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8/3/2019 B. Fk et al- Spin-liquid behavior in a classical Heisenberg kagom antiferromagnet
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Spin-liquid behavior in a classicalHeisenberg kagom antiferromagnet
B. Fk, F.C. Coomer, A. Harrison, D. Visser, M.E. Zhitomirsky(CEA Grenoble, ISIS, U. of Edinburgh)
An inelastic neutron scattering study ofDeuteronium jarosite(D3O)Fe3(SO4)2(OD)6
THE U
N I VE R S I T YOF
E D I N B UR
GH
8/3/2019 B. Fk et al- Spin-liquid behavior in a classical Heisenberg kagom antiferromagnet
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Geometrical frustration
Triangular (2D)(edge-sharing triangles)
Pyrochlore (3D)(corner-sharingtetrahedra)
Kagom (2D)(corner-sharingtriangles)
?
Antiferromagnetic NN interactionH = J Si
.Sj , J>0
on a triangular lattice => frustration
8/3/2019 B. Fk et al- Spin-liquid behavior in a classical Heisenberg kagom antiferromagnet
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Ideal kagom lattice
Classical nearest-neighbor AF spins on a kagom lattice
Strongly degenerate ground state No long-range order Co-planar states favored by thermal fluctuations S(Q) predicted by numerical simulations - but little is known about the dynamics, S()
Roman mosaic, Empurias (c.a. -60)
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Non-ideal kagom lattice
Additional interactions Crystal anisotropy Further neighbor interactions
Dzyaloshinsky-Moriya interactionmay lead to long-range order: k = 0 structure (left): uniform vector chirality k=(2/3,2/3) structure (3 x 3) (right): staggered vector chirality
Vector chirality:C = i,jSi x Sj
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Deuteronium jarosite (D3O)Fe3(SO4)2(OD)6
Well separated kagom layers of undistorted triangles
Strong (NN) antiferromagnetic interactions (CW=-700 K) Small disorder (near full occupancy of Fe3+ ions)
No long-range magnetic order (T>1 K) Wills EPL 42 (1998) 325 Gradual and partial spin freezing at Ts=13.8-17.5 K
SR;Harrison PB 289-290 (2000) 217
IN16; D. Visser (unpubl.) Has been classified as a topological spin glass
Unusual aging and memory effects Wills PRB 62 (2000) R9264
Specific heat ~T2 (rather than ~T) Wills EPL 42 (1998) 325
~50% of the moments are fluctuating: spin liquid !
Most other jarosites (replace H3O by K, ... or Fe by Cr, V,..) order at ~60 Kwith k=0 structure and doubling of unit cell along c(weak interlayer coupling)
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Results from MARI
S(Q,E) = SN(Q,E) + SM(Q,E)
Easy to subtract phonons
Dynamic short-range correlations- characteristic of a spin liquid
Non-dispersive S(Q,E)
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Results from MARI
S(Q,E) = SN(Q,E) + SM(Q,E)
Easy to subtract phonons
Dynamic short-range correlations- characteristic of a spin liquid
Non-dispersive S(Q,E)
8/3/2019 B. Fk et al- Spin-liquid behavior in a classical Heisenberg kagom antiferromagnet
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Temperature dependence of S(Q)
Lines are Monte Carlo simulations:
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Q-dependence
0.0
0.5
1.0
1.5
0 1 2 3 4
SM
(Q)
Q (-1)
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Q-dependence
0.0
0.5
1.0
1.5
0 1 2 3 4
SM
(Q)
(a)
Q (-1)
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Q-dependence
0 1 2 3 4
(b)
Q (-1)
Fit
Monte-Carlo simulation of NN AFM kagom
The 3 x 3 structure hasstaggered vector chirality
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Energy dependence
Continuum of gap-less excitations(gap
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Quasielastic Lorentzian
0
8
0.0
0.4
0 100 200
(meV) '
T (K)
(T) = 0 + T0
50
100
150
0 5 10 15
D3OFe
3(SO
4)2(OD)
6
T=14.5 K
T=21 K
T=36 K
T=61 K
T=121 K
T=238 K
"(E)(mbarn/sr/meV)
Energy (meV)
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/Tscaling ?
2D AFM close to QCP (para -> LRO): expect /T scaling:
"()T= F(/T) S. Sachdev, PRL 69 (1992) 2411
No /T scaling !
200
500
1000
2000
5000
0.01 0.1 1
T=14.5 KT=21 KT=36 KT=61 KT=121 K
T=238 K"T
(Kmbarn/SR/meV)
/T (meV/K)
D3OFe
3(SO
4)2(OD)
6
(T) = 0 + T
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Non-Lorentzian response
Deviations from a single Lorentzian at low energy
0
50
100
150
200
0 5 10 15
D3OFe
3(SO
4)2(OD)
6
T=14.5 K
T=21 K
T=36 K
T=61 K
T=121 K
T=238 K
"(E)(mbarn/sr/meV)
Energy (meV)
14.521
36
61
121
238
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Scaling ?
2D AFM close to QCP (para -> spin-glass): expect
"() ~ S. Sachdev, PRL 69 (1992) 2411with
-1
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SCGO(x) = SrCr8-xGa4+xO19
C. Broholm, PRL 65 (1990) 3173
Spin glass behavior in a pyrochlore slab
[coupled (partially occupied) kagom planes]
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KCr3(SO4)2(OD)6
S.-H. Lee, PRB 56 (1997) 8091
S=3/2, 76% site occupancy
orders at 1.6 K shows gap-less spin fluctuations
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Y0.5Ca0.5BaCo4O7
W. Schweika, PRL 98 (2007) 067201
CW=-2200 K
Co2+ (S=3/2) forms kagom layersCo3+ (S=0) occupy interlayer sites
S(Q,E) from temperature
difference 150-40 K
S(Q) indicatesstaggered chirality
Valence disorder?
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ZnCu3Cl2(OH)6
J.S. Helton, PRL 98 (2007) 107204
Herbertsmithite or paratacamite
S=1/2 kagom with 90% occupancy and no gap (!)
"() ~ 0.7
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ZnxCu4-xCl2(OH)6
S.-H. Lee, Nat. Mat. 4 (2005) 323
x0.66 diluted kagom (
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Conclusions
S(Q) very similar to Monte-Carlo simulations of the NN AFM kagom 3 x 3 type correlations
indirect evidence of staggered vector chirality
"(E) continuum of (probably) gapless excitations (gap < 0.5 meV) that
extends out to 20 meV
single-Lorentzian component with (T)=1.5+aT meV and additional contributions (multiple time scales) or a non-Lorentzian line shape ("() ~ 0.68) no dynamic scaling behavior
Inelastic neutron scattering measurements on the classical
Heisenberg kagom antiferromagnet (D3O)Fe3(SO4)2(OD)6 showclear spin-liquid behavior: dynamic short-range correlations
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Key experimental features
These results were made possible because of
Excellent deuteration (H/D