Quantum Magnets in High Magnetic Fields

1
Quantum Magnets in High Magnetic Fields
Collin Broholm Johns Hopkins University and NIST
Center for Neutron Research

• Introduction
• Quantum Magnetism
• Neutron Scattering
• Field effects in gapless systems
• Field induced incommensurate phase in spin-1/2
  chains
• Staggered fields and the quantum Sine Gordon
  Model
• Field effects in gapful systems
• Driving the gap to zero with a field
• Probing impurity states below the gap
• Quantum disorder in Dgt1
• Conclusions

2
G. Aeppli M. Azuma Y. Chen D. Dender J. F.
DiTusa M. Enderle C. D. Frost D. V. Ferraris Z.
Honda T. Ito K. Katsumata T. Lectka
K. Oka R. Paul Y. Qiu L. P. Regnault D. H. Reich
J. Rittner M. B. Stone H. Takagi G. Xu H.
Yardimci I. Zaliznyak A. Zheludev
Acknowledgements
Acknowledgements
NIST Center for Neutron Research ISIS Facility,
Rutherford Appleton Laboratory National Science
Foundation Civilian Research and Development
Foundation
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The beauty of magnetic dielectrics

• Well defined low energy Hamiltonian
• Chemistry provides qualitatively different H
• Vary H with pressure, magnetic field
• Efficient experimental techniques

Exchange interaction
Single ion anisotropy
Dipole in magnetic field (Zeeman)
4
Types of Quantum magnets

• Definition small or vanishing frozen moment at
  low T
• Conditions that yield quantum magnetism
• Low effective dimensionality
• Weak connectivity
• Low spin quantum number
• Geometrical frustration

5
Gapped phases in isotropic spin systems?

• n number of spins per primitive unit cell
• S the spin quantum number
• m the magnetization per spin
• n(S-m)
• Oshikawa, Yamanaka, and Affleck (1997)
  and Oshikawa (2000)
• gaps in non-magnetized spin chains?
• Uniform spin ½ chain 1.½ ½ no
  gap
• Alternating spin ½ chain 2.½ 1
  perhaps
• (2n1) leg spin ½ ladder (2n1).½ n½ no
  gap
• 2n leg spin ½ ladder 2n.½
  n perhaps
• Uniform spin 1 chain 1.1 1
  perhaps

Integer gap possible
Non-Integer gap impossible
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Magnetic Neutron Scattering
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Sum rules and the single mode approximation
The dynamic spin correlation function obeys
sum-rules
When a coherent mode dominates the spectrum
Sum-rules link S(q) and e(q)
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NIST Center for Neutron Research
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SPINS cold neutron triple axis spectrometer at
NCNR
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Detection system on SPINS neutron spectrometer
Focusing Analyzer
Dispersive Analyzer
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MAPS Spectrometer at ISIS in UK
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Y2BaNiO5 Ito, Oka, and Takagi
Cu(NO3)2.2.5 D2O Guangyong Xu
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Varying the dimensionality of spin systems

• The crystals are actually three dimensional
• Exchange links spins on low-D network only

Chain direction
Anisotropic bonding in tetragonal KCuF3
Non-magnetic spacer molecules in NDMAP
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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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Scattering from spinons

• Neutrons scatter from spinon gas by creating or
  anihilating quasi-particle quasi-hole pairs
• Momentum and energy conservation require
• Scattering is therefore a bounded continuum
• SzSz term brings us from ideal gas to Luttinger
  liquid
• Spinon energies renormalize by factor p/2 so that

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From band-structure to bounded continuum
J
e/J
w
h
q (p)
Q (p)
Exact two spinon contribution to S(Q,w) for
Heisenberg case see Karbach et al PRB (1997)
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Two spinon continuum in uniform spin ½ chain
I (meV-1)
Dender et al PRB 96
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Solid lines are resolution convoluted Muller
form for two spinon continuum
Dender et al PRB 96
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Spin ½ chain in a field
p-2pm
-
q (p)
Q (p)
The magnetized state is analogous to flux line
lattice in type II superconductor. Magnetization
is carried by incommensurate defect
lattice References Karbach and Muller PRB
2000 (Dynamic Structure factor in a field)
Chitra and Giamarchi PRB 1997 (Quantum magnets
in a field)
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Field Induced Incommensurate Soft Modes
Copper Benzoate
Dender et al PRL 97
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Field induced gap in spin-1/2 chain
Dender et al PRL 97
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From uniform to staggered field
Correct Zeeman term for low symmetry
environment
A staggered g-tensor breaks translational
symmetry for Hgt0 only
Similar effect from staggered Dzyalozhinsky-Moriya
interaction. Oshikawa and Affleck calculated the
effect of staggered field
R(H) is compactification radius for staggered
field operator
Essler, Tsvelik, Affleck, and Oshikawa showed
that a spin ½ chain in a staggered field is a
Sine Gordon model with soliton and breather
excitations consistent with data
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Spin-1/2 chain in uniform field
Cu(C4H4N2)(NO3)2 CuPzN
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Are there incommensurate features in gapless
magnetized phases of other quantum magnets
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Simple example of magnet with gapped spectrum
Cu(NO3)2.2.5D2O dimerized spin-1/2 system
Only Inelastic magnetic scattering
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Triplet waves in dimerized copper nitrate
Xu et al PRL May 2000
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Qualitative description of excited states

