spinons in strongly correlated chain cuprates

SNS-HFIR User MeetingSNS-HFIR User MeetingOctober 8 - 12, 2007 October 8 - 12, 2007

Igor ZaliznyakIgor Zaliznyak

Neutron Scattering GroupCondensed Matter Physics and Material Science Department

OutlineOutline

• Introduction: who, what, why, and how?

• Structure and electronic properties of chain cuprates

– high-energy spinons, itinerancy, and spin-charge separation

• Dimensional cross-over and low-energy excitations

– unbound spinons in 2D?

OutlineOutline

• Introduction: who, what, why, and how?

• Structure and electronic properties of chain cuprates

– high-energy spinons, itinerancy, and spin-charge separation

• Dimensional cross-over and low-energy excitations

– unbound spinons in 2D?

Spinons in strongly correlated chain cupratesSpinons in strongly correlated chain cupratesSpinons in strongly correlated chain cupratesSpinons in strongly correlated chain cuprates


Neutron ScatteringNeutron Scattering

A. Walters, T. Perring, C. Frost (ISIS)

A. Savici, H. Woo (BNL)

S. Park (NIST NCNR)

C. Broholm (JHU)

Neutron ScatteringNeutron Scattering

A. Walters, T. Perring, C. Frost (ISIS)

A. Savici, H. Woo (BNL)

S. Park (NIST NCNR)

C. Broholm (JHU)

Contributors and CollaboratorsContributors and CollaboratorsContributors and CollaboratorsContributors and Collaborators

Chain cupratesChain cuprates

SrCuO2, Sr2CuO3, Sr2CuO3+y

Chain cupratesChain cuprates

SrCuO2, Sr2CuO3, Sr2CuO3+yMaterial syntesis and crystal growthMaterial syntesis and crystal growth

G. Gu (BNL)

H. Takagi (U. Tokyo)

Material syntesis and crystal growthMaterial syntesis and crystal growth

G. Gu (BNL)

H. Takagi (U. Tokyo)

Theory & AdviceTheory & Advice

J.-S. Caux (U. Amsterdam)

F. Essler (Oxford, BNL)

J. Bhaseen (Oxford, BNL)

A. Tsvelik (BNL)

Theory & AdviceTheory & Advice

J.-S. Caux (U. Amsterdam)

F. Essler (Oxford, BNL)

J. Bhaseen (Oxford, BNL)

A. Tsvelik (BNL)


Low-dimensional electron/spin systems: fundamental Low-dimensional electron/spin systems: fundamental importanceimportance

Low-dimensional electron/spin systems: fundamental Low-dimensional electron/spin systems: fundamental importanceimportance

• Quantum effects and fluctuations are important– disorder, quantum criticality, spin-liquid states

• Excitation fractionalization by dimensional confinement– topological excitations with fractional quantum numbers

(spinons)– spin-charge separation, Luttinger liquid phase

• Dimensional cross-over and confinement of fractional excitations

• Mott-insulating state in 1D

• Quantum effects and fluctuations are important– disorder, quantum criticality, spin-liquid states

• Excitation fractionalization by dimensional confinement– topological excitations with fractional quantum numbers

(spinons)– spin-charge separation, Luttinger liquid phase

• Dimensional cross-over and confinement of fractional excitations

• Mott-insulating state in 1D


Low-dimensional electron/spin systems: practical Low-dimensional electron/spin systems: practical significancesignificance

Low-dimensional electron/spin systems: practical Low-dimensional electron/spin systems: practical significancesignificance

• Chains/planes are the building blocks of– high-Tc superconductors, chain cuprates, MgB2, NaCoO2, …

• Low-D physics governs nano-scale functional materials– nanotubes (Luttinger liquid, 1D Mott insulator)– thin films, multilayers, graphene (2D)

• Low-D systems are generated by electronic phase segregation, e.g. in doped oxides, etc. – stripes in cuprates => spin ladders (J. Tranquada, et. al.)

• Chains/planes are the building blocks of– high-Tc superconductors, chain cuprates, MgB2, NaCoO2, …

• Low-D physics governs nano-scale functional materials– nanotubes (Luttinger liquid, 1D Mott insulator)– thin films, multilayers, graphene (2D)

• Low-D systems are generated by electronic phase segregation, e.g. in doped oxides, etc. – stripes in cuprates => spin ladders (J. Tranquada, et. al.)


