B. Fåk et al- Spin-liquid behavior in a classical Heisenberg kagomé antiferromagnet

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


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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


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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)


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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

Documents

B. Fåk et al- Spin-liquid behavior in a classical Heisenberg kagomé antiferromagnet