• A spin-1/2 pair with AFM exchange has a singlet -
  triplet gap

• Inter-dimer coupling allows coherent triplet
  propagation and
• produces well defined dispersion relation

• Triplets can also be produced in pairs with total
  Stot1

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Creating two triplets with one neutron
Two magnon
One magnon
Tennant et al (2001)
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Magnetizing a gapped quantum magnet
Copper Nitrate T0.1 K
Field induced order
Eckert et al (1980)
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Excitations in magnetized quantum magnet
Excited dispersive triplet
Split into three bands with Different polarization
Two-sublattice Ferromagnet in a field
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Excitation gap versus applied field
Higher resolution experiments required to probe
dispersion of lowest energy mode
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One dimensional spin-1 antiferromagnet Y2BaNiO5
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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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Zeeman resonance of chain-end spins
g2.16
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hw (meV)
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0 2 4 6 8
H (Tesla)
10
I(H9 T)-I(H0 T) (cts. per min.)
0
-5
0 0.5 1 1.5
2
Zaliznyak et al. (2001)
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Form factor of chain-end spins
Y2BaNi1-xMgxO5 x4
Q-dependence reveals that resonating object is
AFM. The peak resembles S(Q) for pure system.
Chain end spin carry AFM spin polarization of
length x back into chain
Zaliznyak et al. (2001)
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Spin-1 chain with staggered g-tensor Dynamics
0 T
NENP T35 mK
Field dependence of energies
12 T
13 T
Dispersion in high fields
14.5 T
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Spin-1 chain with staggered g-tensor Statics
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(110) B2 T
2
Intensity (103 cts/min.)
1
0
0 2 4 6 8
10
T (K)
Translational symmetry is broken by the field
Not a Phase transition but a cross
over instead
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Spin-1 chain without staggered field Statics
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Frozen short range ordered phase in SrCuO2
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Dgt1 Quantum disordered SrCu2(BO3)2
Plateaus may indicate gapped phases
with spontaneous broken translational symmetry
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Dgt1 Quantum Disordered Magnets
(C4H12N2)Cu2Cl6 PHCC
Cu2(1,4-diazacycloheptane)2Cl4 CuHpCl
LRO
Quantum Disordered
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Previously Accepted Model for CuHpCl

• Quasi 1D 2-leg Spin Ladder
• J11.1 meV
• J20.2 J1
• Ladder axis 1 0 1
• Predictions of ladder model
• Magnetic excitation spectrum
• Dispersion along (101)
• No dispersion (101)

J2
J1
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Signs of problems with spin ladder model
Chabboussant et al (1998)
Hammar et al (1998)
Absence of singularity
Absence of DOS van-Hove singularity
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CuHpCl hydrogenous single crystals
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Dimensionality of CuHpCl Dgt1
A0 1.00(2) meV 1.21(2) meV A1 -0.04(2) -0.03(2)
A2 -0.02(2) 0.00(2) A3 -0.07(2)
0.01(2) A4 -0.02(2) -0.03(2)
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Frustration in CuHpCl
frustration
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Which are the important interactions?
(z 0 z)
c
(101)
(001)
(z 0 1-z)
(z 0 0)
a
(100)
Point size First moment
(1 0 z)

• Strongest modulation along (101) implies strong
  bond parallel to 101
• 3 Cu-Cu bonds are important
• One bond is frustrated

(1 z 0)
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Possible magnetic lattices for CuHpCl
View down 010 Distorted triangular lattice
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PHCC is Frustrated and Quasi-2D
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Conclusions

• Observation of field induced gapless
  incommensurate phase in uniform spin-½ chain
• Staggered g-tensor induces gap in excitation
  spectrum of magnetized spin ½ chain
• Observation of edge states in uniform spin 1
  chain
• Field induced quantum phase transition in spin-1
  chain to 3D LRO or quasi-two-dimensional frozen
  phase
• Dgt1 Quantum disordered phases can occur when
  frustration suppresses long range order