Low-dimensional orbital networks in copper oxides

SrCuOSrCuO22, YBa, YBa22CuCu44OO88,, SrSr1414CoCo2424OO4141, other ladder systems., other ladder systems.SrSr22CuOCuO33, YBa, YBa22CuCu33OO77, Sr, Sr1414CuCu2424OO4141, …, …

LaLa22CuOCuO44, etc., etc.

- O – Cu – O – Cu – O – Cu – O – Cu – O– Cu – O -

Fundamental minimal model: 1-band Hubbard HamiltonianHH= - tm(cj,

+ cj+m, + H.c.) + (U/2) (n jn j- + H.c.)

Fundamental minimal model: 1-band Hubbard HamiltonianHH= - tm(cj,

+ cj+m, + H.c.) + (U/2) (n jn j- + H.c.)

Low-dimensional electron systems: practical significanceLow-dimensional electron systems: practical significanceLow-dimensional electron systems: practical significanceLow-dimensional electron systems: practical significance


Spin excitations in S=1/2 CuSpin excitations in S=1/2 Cu2+2+ chains: spinons in KCuF chains: spinons in KCuF33 Spin excitations in S=1/2 CuSpin excitations in S=1/2 Cu2+2+ chains: spinons in KCuF chains: spinons in KCuF33

Mean-field (MF) picture of spinon attraction in the ordered phase.

U >> t charge gap (~ U, few eV) >>

spin bandwidth ~ 0.1 eV (J 34 meV)U >> t charge gap (~ U, few eV) >>

spin bandwidth ~ 0.1 eV (J 34 meV)

S=1/2 Heisenberg spin chainH = J Si Si+1

S=1/2 Heisenberg spin chainH = J Si Si+1

Dimensional cross-over: 3D order at TN 39 K, <µ> 0.5µB

Dimensional cross-over: 3D order at TN 39 K, <µ> 0.5µB

[A. Tennant et al (2001)].


Spin waves in LaSpin waves in La22CuOCuO44: itinerancy effects in 2D Mott insulator: itinerancy effects in 2D Mott insulatorSpin waves in LaSpin waves in La22CuOCuO44: itinerancy effects in 2D Mott insulator: itinerancy effects in 2D Mott insulator

R. Coldea, et al, PRL (2001)

J 0.13 eV, optic gap ~ 1.2 eV => spin bandwidth ~ 0.3 eV is NOT MUCH SMALLER than charge gap.

J 0.13 eV, optic gap ~ 1.2 eV => spin bandwidth ~ 0.3 eV is NOT MUCH SMALLER than charge gap.

S=1/2 square lattice Heisenberg AFM with ring exchange

H = J Si Sj+Jc [(Si Sj)(SkSl)+ (Si Sl)(SkSj)- (Si Sk)(SjSl)]

S=1/2 square lattice Heisenberg AFM with ring exchange

H = J Si Sj+Jc [(Si Sj)(SkSl)+ (Si Sl)(SkSj)- (Si Sk)(SjSl)]

Follows from half-filled Hubbard modelFollows from half-filled Hubbard model

U 2.5 eV t 0.3 eVJc 0.27J


Itinerancy effects in 1D Mott insulator?Itinerancy effects in 1D Mott insulator?Itinerancy effects in 1D Mott insulator?Itinerancy effects in 1D Mott insulator?

M. J. Bhaseen, et al, PRB (2005)

What happens in 1D when spin bandwidth IS NOT MUCH SMALLER than charge gap, i.e. for 2t ~ U?

What happens in 1D when spin bandwidth IS NOT MUCH SMALLER than charge gap, i.e. for 2t ~ U?

Spin sector separates: same spinon dispersion Spectral weight transferred to upper boundary Spin sector separates: same spinon dispersion Spectral weight transferred to upper boundary


Chain copper oxides: 1D Mott-Hubbard insulators.Chain copper oxides: 1D Mott-Hubbard insulators.Chain copper oxides: 1D Mott-Hubbard insulators.Chain copper oxides: 1D Mott-Hubbard insulators.

