic states and magnetic properties of edge-sharing Cu-O chains
journal, March 1998


Soliton approach to spin-Peierls antiferromagnets:  Large-scale numerical results
journal, December 1998


Orphan Spins in the S = 5 2 Antiferromagnet CaFe 2 O 4
journal, December 2017


Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E 8 Symmetry
journal, January 2010


Peierls instability in Heisenberg chains
journal, December 1974


Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973

  • Kosterlitz, J M; Thouless, D J
  • Journal of Physics C: Solid State Physics, Vol. 6, Issue 7, p. 1181-1203
  • DOI: 10.1088/0022-3719/6/7/010

Dynamical structure factor in copper benzoate and other spin-1/2 antiferromagnetic chains
journal, August 2003


Spinon confinement in the one-dimensional Ising-like antiferromagnet SrCo 2 V 2 O 8
journal, April 2015


Spin susceptibility and superexchange interaction in the antiferromagnet CuO
journal, December 2003


Tomonaga–Luttinger liquid behavior and spinon confinement in YbAlO3
journal, February 2019


Zur Theorie der Metalle: I. Eigenwerte und Eigenfunktionen der linearen Atomkette
journal, March 1931


Field-Induced Gap in S = 1 / 2 Antiferromagnetic Chains
journal, October 1997


Direct Observation of Field-Induced Incommensurate Fluctuations in a One-Dimensional S = 1 / 2 Antiferromagnet
journal, September 1997


Dynamical effects of phonons on soliton binding in spin-Peierls systems
journal, October 1998


Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies
journal, September 1999


Solitary Magnons in the S = 5 2 Antiferromagnet CaFe 2 O 4
journal, June 2016


Magnetic Phase Equilibrium in Chromium-Substituted Calcium Ferrite
journal, August 1967