Quasiparticle breakdown in quantum spin liquid
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O AK R IDGE N ATIONAL L ABORATORY. Quasiparticle breakdown in quantum spin liquid. Igor Zaliznyak Neutron Scattering Group, Brookhaven National Laboratory. Collaborators M. B. Stone D. Reich, T. Hong C. Broholm. &. What is liquid? no shear modulus

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Quasiparticle breakdown in quantum spin liquid

OAK RIDGE NATIONAL LABORATORY

Quasiparticle breakdown in quantum spin liquid

Igor Zaliznyak

Neutron Scattering Group, Brookhaven National Laboratory

Collaborators

  • M. B. Stone

  • D. Reich, T. Hong

  • C. Broholm

&


What is quantum liquid

  • What is liquid?

    • no shear modulus

    • no elastic scattering = no static correlation of density fluctuations

      ‹ρ(r1,0)ρ(r2,t)›→ 0

t → ∞

What is quantum liquid?

  • What is quantum liquid?

    • all of the above at T→ 0 (i.e. at temperatures much lower than inter-particle interactions in the system)

  • Elemental quantum liquids:

    • H, He and their isotopes

    • made of light atoms  strong quantum fluctuations


Excitations in quantum bose liquid superfluid 4 he

ε(q) (Kelvin)

whatsgoingon?

q (Å-1)

Excitations in quantum Bose liquid: superfluid 4He

maxon

roton

phonon

Woods & Cowley, Rep. Prog. Phys. 36 (1973)


The cutoff point of the quasiparticle spectrum in the quantum bose liquid

The “cutoff point” of the quasiparticle spectrum in the quantum Bose-liquid


Spectrum termination in 4 he experiment

Spectrum termination in 4He: experiment


What is quantum spin liquid

Coupled planes J||/J<<1

  • no static spin correlations

    ‹Siα(0)Sjβ(t)›→ 0, i.e. ‹Siα(0)Sjβ (t)›= 0

  • hence, no elastic scattering (e.g. no magnetic Bragg peaks)

Coupled chains

J||/J>> 1

t → ∞

What is quantum spin liquid?

  • Quantum liquid state for a system of Heisenberg spins

    H = J||SSiSi+||+ JS SiSi+D

  • Exchange couplings J||, Jthrough orbital overlaps may be different

    • J||/J >> 1 (<<1) parameterize quasi-1D (quasi-2D) case


Simple example coupled s 1 2 dimers

J0 > 0

triplet

0 = J0

singlet

Simple example: coupled S=1/2 dimers

Single dimer: antiferromagnetically coupled S=1/2 pair

H = J0 (S1S2) = J0/2 (S1 + S2)2 + const.


Simple example coupled s 1 2 dimers1

J0

J1

e(q)

0 = J0

q/(2p)

Simple example: coupled S=1/2 dimers

Chain of weakly coupled dimers

H = J0 S(S2iS2i+1) + J1S (S2iS2i+2)

Dispersione(q) ~ J0 + J1cos(q)

triplet


Dimers in 1d aka alternating chain

Dimers in 1D (aka alternating chain)

Chains of weakly interacting dimers in

Cu(NO3)2x2.5D2O

Cu2+ 3d9

S=1/2

E (meV)


Weakly interacting dimers in cu no 3 2 x2 5d 2 o

Weakly interacting dimers in Cu(NO3)2x2.5D2O

D. A. Tennant, C. Broholm, et. al. PRB 67, 054414 (2003)

Spin excitations never cross into 2-particle continuum and live happily ever after


2d quantum spin liquid a lattice of frustrated dimers

strong interaction

weak interaction

2D quantum spin liquid: a lattice of frustrated dimers

M. B. Stone, I. Zaliznyak, et. al. PRB (2001)

(C4H12N2)Cu2Cl6 (PHCC)

Cu2+ 3d9

S=1/2

  • singlet disordered ground state

  • gapped triplet spin excitation


Phcc a two dimensional quantum spin liquid

  • Single dispersive mode along h

  • Single dispersive mode along l

  • Non-dispersive mode along k

PHCC: a two-dimensional quantum spin liquid

  • gap D = 1 meV

  • bandwidth = 1.8 meV


Quasiparticle spectrum termination line in phcc

Quasiparticle spectrum termination line in PHCC

max{E2-particle (q)}

min{E2-particle (q)}

Spectrum termination line

E1-particle(q)