SrSr22CuOCuO33 SrCuOSrCuO22

Cu-O bond length 1.95 Å, exchange coupling J ~ 0.2-0.3 eV (!)


Sr2CuO3: static, long-range (Bragg) order

Q=(h,0.5,0.5)Points: magnetic scatteringLine: nuclear scattering

TTNN 5 K 5 K

k hSrCuO2: decoupling in zigzag ladders leads to short-range anisotropic static order

Weakly coupled S=1/2 -Cu-O-Cu- chains: frustration and Weakly coupled S=1/2 -Cu-O-Cu- chains: frustration and spin freezing vs long-range orderspin freezing vs long-range order

Weakly coupled S=1/2 -Cu-O-Cu- chains: frustration and Weakly coupled S=1/2 -Cu-O-Cu- chains: frustration and spin freezing vs long-range orderspin freezing vs long-range order

K. Kojima et al,

PRL (1997)

<µ> 0.06µB

I. Zaliznyak et al, PRL (1999)<µ> 0.035µB


“Inelastic neutron scattering experiments are much desired”, Maekawa & Tohyama, Rep. Prog. Phys. (2001), T. Rice, Physica B (1992).

Temperature dependence of the magnetic susceptibility (N. Motoyama et al, PRL (1996))

J = 0.19(2) eV

J = 0.26(1) eV

??

Electron + Xray spectroscopy + band structure calculations (Neudert et al, PRL 81 (1998), Rosner et al, PRB 56 (1997), Kim, et al (2006), Koitzsch, et al (2006))

U 4.2 eV V 0.8 eVt 0.55 eV

J = 4t2/(U-V) - |K| ~ 0.25-0.36 eV (!?)

J~ 0.5 - 1 meV

Record-high Record-high J, J, record-low record-low JJ/J/J

Infrared absorption below the optical band gap (H. Suzuura et al, PRL (1996))

How do we know exchange coupling J?How do we know exchange coupling J?How do we know exchange coupling J?How do we know exchange coupling J?


EEii = 100 meV = 100 meV




phonons

SrCuOSrCuO22

Triplet spectrum of two-spinon states, combined set of 4 measurements on MAPS at ISIS

spinons

Measure the spin part of one-dimensional electrons directlyMeasure the spin part of one-dimensional electrons directlyMeasure the spin part of one-dimensional electrons directlyMeasure the spin part of one-dimensional electrons directly

I. Zaliznyak, S.-H. Lee, in “Modern Techniques for Characterizing Magnetic Materials”, Ed. Y. Zhu, Springer (2005)

Single crystal sample (H. Takagi)m = 3.9 gMosaic ~ 0.5T= 12 K


2-parameter fit (J, A) to “Muller ansatz”:2-parameter fit (J, A) to “Muller ansatz”:




Intensity variation: anisotropic Cu2+ magnetic formfactor! Intensity variation: anisotropic Cu2+ magnetic formfactor!


CuCu2+2+ anisotropic magnetic formfactor anisotropic magnetic formfactorCuCu2+2+ anisotropic magnetic formfactor anisotropic magnetic formfactor

I. Zaliznyak, S.-H. Lee, in “Modern Techniques for Characterizing Magnetic Materials”, Ed. Y. Zhu, Springer (2005)



Account for anisotropic Cu2+ magnetic formfactor => A is ~ E-independentAccount for anisotropic Cu2+ magnetic formfactor => A is ~ E-independent


Maps of the absolute net scattering intensity measured in SrCuO2 for incident neutron energies (e) EI = 1003 meV, (f) EI = 517 meV, (g) EI = 240 meV, (h) EI = 98 meV. Corresponding resolution-broadened intensity maps calculated from S(Q,E) for free spinons (Müller ansatz) are shown in (a)-(d).

