leon balents- frustrated magnets (2) materials survey
TRANSCRIPT
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AB2X4 spinels
One of the most
common mineralstructures
Common valence:
A2+
,B3+
,X2-
X=O,S,Se
A
X
B
cubic Fd3m
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Deconstructing the
spinel
A atoms: diamond lattice
Bipartite: notgeometrically
frustrated A
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Deconstructing the spinel
B atoms: pyrochlore
decorate the plaquettes
of the diamond lattice
B
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ACr2O4 spinelspyrochlore lattice
S=3/2 Isotropicmoment
X=O spinels: B-Bdistance close enough
for direct overlap
dominant AFnearest-neighborexchange
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H=0 Susceptibility
Frustration:
T
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DegeneracyHeisenberg model
Ground state constraint: total spin 0 per
tetrahedron
Quantum mechanically: not possible
H =
ij
Si Sj =
1
2
t
it
Si
2
+ const.
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Classical spin liquid
No LRO (Reimers)
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Classical spin liquid
No LRO (Reimers)
Dipolar correlations
Si = b
ab
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Classical spin liquid
No LRO (Reimers)
Dipolar correlations
Si = b
ab
a
bi
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Classical spin liquid
Unusual ringcorrelations seen inCdCr2O4 related
Y2Ru2O7: J. van Duijn
et al, 2007
2
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Broholm et al
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Ordering
Many perturbations
important forordering:
Spin-latticecoupling
Further exchangeSpin-orbit effects
Quantumcorrections
ZnCr2O4
CdCr2O4
HgCr2O4
S.H. Lee + many others
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Magnetization Plateaus
Classically: M = Ms H/Hs
Plateau indicates 3:1structure
H. Ueda at al, 2005/6
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Magnetization PlateausPlateau mechanism:
spin-lattice couplingfavors collinearity
Order on plateau maybe selected by
spin-lattice
quantum effects
R state observedin neutrons
Matsuda et al
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A-site spinelsSpectrum of materials
1 900
FeSc2S4
10 205
CoAl2O4
MnSc2S4
MnAl2O4
CoRh2O4 Co3O4
V. Fritsch et al. PRL 92, 116401 (2004); N. Tristan et al. PRB 72, 174404 (2005); T. Suzuki et al. (2006)
s = 5/2
s = 3/2
Orbitaldegeneracy
s = 2
Naively unfrustrated
f=|CW |
TN
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Why frustration?
Roth, 1964: 2nd and
3rd neighborexchange notnecessarily small
Exchange paths:A-X-B-X-B
comparableMinimal modelJ1-J2 exchange
J1J2
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Ground state evolutionCoplanar spirals
q0 1/8
Neel
J2/J1
J2/J1 = 0.2 J2/J1 = 0.4 J2/J1 = 0.85 J2/J1 = 20
Spiral surfaces:
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Monte Carlo
f = 11 atJ2/J1 = 0.85
MnSc2S4
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Phase Diagram0
Spiral spinliquid
paramagnet
MnSc2S4
J3
CWTN
ObD
ObJ3
Entropy and J3compete to determineordered state
Spiral spin liquidregime has intensity
over entire spiralsurface
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Diffuse scattering
Ordered state
(qq0) spiral
Specific heat?
Comparison to Expt.Expt. Theory
agrees withtheory for FM J1
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Cs2CuCl4Spatially anisotropictriangular lattice
Cu2+ spin-1/2 spins
couplings:
H=1
2
ij
Jij
Si Sj
Dij Si
Sj
J=0.37meV
J=0.3JD=0.05J
D = Da
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Neutron scatteringColdea et al, 2001/03: a 2d spin liquid?
Very broad spectrumsimilar to 1d (in somedirections of k space).Roughly fits power law.
Fit of peak dispersion tospin wave theory requiresadjustment of J,J by 40%- in opposite directions!
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Dimensional reduction?Frustration of interchain coupling makes itless relevant
First order energy correction vanishes
Leading effects are in fact O[(J)4/J3]!
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Dimensional reduction?Frustration of interchain coupling makes itless relevant
First order energy correction vanishes.Numerics: J/J < 0.7 is weak
Weng et al,2006
Very different fromspin wave theory
Very weak inter-chaincorrelations
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Build 2d excitations from 1d spinons
Exchange:
Expect spinon binding to lower inter-chainkinetic energy
Use 2-spinon Schroedinger equation
ExcitationsJ
2
S+
i S
j + S
i S+
j
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Broad lineshape: free spinonsPower law fits well to free spinon resultFit determines normalization
J(k)=0 here
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Bound stateCompare spectra at J(k)0:
Curves: 2-spinon theory w/ experimental resolution Curves: 4-spinon RPA w/ experimental resolution
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Transverse dispersion
Bound state andresonance
Solid symbols: experiment
Note peak (blue diamonds) coincides
with bottom edge only for J(k)
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Spectral asymmetry
Comparison:
Vertical lines: J(k)=0.