Phcc dispersion along the diagonal

Q = (0.15,0,-1.15)

200

resolution-corrected fit

800

150

600

100

400

50

200

150

Q = (0.1,0,-1.1)

0

resolution-corrected fit

0

100

400

50

300

0

200

200

Q = (0,0,1)

120

resolution-corrected fit

100

150

80

100

0

40

50

0

0

1

2

3

4

5

6

7

1

2

3

4

5

6

7

PHCC: dispersion along the diagonal

Q = (0.5,0,-1.5)

resolution-corrected fit

Intensity (counts in 1 min)

Q = (0.25,0,-1.25)

resolution-corrected fit

Q = (0.15,0,-1.15)

resolution-corrected fit

E (meV)

E (meV)


2d map of the spectrum along both directions

1.0

1.5

2.0

2.5

3.0

log(intensity)

7

6

5

E (meV)

4

3

2

1

0

0.20

6

Total

a

5

Triplon

4

Continuum

0.15

3

Integrated int (arb.)

(meV)

0.10

2

G

0.05

100

9

0

8

0.5

0.4

0.3

0.2

0.1

0

0

0.1

0.2

0.3

0.4

0.5

0.4

0.3

0.2

0.1

0

(0.5,0,-1-l)

(h,0,-1-h)

(h 0 -1-h)

2D map of the spectrum along both directions


Compare spectrum end point in helium 4

Compare: spectrum end point in helium-4


Summary and conclusions

Summary and conclusions

  • Quasiparticle breakdown at E > 2 is a generic property of quantum Bose (spin) fluids

    • observed in the superfluid 4He

    • observed in the Haldane spin chains in CsNiCl3 (I. Zaliznyak, S.-H. Lee and S. V. Petrov, PRL 017202 (2001))

    • observed in the 2D frustrated quantum spin liquid in PHCC

  • A real physical alternative to the ad-hoc “excitation fractionalization” explanation of scattering continua

  • Implications for the high-Tc cuprates: spin gap implies disappearance of coherent spin modes at high E


Temperature dependence in phcc

Temperature dependence in PHCC


Temperature dependence in copper nitrate

Temperature dependence in copper nitrate


Dispersion along the side l in phcc

800

Q = (0.5,0,-1.5)

resolution-corrected fit

600

400

200

0

Q = (0.5,0,-1.15)

400

Q = (0.5 0 -1)

300

resolution-corrected fit

resolution-corrected fit

300

200

200

100

100

0

0

1

2

3

4

5

6

7

400

Q = (0.5,0,-1.1)

resolution-corrected fit

300

200

100

0

Dispersion along the side (l) in PHCC

Intensity (counts in 1 min)

E (meV)


What would be a spin solid

  • ground state has static Neel order (spin density wave with propagation vector q = p)

  • quasiparticles are gapless Goldstone magnons

    e(q) ~ sin(q)

Sn = S0 cos(p n)

n

n+1

e(q)

  • elastic magnetic Bragg scattering at q = p

q/(2p)

What would be a “spin solid”?

Heisenberg antiferromagnet with classical spins, S >> 1


1d quantum spin liquid haldane spin chain

  • short-range-correlated “spin liquid” Haldane ground state

  • quasiparticles with a gap  ≈ 0.4J at q = p

    e2 (q) = D2 + (cq)2

Quantum Monte-Carlo for 128 spins.

Regnault, Zaliznyak & Meshkov, J. Phys. C (1993)

e(q)

2

q/(2p)

1D quantum spin liquid: Haldane spin chain

Heisenberg antiferromagnetic chain with S = 1


Spin quasiparticles in haldane chains in csnicl 3

Ni2+ 3d8

S=1 chains

J = 2.3 meV = 26 K

J = 0.03 meV = 0.37 K = 0.014 J

D = 0.002 meV = 0.023 K = 0.0009 J

3D magnetic order below TN = 4.84 K

unimportant for high energies

Spin-quasiparticles in Haldane chains in CsNiCl3


Spin quasiparticles in haldane chains in csnicl 31

Spin-quasiparticles in Haldane chains in CsNiCl3


Spectrum termination point in csnicl 3

Spectrum termination point in CsNiCl3

I. A. Zaliznyak, S.-H. Lee, S. V. Petrov, PRL 017202 (2001)


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