Momentum Ql (units of 2/c)

En

erg

y tr

an

sfe

r, E

, (m

eV

)

S(Q

,E)

(mb

arn

/me

V/s

r/C

u)

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

600

500

400

300

-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1

(a)

(f)

(e)

(b)

(c)

(d)

(g)

(h)

400

300

200

0.1

0.0

0.1

0.0200

150

100

70

50

30

0.6

0.3

0.0

2.0

1.0

0.0

Spin part of one-dimensional electrons in SrCuOSpin part of one-dimensional electrons in SrCuO22Spin part of one-dimensional electrons in SrCuOSpin part of one-dimensional electrons in SrCuO22

Effective single-band 1D Hubbard model at half-filling, only 2 parameters: U 4.2 eV, t 0.55 eV

• Holon (charge) gap: m 0.75 eV

• Optic gap: = 2m 1.5 eV

•Two-spinon band: πJ 0.7 eV

Calculated (left) and measured (right) magnetic scattering in Calculated (left) and measured (right) magnetic scattering in 1D Mott insulator SrCuO2. (I. Zaliznyak, et. al., PRL, 2004)1D Mott insulator SrCuO2. (I. Zaliznyak, et. al., PRL, 2004)

Calculated (left) and measured (right) magnetic scattering in Calculated (left) and measured (right) magnetic scattering in 1D Mott insulator SrCuO2. (I. Zaliznyak, et. al., PRL, 2004)1D Mott insulator SrCuO2. (I. Zaliznyak, et. al., PRL, 2004)


Summary ISummary ISummary ISummary I

• dCP continuum dominates electron spin dynamics in -Cu-O- chains up to 0.7 eV

– no evidence for itinerancy effects in spinon spectral weight

– consistent with theoretical calculation by Benthien & Jeckelmann, PRB (2007)

• “Muller alsatz” (MA) fits data quite well

– disappointing, as there are notable differences at higher energies between MA and exact results by Bougourzi, et al (1997), Caux et al (2005, 2006).

• dCP continuum dominates electron spin dynamics in -Cu-O- chains up to 0.7 eV

– no evidence for itinerancy effects in spinon spectral weight

– consistent with theoretical calculation by Benthien & Jeckelmann, PRB (2007)

• “Muller alsatz” (MA) fits data quite well

– disappointing, as there are notable differences at higher energies between MA and exact results by Bougourzi, et al (1997), Caux et al (2005, 2006).

Benthien & Jeckelmann, PRB (2007)Karbach, et al, PRB (1997)

Muller atsatz

Exact 2-spinon


Spin excitations in SrSpin excitations in Sr22CuOCuO33Spin excitations in SrSpin excitations in Sr22CuOCuO33




SrSr22CuOCuO33

Triplet spectrum of two-spinon states, combined set of 3 measurements on MAPS at ISIS is shown

spinons

Three co-aligned crystalsmtotal = 18.45 gMosaic < 0.3T= 6 K


Qchain (2/b)

Ene

rgy

Tra

nsfe

r (m

eV)

S(Q

,)

(mba

rn/s

r/m

eV/C

u2+)

Ei=240 meV

Ei=516 meV

Ei=794 meV

Ei=1088 meV

Normalized INS data from Sr2CuO3 crystalsNormalized INS data from Sr2CuO3 crystals

Four neutron incident energies used – Ei = [240, 516, 794,1088]

meV

– Energy resolution Ei

Detailed fitting done on multiple “cuts” at constant energy transfer for each Ei

Figure: comparison of background-subtracted normalized data (left column) and best fit to Muller ansatz expression corrected for the instrumenal resolution (right column)

Four neutron incident energies used – Ei = [240, 516, 794,1088]

meV

– Energy resolution Ei

Detailed fitting done on multiple “cuts” at constant energy transfer for each Ei

Figure: comparison of background-subtracted normalized data (left column) and best fit to Muller ansatz expression corrected for the instrumenal resolution (right column)


Fits of the constant-E cuts in SrFits of the constant-E cuts in Sr22CuOCuO33Fits of the constant-E cuts in SrFits of the constant-E cuts in Sr22CuOCuO33


Deviation #1

J (m

eV)

A

<A> = 0.44(8)

<J> = 240(7) meV

Incident Energies: 240 meV516 meV794 meV

1088 meV

Energy Transfer (meV)

Fits to the Muller ansatzFits to the Muller ansatzFits to the Muller ansatzFits to the Muller ansatz

Results are qualitatively similar to SrCuO2

However, now observe clear deviations outside error bars– Energy-dependent exchange

coupling J decreasing at low E

– Energy-dependent intensity prefactor A decreasing at high E

Sr2CuO3 data clearly deviate from Muller ansatz!

