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

1
Spinons, Solitons, and Breathers in
Quasi-One-Dimensional Magnets

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

2
Acknowledgements
G. Aeppli UCL C. D. Batista Los Alamos Y. Chen
LANL D. C. Dender NIST M. Kenzelmann JHU
NIST C. P. Landee Clarke University K. Lefmann
Risø National Lab Y. Qiu NIST Univ.
Maryland D. H. Reich JHU C. Rische Univ. of
Copenhagen M. B. Stone Penn State University M.
M. Turnbull Clarke University
3
Outline

• Introduction to spin-1/2 chains
• Materials properties
• Neutron Scattering
• Spin dynamics under varying conditions
• H0 Two spinon continuum
• Tgt0 Quantum critical scaling
• Hgt0 Adjusting the spinon chemical potential
• hsgt0 Spinons form solitons and breathers
• Conclusions

4
Spin-1/2 chain preliminaries

• Simple Hamiltonian complex properties
• Good model materials and experimental tools
• Integrable through Bethe Ansatz
• Ground state energy
• Equal time correlation function
• Quantum critical
• Exact results for dynamic spin correlations

5
Copper pyrazine dinitrate
Hammar et al. (1999)
Cu(C4H4N2)(NO3)2
6
Magnetic Neutron Scattering
NIST Center for Neutron Research
7
Neutron Scattering from Spin-1/2 chain
Stone et al., PRL (2003)
8
Disintegration of a spin flip
Flip a spin-1/2 DS1
DS1/2
DS1/2
Spinon
Spinon
9
From band-structure to bounded continuum
J
e/J
w
h
Q (p)
q (p)
10
Neutron Scattering
Stone et al. (2003).
Exact two-spinon cross-section
Karbach et al. 2000
11
Quantum Critical Regime
12
Quantum Critical Spin-1/2 chain
1
2
3
4
5
0
Damle and Huse PRL (2002)
13
Finite T scaling at the QCP
Exact low energy scaling form is known for
spin-1/2 chain
From it follow expressions for the critical qp
response
And for the q-integrated local response
H. J. Schultz PRB (1986)
14
Critical qp response of spin-1/2 chain
Dender Ph. D. thesis JHU (1997)
15
Local response of spin-1/2 chain
Dender Ph. D. thesis JHU (1997)
16
Spin-½ chain in uniform field
17
Spinons in magnetized spin- ½ chain
Broholm et al. (2002)
18
Uniform Spin ½ chain
0.0 T
Stone et al. (2003)
19
Uniform Spin ½ chain
8.7 T


Stone et al. (2003)
20
Diagonalization of spin-½ chain in a field

Stone et al. (2003)
21
Neutron Scattering
Exact diagonalization
Stone et al. (2003)
22
Spin-½ chain in staggered field
23
Spin-½ chain with two spins per chain unit
Landee et al. (1986)
CuCl2.2(dimethylsulfoxide)
Xia and Riseborough (1988)
Oshikawa and Affleck (1997)

24
H0 T
Kenzelmann et al. (2003)
25
H11 T
Kenzelmann et al. (2003)
26
Bound states from 2-spinon continuum
Kenzelmann et al. (2003)
27
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
28
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)
Xia and Riseborough (1988)
29
Bound states from 2-spinon continuum
Breathers n1,2 and possibly 3
Soliton, M
Kenzelmann et al. (2003)
30
Testing sine-Gordon predictions
Neel order
Kenzelmann et al. (2003)
31
Comparison to exact diagonalization
Kenzelmann et al (2005)
32
Conclusions S½ Chain in Uniform Field

• H0 data well described by exact two-spinon
  continuum scattering
• Tgt0 Quantum Critical regime
• Hgt0
• Incommensurate correlations from shifted fermi
  points
• Gapless excitation at qp and qp-2pm
• Neutron scattering data in excellent agreement
  with finite chain calculations

Publications and viewgraphs at http//www.pha.jhu.
edu/broholm/homepage/
33
Conclusions S½ Chain in Staggered Field

• Staggered g-tensor and DM interaction inherent to
  multi-atom cell and produce effective staggered
  field
• Staggered field yields bound states
• Features described by sine-Gordon model
• Relative energies of bound states at qp and p-2p
  m
• Relative intensities of breather excitations
• Field dependent incommensurability
• Excellent experimental realization of
• quantum sine-Gordon model

Publications and viewgraphs at http//www.pha.jhu.
edu/broholm/homepage/