Neutron Scattering of Frustrated Antiferromagnets

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Neutron Scattering of Frustrated Antiferromagnets
Collin Broholm Johns Hopkins University and NIST
Center for Neutron Research

• Satisfaction without LRO
• Paramagnetic phase
• Low Temperature phase
• Spin glass phase
• Long range order
• Spin Peierls like phase
• Conclusions

SrCr9pGa12-9pO19 KCr3(OD)6(SO4)2 ZnCr2O4
Supported by the NSF through DMR-9453362 and
DMR-0074571
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Collaborators
S.-H. Lee NIST and University of MD M.
Adams ISIS Facility, RAL G. Aeppli NEC Research
Institute E. Bucher University of Konstanz C. J.
Carlile ISIS Facility, RAL S.-W. Cheong Bell
Labs and Rutgers Univ. M. F. Collins McMaster
University R. W. Erwin NIST L. Heller McMaster
University B. Hessen Bell Labs/Shell T. J. L.
Jones ISIS Facility, RAL T. H. Kim Rutgers
University C. Kloc Bell Labs N. Lacevic Johns
Hopkins University T. G. Perring ISIS Facility,
RAL A. P. Ramirez Bell Labs W. Ratcliff
III Rutgers University A. Taylor ISIS Facility,
RAL
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A simple frustrated magnet La4Cu3MoO12
Masaki Azuma et al. (2000)
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Magnetization and order of composite trimer spins
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Theory of spins with AFM interactions on
corner-sharing tetrahedra

• What is special about this lattice and this spin
  system?
• Low coordination number
• Triangular motif
• Infinite set of mean field ground states with
  zero
• net spin on all tetrahedra
• No barriers between mean field ground states
• Q-space degeneracy for spin waves

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SrCr9pGa12-9pO19 Kagome sandwich
Isolated spin dimer
Kagome-Triangular-Kagome sandwich (111) slab of
pyrochlore/spinel AFM
A. P. Ramirez et al. PRL (1990)
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Fe Cr Jarosite coupled Kagome layers
AM3(OH)6(SO4)2
KCr3(OH)6(CrO4)2
A. S. Wills et al. (2000)
Townsend et al (1986)
Lee et al. (1997)
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ZnCr2O4 Corner sharing tetrahedra
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Magnetic Neutron Scattering
The scattering cross section is proportional to
the Fourier transformed dynamic spin correlation
function
Fluctuation dissipation theorem
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NIST Center for Neutron Research
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(No Transcript)
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Detection system on SPINS neutron spectrometer
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Spatial correlation length saturates for T 0
SrCr9pGa12-9pO19
for TltQCW
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Relaxation Rate decreases for T 0
SrCr9pGa12-9pO19
SrCr9pGa12-9pO19
Paramagnetic state Fluctuating AFM spin
clusters that largely satisfy exchange
interactions
dimer
Kagome sandwich
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Spin glass in concentrated frustrated AFM

• Does quenched disorder play a role?
• What is structure of SG phases?
• What are excitations in SG phases?

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Spin glass transition in SCGO(p0.92)
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The role of disorder at SG transition
Martinez et al. (1992)
Higher Tf Sharper features in S(Q)
Higher Cr concentration

• Two scenarios remain viable
• A) Strong sensitivity to low levels of disorder
• B) Intrinsic disordered frozen phase

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Structure of frozen phase
Kagome tri-layer correlations
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Excitations in a frustrated spin glass
SCGO(p0.92)
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Long range order in frustrated AFM

• Clarify role of symmetry breaking interactions,
  quenched disorder and order by disorder effects
  in stabilizing LRO.
• Are there anomalous critical properties at phase
  transitions to LRO?
• What are the excitations in the ordered phase of
  a highly frustrated magnet?

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Phase transition to LRO in Cr-Jarosite
gt90 Cr
75-90 Cr
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Weak order / strong fluctuations
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Impurity enhanced LRO in (DO3)Fe3-xAly(SO4)2(OD)6
100 Fe
Wills et al (1998)
Only reported Jarosite w/o LRO
89 Fe
Wills et al. (2000)
Diamagnetic impurities yield LRO
DIntensity (arb)
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Magneto-elastic effects in frustrated AFM

• Can magneto-elastic coupling relieve frustration?
• What is magnetic and lattice strain configuration
  in ordered phase?
• Determine energetics of a spin-Peierls like
  transition for frustrated magnets.
• What are excitations from the ordered phase?

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First order phase transition in ZnCr2O4

• Dynamics
• Low energy paramag.
• Fluctuations form a
• resonance at 4.5 meV

• Statics
• Staggered magnetization
• tetragonal lattice distortion

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Local spin resonance in ordered phase
Paramagnetic fluctuations in frustrated AFM
Local spin resonance in magneto-elastic LRO phase
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Low T excitations in ZnCr2O4
Magnetic DOS
Q-dep. of E-integ. intensity
C
A Bragg peaks B Spin waves C Resonance D
Upper band
A
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Spectra at specific Q
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Dispersion relation for resonance
ZnCr2O4 single crystals T1.5 K
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Structure factor for resonance
ZnCr2O4 T1.4 K
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Comparing resonance to PM fluctuations
15 K
1.4 K

• Paramagnetic fluctuations and resonance satisfy
• same local constraints.
• Transition pushes low energy fluctuations into a
  resonance
• w/o changing spatial correlations

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Why does tetragonal strain encourage Neel order?
Edge sharing n-n exchange in ZnCr2O4 depends
strongly on Cr-Cr distance, r
From series of Cr-compounds
r
The effect for a single tetrahedron is to make 4
bonds more AFM and two bonds are less AFM. This
relieves frustration!
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Magnetic order in ZnCr2O4-Viewed along
tetragonal c-axis

• tetrahedra have zero net moment
• gt this is a mean field ground
• state for cubic ZnCr2O4
• Tetragonal distortion lowers energy
• of this state compared to other
• mean field ground states

• In a strongly correlated magnet
• this shift may yield

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Analysis of magneto-elastic transition in ZnCr2O4
Cubic paramagnet
Tetrag. AFM
Free energy of the two phases are identical at TC
From this we derive reduction of internal energy
of spin system
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Direct measurement of confirms validity of
analysis
From first moment sum-rule for the dynamic spin
correlation function we find
When a single Heisenberg exchange interaction
dominates. Inserting magnetic scattering data
acquired at 15 K and 1.7 K we get
LRO develops from a strongly correlated state
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Analogies with Spin Peirls transition?
There are similarities as well as important
distinctions!
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Conclusions

• Low connectivity and triangular motif yields
• cooperative paramagnet forT/QCWltlt1.
• The paramagnet consists of small spin clusters
  with no net moment, which fluctuate at a rate of
  order kBT/ h.
• Spinels can have entropy driven magneto-elastic
  transition to Neel order with spin-Peirls
  analogies.
• The ordered phase has a spin-resonance, as
  expected for under-constrained and weakly
  connected systems.
• Pyrochlores can have a soft mode transition to a
  spin-glass even when there is little or no
  quenched disorder.
• Variations of sub-leading interactions in
  pyrochlores give different types of SRO in
  different compounds.
• Lattice distortions may be a common route to
  relieving frustration and lowering the free
  energy of geometrically frustrated magnets.

ZnCr2O4
Y2Mo2O7
Tetragonal