Results are qualitatively similar to SrCuO2

However, now observe clear deviations outside error bars– Energy-dependent exchange

coupling J decreasing at low E

– Energy-dependent intensity prefactor A decreasing at high E

Sr2CuO3 data clearly deviate from Muller ansatz!

Deviation #2


J.-S. Caux et al. J. Stat. Mech. (2006)

<A> ≈ 0.32

<J> = 243(6) meV

Fits to exact expressions for 2- and 4-spinon continuaFits to exact expressions for 2- and 4-spinon continuaFits to exact expressions for 2- and 4-spinon continuaFits to exact expressions for 2- and 4-spinon continua

<A> ≈ 0.43

2-spinon

2-spinon + 4-spinon


J.-S. Caux et al. J. Stat. Mech. (2006)

Energy Transfer (meV)

J (m

eV)

A

<A> = 0.32(5)

<J> = 243(6) meV

Incident Energies:240 meV516 meV794 meV

1088 meV

Fits to exact expressions for 2- and 4-spinon continuaFits to exact expressions for 2- and 4-spinon continuaFits to exact expressions for 2- and 4-spinon continuaFits to exact expressions for 2- and 4-spinon continua

• Both J and intensity prefactor A are now E-independent

– agrees with physical expectation

• A is dramatically reduced compared to expected value A ≈ 1

– two-spinon and four-spinon excitations must account for ≈ 98% of total spin spectral function

– Mystery of missing factor ~3 ≈ π ?

• Both J and intensity prefactor A are now E-independent

– agrees with physical expectation

• A is dramatically reduced compared to expected value A ≈ 1

– two-spinon and four-spinon excitations must account for ≈ 98% of total spin spectral function

– Mystery of missing factor ~3 ≈ π ?


Summary IISummary IISummary IISummary II

• Spin response in Sr2CuO3 is similar to SrCuO2 but measured with much better precision

– multispinon dCP continuum dominates dynamical electronic properties in -Cu-O- chains up to 0.7 eV

– no evidence for itinerancy effects in spin spectral weight, consistent with theoretical calculation by Benthien & Jeckelmann, PRB (2007)

• “Muller alsatz” (MA) DOES NOT fit the data !

– notable differences at higher energies between MA and exact results by Bougourzi, et al (1997), Caux et al (2005, 2006) are experimentally observed

• Mystery of anomalously small intensity (prefactor A) does not (yet) allow to claim observation of 4-spinon contribution

• Spin response in Sr2CuO3 is similar to SrCuO2 but measured with much better precision

– multispinon dCP continuum dominates dynamical electronic properties in -Cu-O- chains up to 0.7 eV

– no evidence for itinerancy effects in spin spectral weight, consistent with theoretical calculation by Benthien & Jeckelmann, PRB (2007)

• “Muller alsatz” (MA) DOES NOT fit the data !

– notable differences at higher energies between MA and exact results by Bougourzi, et al (1997), Caux et al (2005, 2006) are experimentally observed

• Mystery of anomalously small intensity (prefactor A) does not (yet) allow to claim observation of 4-spinon contribution


Dimensional cross-over: effect of inter-chain couplingDimensional cross-over: effect of inter-chain couplingDimensional cross-over: effect of inter-chain couplingDimensional cross-over: effect of inter-chain coupling

What happens in the ordered phase?

T << TN ≈ 5 K << J ≈ 2,800 KWhat happens in the ordered phase?

T << TN ≈ 5 K << J ≈ 2,800 K


Extremely weak coupling between S=1/2 antiferromagnetic spin chains in SrCuO2 and Sr2CuO3 results in static order but marginal modulation of the inelastic spectrum.

Effect of inter-chain coupling on spin dynamics: SrCuOEffect of inter-chain coupling on spin dynamics: SrCuO22. . Effect of inter-chain coupling on spin dynamics: SrCuOEffect of inter-chain coupling on spin dynamics: SrCuO22. .

J 226 meV, TN 5 K, <µ> 0.035µB I. Zaliznyak et al, PRL (1999,2004).


