Spinons, Solitons, and Breathers in Quasi-One-Dimensional Magnets

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Spinons, Solitons, and Breathers in
Quasi-One-Dimensional Magnets

• Collin Broholm
• Johns Hopkins University
• NIST Center for Neutron Research

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condensed matter
Standard model
New Physics

• Single energy scale controls all
• Simple Linear Response to
• Impurities
• Electric fields
• Magnetic fields
• Temperature
• No phase transition below
• melting point

• Low energy degrees of freedom
• Non-linear Response to
• Impurities
• Electric fields
• Magnetic fields
• Temperature
• Phase transitions
• below the melting point

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Spin degrees of freedom Magnetism
Ti V Cr Mn Fe Co Ni Cu
Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm
U Np Pu Am Cm
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No interactions Magnetic Ideal gas
FeBr(C44H28N4)
Susceptibility data for paramagnetic salt
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Coulomb Pauli Heisenberg
Coulomb interactions plus Pauli principle split
4-fold spin degeneracy
The level scheme is reproduced by Heisenberg
Exchange Hamiltonian
Triplet gnd. State J lt 0
Singlet gnd. State J gt 0
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Interactions cooperative phenomena
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Overview

• Introduction
• Why we like magnets
• Neutron Scattering
• Magnetic spaghetti
• Strange excitations in a spin chain
• The experimental result
• The theoretical explanation Spinons
• Are spinons for real?
• Theoretical expectations in a field
• High field neutron scattering
• Can we tie them together?
• Experimental observation of bound spinons
• Quantum sine-Gordon model
• Conclusions and outlook

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Acknowledgements
D. H. Reich JHU G. Aeppli UCL C. P.
Landee Clarke University M. M. Turnbull Clarke
University M. Kenzelmann JHU NIST M. B.
Stone Penn State University Y. Chen LANL D. C.
Dender NIST Y. Qiu NIST Univ. Maryland K.
Lefmann Risø National Lab C. Rische Univ. of
Copenhagen
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Inelastic Magnetic Neutron Scattering

• We can measure dispersion relations
• We determine structure through transition rate

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SPINS cold neutron spectrometer at NCNR
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Spin waves in antiferromagnet
La2CuO4
Coldea et al. PRL (2001)
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Can quantum fluctuations break order?
1. Assume Neel order, derive spin wave dispersion
relation 2. Calculate the reduction in
staggered magnetization due to quantum
fluctuations 3. If then Neel
order is an inconsistent assumption
There can be no Neel order in one dimension
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Copper pyrazine dinitrate
Hammar et al. (1999)
Cu(C4H4N2)(NO3)2
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Neutron Scattering from Spin-1/2 chain
Stone et al., PRL (2003)
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Disintegration of a spin flip
Spinon
Spinon
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Fermions in spin ½ chain
Uniform spin-1/2 chain (XY case for simplicity)
Jordan-Wigner transformation
Diagonalizes H
e/J
Non interacting fermionic lattice gas
q (p)
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From band-structure to bounded continuum
J
e/J
w
h
Q (p)
q (p)
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Neutron Scattering
Stone et al. (2003).
Exact two-spinon cross-section
Karbach et al. 2000
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Neutron Data Two-Spinon Cross section
1.0
Stone et al., PRL (2003)
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Are spinons for real?
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Spinons in magnetized spin- ½ chain
Broholm et al. (2002)
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Uniform Spin ½ chain
0.0 T
Stone et al. (2003)
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Uniform Spin ½ chain
8.7 T


Stone et al. (2003)
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Neutron Scattering
Pentium Scattering
Stone et al. (2003)
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Can we tie them together?
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Why staggered field yields bound states
Zero field state quasi-long range AFM order
Without staggered field distant spinons dont
interact
With staggered field solitons separate good
from bad domains, which leads to interactions
and bound states
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Spin-½ chain with two spins per chain unit
Landee et al. (1986)
CuCl2.2(dimethylsulfoxide)
Oshikawa and Affleck (1997)
The staggered field is given by
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H0 T
Kenzelmann et al. (2003)
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H11 T
Kenzelmann et al. (2003)
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Bound states from 2-spinon continuum
Kenzelmann et al. (2003)
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Sine-Gordon mapping of spin-1/2 chain
Effective staggered uniform field spin
hamiltonian
Spin operators are represented through a phase
field relative to incommensurate
quasi-long-range order with Lagrangian density

• This is sine-Gordon model with interaction term
  proportional to hs
• Spectrum consists of
• Solitons, anti-solitons
• Breather bound states

Oshikawa and Affleck (1997)
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Bound states from 2-spinon continuum
Breathers n1,2 and possibly 3
Soliton, M
Kenzelmann et al. (2003)
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Testing sine-Gordon predictions
Neel order
0
Kenzelmann et al. (2003)
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What we learned about spin-1/2 chains

• A quantum liquid without spin order at T0
• Fundamental excitations are spinon pairs
• Spinons form a fermionic liquid with field
  dependent chemical potential
• A staggered field confines spinons
• masses and structure factors consistent with
  sine-Gordon solitons and breathers

Publications and viewgraphs at http//www.pha.jhu.
edu/broholm/homepage/
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Are there quantum liquids for Dgt1
What is special about D1? Order in one part of
lattice does not constrain surroundings
Maybe, when there is frustration and/or low
connectivity
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Better Instruments at Existing Sources
MACS Cold Neutron Spectrometer at NCNR To be
completed June 2005
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New and Brighter Neutron Sources
US 1.4 MW Spallation Neutron Source To be
completed in 2006