Spinons, Solitons, and Breathers in Quasi-one-dimensional Magnets

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Spinons, Solitons, and Breathers in
Quasi-one-dimensional Magnets
Frustrated Magnetism Heavy Fermions

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

SCES 2004 Karlsruhe, Germany 7/29/2004
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Overview

• Introduction
• Frustrated magnetism in insulators
• Order from competing interactions
• Near critical systems
• Quantum liquids
• Metals with frustrated magnetism
• Spinel vanadates
• Spinels with rare earth ions
• Frustration in heavy fermions?
• Conclusions

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Acknowledgements
Ni3V2O8 G. Lawes, M. Kenzelmann, N. Rogado, K.
H. Kim, G. A. Jorge, R. J. Cava, A. Aharony, O.
Entin-Wohlman, A. B. Harris, T. Yildirim, Q. Z.
Huang, S. Park, and A. P. Ramirez, and Yiming
Qiu ZnCr2O4 S.-H. Lee, W. Ratcliff II, S.-W.
Cheong, T. H. Kim, Q. Huang, and G.
Gasparovic PHCC M. B. Stone, I. A. Zaliznyak,
Daniel H. Reich PrxBi2-xRu2O7 J. van Duijn, K.H.
Kim, N. Hur, D. T. Adroja, M. Adams, Q. Z. Huang,
S.-W. Cheong, and T.G. Perring V2O3 Wei Bao,
G. Aeppli, C.D. Frost, T. G. Pering, P. Metcalf,
J. M. Honig
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Destabilizing Static LRO
Weak connectivity Order in one part of lattice
does not constrain surroundings
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Effective low dimensionality from frustration
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
diverges if on planes
in Q-space
Frustration weak connectivity can produce
local soft modes that destabilize Neel order
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Renormalized Classical
T/J
H, P, x, 1/S
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Magnetism on a kagome Staircase
Ni3V2O8

• S½ spinons above small gap
• S8 No order or spin glass
• Ising no phase transition
• 3-state Potts model
• is critical at T0

Coleman, Huse, Chandra, Sachdev
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Order from kagome critical state
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Non-collinear order from competition
Spiral reduces Amplitude modulation
Anisotropy overpowers NNN interaction
Spine ANNNI model
Tlt9 K
Tlt6.5K
Tlt2.1 K
Kenzelmann et al. (2004)
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From quasi-elastic to local resonance
T30 K
T1.5 K
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Near Quantum Critical
Renormalized Classical
T/J
?
H, P, x, 1/S
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Frustration and short range correlations
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TNltTltQCW Short range correlations
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TNltTltQCW Dynamic Short Range Order

• Points of interest
• 2p/Qr01.4
• ? nn. AFM correlations
• No scattering at low Q
• ? satisfied tetrahedra

S.-H. Lee et al. PRL (2000)
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TltTN Resonant mode and spin waves

• Points of interest
• 2p/Qr01.4
• ? nn. AFM correlations
• No scattering at low Q
• ? satisfied tetrahedra
• Resonance for hw J
• Low energy spin waves

S.-H. Lee et al. PRL (2000)
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Average form factor for AFM hexagons
S.-H. Lee et al. Nature (2002)
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Sensitivity to impurities near quantum criticality
TN
Tf
Ratcliff et al. PRB (2002)
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Low T spectrum sensitive to bond disorder
5 Cd
0 0.5 1.0 1.5
2.0 2.5
Q (Å-1)
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T/J
H, P, x, 1/S
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Singlet Ground state in PHCC
J112.5 K a0.6
c/cmax
Daoud et al., PRB (1986).
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2D dispersion relation
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Neutrons can reveal frustration
The first w -moment of scattering cross section
equals Fourier transform of bond energies

• bond energies are small if
  small
• Positive terms correspond to frustrated bonds

gt

lt
S
S
and/or

J

d
r
r
d
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Frustrated bonds in PHCC
Green colored bonds increase ground state energy
The corresponding interactions are frustrated
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Near Quantum Critical
T/J
?
H, P, x, 1/S
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Colossal T-linear C(T) in PrxBi2-xRu2O7
K. H. Kim et al.
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Resilient non-dispersive spectrum
T90 K
J. Van Duijn et al. (2004)
T30 K
hw (meV)
T1.5 K
Q (Å-1)
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Properties of disordered two-level system
Generalized susceptibility for two level system,
D
Generalized susceptibility with distributed
splitting,
How to derive the distribution function from
scattering law
How to derive specific heat from distribution
function
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Identify Scaling form for S(w)
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Colossal g from inhomogeneously split doublet

• What is the role of frustration?
• It allows high DOS without
• order far above percolation
• What do we learn from this?
• Be aware of non-kramers
• doublets in alloys
• There may be interesting
• magneto-elastic effects
• associated with frustrated
• non-kramers systems

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Metal Insulator transition in V2O3
Mott
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Short Range order in Paramagnetic Insulator
B.Z.
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Spin wave dispersion Exchange constants
0.6 meV
-22 meV
-22 meV
Bao et al. Unpublished
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Orbital occupancy orderMagnetic order
Orbital fluctuationsMagnetic SRO
TltTC
TgtTC
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Orbital frustration in V2O3?

• An interesting possibility
• Bonds occupy kagome lattice
• Ising model on kagome lattice
• has no phase transition whence
• the low TC
• Orbital occupational order
• eventually occurs because it
• enables lower energy spin state

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Competing Interactions in URu2Si2?
T22 K
Wiebe et al. (2004)
Broholm et al. (1991)
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Effective low dimensionality of CeCu6
H.v. Lohneysen et al. (2000)
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Conclusions

• Frustration is a central aspect of SCES
• Frustrated insulators display
• Reduced TN with complex phase diagrams
• Composite spin degrees of freedom
• Magneto-elastic effects close to criticality
• Hypersensitivity to quenched disorder
• Singlet ground state phases are common when
  symmetry low
• Metals with Frustrated magnetism
• Large g from quenched disorder in frustrated
  non-kramers doublet systems
• Orbital frustration may help to expose MIT in
  V2O3
• A possible role of frustration in U and Ce based
  HF systems