Magnetic Bragg peak

Magnon

A

A

AB

C

C

B

A. Zheludev et al, PRB 65 014402 (2001). J 24 meV, TN 9 K, <µ> 0.15µB

Weak inter-chain coupling of the S=1/2 chains: effect of the Weak inter-chain coupling of the S=1/2 chains: effect of the static order on spin dynamics.static order on spin dynamics.

Weak inter-chain coupling of the S=1/2 chains: effect of the Weak inter-chain coupling of the S=1/2 chains: effect of the static order on spin dynamics.static order on spin dynamics.


Inter-chain dispersion of spin excitations in SrInter-chain dispersion of spin excitations in Sr22CuOCuO33 Inter-chain dispersion of spin excitations in SrInter-chain dispersion of spin excitations in Sr22CuOCuO33

0 2 4 6E (meV)

0

50

100

150

200 ( 0.0,0.5,1.0)

( 0.0,0.5,0.75)

Neu

tron

cou

nts

in 1

0 m

inm

onit

or=5

.0e+

06

0 2 4 6E (meV)

0 2 4 6E (meV)

( 0.0,0.5,0.65)

Neu

tron

cou

nts

in 1

0 m

inN

eutr

on c

ounts

in 1

0 m

inm

onit

or=5.

0e+06

Neu

tron

cou

nts

in 1

0 m

in

0

100

200

300

400

0

50

100

150

200

0

50

100

150

200

( 0.0,0.5,0.575) Where are magnons?

No evidence for any coherent quasiparticle excitation at all!?

A

B D

C



Intensity and continuum gap fixed at values

found for l=0.575

Intensity and continuum gap refined in a fit



Try higher energy resolution

0 2 4 6E (m eV )

0

50

100

150

200 ( 0.0,0.5,0.25)

( 0.0,0.5,0.375)

mon

itor

=5.

0e+

06

0 2 4 6E ( m e V )

0 2 4 6E ( m e V )

( 0.0,0.5,0.425)

Net

in

ten

sity

(co

un

ts i

n 1

0 m

in)

0

5 0

1 0 0

1 5 0

2 0 0

0

5 0

1 0 0

1 5 0

2 0 0

( 0.0,0.5,0.5)

0

5 0

1 0 0

1 5 0

2 0 0



Intensity and continuum gap fixed at values for l=0.5

Intensity and continuum gap refined I a fit


““Confederate flag”: a fine-tuned model with compensated Confederate flag”: a fine-tuned model with compensated mean field mean field

““Confederate flag”: a fine-tuned model with compensated Confederate flag”: a fine-tuned model with compensated mean field mean field

J’

J

J’/2

A. A. Nersesyan and A. M. Tsvelik, PRB 67 024422 (2003).J’/J <<1, J’ = 2J”

Frustration relieves the mean-field spinon attraction and a need for their confinement into magnons:

2D propagating (weakly bound?) S=1/2 spinons

Frustration relieves the mean-field spinon attraction and a need for their confinement into magnons:

2D propagating (weakly bound?) S=1/2 spinons

J

J’/2


Realization of the frustrated “confederate flag” model in Realization of the frustrated “confederate flag” model in SrSr22CuOCuO33

Realization of the frustrated “confederate flag” model in Realization of the frustrated “confederate flag” model in SrSr22CuOCuO33

J J c≈3.

9c≈

3.9

Ǻ

b≈3.5b≈3.5 Ǻ 2J’ 2J’

J’J’

• Use realistic ionic radii

• Interchain hopping proceeds through Cu-O-O-Cu path!

J’/J ~ (tCu-OtO-O)/O2

Seems to be a realization of Tsvelik-Nersesyan’s “Confederate flag” model!


SummarySummarySummarySummary

• Spin excitations dominate electron dynamics in chain cuprates up to 0.7 eV

– no evidence for itinerancy corrections to spectral weight spin-charge separation in 1D

– spin-only Hamiltonian is sufficient

– Muller ansatz fails exact result fits well except for mystery of small A

• Weakly bound/unbound 2D spinons in the Neel-ordered phase?

