Quantum Coherence in Magnets

1
Quantum Coherence in Magnets
Collin Broholm Johns Hopkins University and NIST
Center for Neutron Research
G. Aeppli M. Azuma R. Bewley W. J. L. Buyers Y.
Chen D. F. DiTusa D. V. Ferraris
C. D. Frost S. Ishiwata T. Ito M.
Kenzelmann T. Lectka K. Oka T. G. Perring Y.
Qiu
D. H. Reich J. Rittner M. B. Stone H. Takagi M.
Takano H. Yardimci I. A. Zalianyak
2
Outline

• Introduction
• Spin order versus quantum order
• How to distinguish using neutrons
• Quantum Order in 0-3 dimensions
• 0. Spin trimers in La4Cu3MoO12
• 1. Haldane spin-1 chains in Y2BaNiO5
• 2. Frustrated bi-layers in PHCC
• 3. 3D Shastry-Sutherland lattice CuHpCl
• Summary and Frontiers

3
Signs of Spin Order
Ferromagnetic EuO
?
4
A brief story of Antiferromangetism
1970 Nobel Prize in Physics to Hannes Alfvén and
Louis Néel
L. Néel 1904-2000
L. Néel From Nobel lecture (1970).
5
Staggered magnetization or QM singlet
1962 Nobel Prize in Physics
L. D. Landau 1908-1968
L. D. Landau from Phys. Zs. UdSSR (1933).
6
Experimental Evidence for Néel order
C. G. Shull 1915-2001
1994 Nobel Prize in Physics to B. N. Brockhouse
and C. G. Shull
7
Is Landaus vision of an AFM possible?
8
Inelastic Neutron Scattering
9
NIST Center for Neutron Research
10
SPINS cold neutron spectrometer at NCNR
11
Focusing analyzer system on SPINS
12
MAPS Spectrometer at ISIS in UK
13
Outline

• Introduction
• Spin order versus quantum order
• How to distinguish using neutrons
• Quantum Order in 0-3 dimensions
• 0. Spin trimers in La4Cu3MoO12
• 1. Haldane spin-1 chains in Y2BaNiO5
• 2. Frustrated bi-layers in PHCC
• 3. 3D Shastry-Sutherland lattice in CuHpCl
• Summary and Frontiers

14
La4Cu3MoO12 A lattice of spin-1/2 trimers
Magnetic susceptibility
(Azuma et. al., PRB 62 R3588)
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Spectroscopy of spin trimers
Phonons
Yiming Qiu et al. cond-mat/0205018
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Frustrated quantum spin triangles
Yiming Qiu et al. cond-mat/0205018
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Strongly fluctuating spin trimer AFM
Yiming Qiu et al. cond-mat/0205018
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Outline

• Introduction
• Spin order versus quantum order
• How to distinguish using neutrons
• Quantum Order in 0-3 dimensions
• 0. Spin trimers in La4Cu3MoO12
• 1. Haldane spin-1 chains in Y2BaNiO5
• 2. Frustrated bi-layers in PHCC
• 3. 3D Shastry-Sutherland lattice in CuHpCl
• Summary and Frontiers

19
Unconventional magnetism in NENP

• Negative Curie Weiss temperature indicates AFM
  interactions
• No phase transition and small for

20
Haldane gap in Y2BaNiO5
1-cosq
S(qw) d(w-e(q))
e(q)
T. Ito, K. Oka and H. Takagi
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Macroscopic singlet ground state of S1 chain

• Magnets with 2Snz have a nearest neighbor
  singlet covering
• with full lattice symmetry.

• This is exact ground state for spin projection
  Hamiltonian

• Excited states are propagating bond triplets
  separated from
• the ground state by an energy gap

Haldane PRL 1983 Affleck, Kennedy, Lieb, and
Tasaki PRL 1987
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Two length scales in a quantum magnet
Triplet Coherence length length of coherent
triplet wave packet
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Coherence in a fluctuating system
Short range G.S. spin correlations
Coherent triplet propagation
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Coherence and correlation lengths versus T
Damle and Sachdev theory of triplon scattering
Including impurity scattering
Jolicoeur and Golinelly Quantum non-linear s
model
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Macroscopic singlet ground state of S1 chain

• Magnets with 2Snz have a nearest neighbor
  singlet covering
• with full lattice symmetry.

• This is exact ground state for spin projection
  Hamiltonian

• Excited states are propagating bond triplets
  separated from
• the ground state by an energy gap

Haldane PRL 1983 Affleck, Kennedy, Lieb, and
Tasaki PRL 1987
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Form factor for chain-end spin
Kenzelmann et al. PRL (2003)
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Outline

• Introduction
• Spin order versus quantum order
• How to distinguish using neutrons
• Quantum Order in 0-3 dimensions
• 0. Spin trimers in La4Cu3MoO12
• 1. Haldane spin-1 chains in Y2BaNiO5
• 2. Frustrated bi-layers in PHCC
• 3. 3D Shastry-Sutherland lattice in CuHpCl
• Summary and Frontiers

28
Singlet Ground state in PHCC
c/cmax
J112.5 K a0.6
Daoud et al., PRB (1986).
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Structure is consistent with spin chains
PHCC C4H12N2Cu2Cl6
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Is PHCC quasi-one-dimensional?
hw (meV)
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A Frustrated Route to Quantum 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
diverges if on planes
in Q-space
Frustration can produce local soft modes that
destabilize Neel order and favor quantum order
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Geometrical Interpretation
Weak connectivity Order in one part of lattice
does not constrain surroundings
This can occur in higher dimensions when there is
frustration and/or low coordination number, z.
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Neutrons can detect frustration
The first w -moment of scattering cross section
equals Fourier transform of bond energies
gt

lt

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

S
S
and/or

J

d
r
r
d
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Measuring Bond Energies
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Frustrated bonds in PHCC
Green colored bonds increase ground state energy
The corresponding interactions are frustrated
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Outline

• Introduction
• Spin order versus quantum order
• How to distinguish using neutrons
• Quantum Order in 0-3 dimensions
• 0. Spin trimers in La4Cu3MoO12
• 1. Haldane spin-1 chains in Y2BaNiO5
• 2. Frustrated bi-layers in PHCC
• 3. 3D Shastry-Sutherland lattice in CuHpCl
• Summary and Frontiers

37
Unconventional magnetism in CuHpCl

• Negative QCW indicates AFM interactions
• No phase transition and
• Spin ladder model consistent with c(T)

38
CuHpCl hydrogenous single crystals
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Acid test for one-dimensionality

Q // to chain
Q to chain
40
Detailed bond energy distribution
c
(101)
(001)
a
(100)
Point size First moment
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Frustrated three dimensional spin liquid
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Conclusions

• Two visions for the behavior of substances with
  AFM interactions between spins
• Néel Two interpenetrating anti-parallel
  ferromagnets
• Landau singlet formation, cooperative
  paramagnetism
• Neutron diffraction confirms Néels order
• Inelastic neutron scattering shows that quantum
  order is also possible in 0-3 dimensions.
• Frustration and weak connectivity can help to
  stabilize quantum order for D 2
• Some materials labeled as 1D magnets based on
  bulk data may form a far more interesting class
  of 2D and 3D quantum ordered systems.