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OAK RIDGE NATIONAL LABORATORYQuasiparticle 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
- 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

ε(q) (Kelvin)

whatsgoingon?

q (Å-1)

Excitations in quantum Bose liquid: superfluid 4Hemaxon

roton

phonon

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

The “cutoff point” of the quasiparticle spectrum in the quantum Bose-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+||+ JS SiSi+D

- Exchange couplings J||, Jthrough orbital overlaps may be different
- J||/J >> 1 (<<1) parameterize quasi-1D (quasi-2D) case

J0 > 0

triplet

0 = J0

singlet

Simple example: coupled S=1/2 dimersSingle dimer: antiferromagnetically coupled S=1/2 pair

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

J0

J1

e(q)

0 = J0

q/(2p)

Simple example: coupled S=1/2 dimersChain of weakly coupled dimers

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

Dispersione(q) ~ J0 + J1cos(q)

triplet

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(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

strong interaction

weak interaction

2D quantum spin liquid: a lattice of frustrated dimersM. B. Stone, I. Zaliznyak, et. al. PRB (2001)

(C4H12N2)Cu2Cl6 (PHCC)

Cu2+ 3d9

S=1/2

- singlet disordered ground state
- gapped triplet spin excitation

Single dispersive mode along h

- Single dispersive mode along l

- Non-dispersive mode along k

- gap D = 1 meV
- bandwidth = 1.8 meV

Quasiparticle spectrum termination line in PHCC

max{E2-particle (q)}

min{E2-particle (q)}

Spectrum termination line

E1-particle(q)

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 diagonalQ = (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)

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 directionsSummary 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

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 PHCCIntensity (counts in 1 min)

E (meV)

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

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 chainHeisenberg antiferromagnetic chain with S = 1

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 CsNiCl3Spectrum termination point in CsNiCl3

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

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