– 2D-dispersive continuum at low E in the ordered phase

– no evidence for the coherent quasiparticle excitations

– no energy-scale separation for a continuum

– fine-tuned Tsvelik-Nersesyan’s “frustrated flag” model is realized by the inter-chain Cu-O-O-Cu hopping ?

• Spin excitations dominate electron dynamics in chain cuprates up to 0.7 eV

– no evidence for itinerancy corrections to spectral weight spin-charge separation in 1D

– spin-only Hamiltonian is sufficient

– Muller ansatz fails exact result fits well except for mystery of small A

• Weakly bound/unbound 2D spinons in the Neel-ordered phase?

– 2D-dispersive continuum at low E in the ordered phase

– no evidence for the coherent quasiparticle excitations

– no energy-scale separation for a continuum

– fine-tuned Tsvelik-Nersesyan’s “frustrated flag” model is realized by the inter-chain Cu-O-O-Cu hopping ?


Thank you!Thank you!Thank you!Thank you!


Spinons in chain copper oxides: giant heat conductance.Spinons in chain copper oxides: giant heat conductance.Spinons in chain copper oxides: giant heat conductance.Spinons in chain copper oxides: giant heat conductance.

A. V. Sologubenko et al, PRB 64, 054412 (2001).


Spinons in chain copper oxides: picosecond relaxation of Spinons in chain copper oxides: picosecond relaxation of optical nonlinearity.optical nonlinearity.

Spinons in chain copper oxides: picosecond relaxation of Spinons in chain copper oxides: picosecond relaxation of optical nonlinearity.optical nonlinearity.

T. Ogasawara et al, PRL 85, 2204 (2000).SrSr22CuOCuO33


Planned projects and directions for future studiesPlanned projects and directions for future studiesPlanned projects and directions for future studiesPlanned projects and directions for future studies

• Itinerancy effects in the two-spinon spectrum of chain cuprates – refine analysis of SrCuO2 data, measure Sr2CuO3

• Itinerancy effects in the two-spinon spectrum of chain cuprates – refine analysis of SrCuO2 data, measure Sr2CuO3

M. J. Bhaseen, F. S. H. Essler, and A. Grage, cond-mat/0312055

• Oxygen-doping chain cuprate Sr2CuO3+y – two-spinon response (incommensurability?)– effect on the inter-chain hopping and dimensional cross-over

• Oxygen-doping chain cuprate Sr2CuO3+y – two-spinon response (incommensurability?)– effect on the inter-chain hopping and dimensional cross-over

T. Valla, et. al.,cond-mat/0403486

• Model Heisenberg spin systems: ABX3x2D2O, PHCC, …– instability of Bose-quasiparticles in spin liquids– dimensional and quantum-classical cross-over in spin chains

• Model Heisenberg spin systems: ABX3x2D2O, PHCC, …– instability of Bose-quasiparticles in spin liquids– dimensional and quantum-classical cross-over in spin chains

• Layered perovskites La2-xSrx(Co,Mn)O4

– effect of charge-order superstructure, disorder, etc. on spin dynamics

• Layered perovskites La2-xSrx(Co,Mn)O4

– effect of charge-order superstructure, disorder, etc. on spin dynamics


SrCuO2Sr2CuO3

Crystal structure of chain cupratesCrystal structure of chain cupratesCrystal structure of chain cupratesCrystal structure of chain cuprates

1D Hubbard model: only 2 parameters, U 4.2 eV, t 0.55 eV

Spin bandwidth, πJ ≈ 4πt2/U ~ 0.75 eV

Optic gap 1.5 eV






phonons

SrCuOSrCuO22

Triplet spectrum of two-spinon states, combined set of 4 measurements on MAPS at ISIS

• Effective single-band Hubbard model at half-filling t1

t2

• Spin-charge separation

• Holon gap

m 0.75 eV

• Optic gap

= 2m 1.5 eV

•Two-spinon band

πJ 0.7 eV

spinons

Spin part of one-dimensional electronsSpin part of one-dimensional electronsSpin part of one-dimensional electronsSpin part of one-dimensional electrons

spinons in strongly correlated chain cuprates

Documents

spin excitations

ev spin bandwidth

spin ladders

spin waves

j s si si

dlowd systems

d order

d mott insulatorj