Magnetic and non-magnetic phases of a quantumspin liquid

Shouvik Sur

October 18, 2011

Introduction + Motivation The Experiment Comparison with Theory 1/13

Outline

1 Introduction + Motivation

2 The Experiment

3 Comparison with Theory

Introduction + Motivation The Experiment Comparison with Theory 2/13

Why Quantum Spin Liquids?

Qualitatively new physics:

Excitations with fractional quantum numbers.

Artificial gauge fields.

New phases of matter: Strange Metals, Topologically orderedstates, etc.

Possibly associated with High TC superconductors.

Introduction + Motivation The Experiment Comparison with Theory 3/13

More about QSLThe Picture:

RVB states

Expected to be found in:

Frustrated magnetic sytems, eg. Kagome, Triangular, etc.Close to Mott transition, eg. Present sytem, etc.

H = −t∑<i ,j>

(c†i cj + h.c.

)+ U

∑ni ,↑ni ,↓

Introduction + Motivation The Experiment Comparison with Theory 4/13

About κ− (BEDT − TTF )Cu2(CN)3

Organic, layered molecular system.(BEDT-TTF: bis(ethylenedithio)-tetrathiafulvalene)

Half filled, Mott insulator: 1electron/site.

2 D, almost isotropic, triangularlattice with J ′/J ∼ 0.9.

J ∼ 250K , butno magnetic ordering down to20mK .

Introduction + Motivation The Experiment Comparison with Theory 5/13

About κ− (BEDT − TTF )Cu2(CN)3

Yamashita et. al., Nature Phys. 4(2008) Shimizu et. al., PRL 91 (2003)

Introduction + Motivation The Experiment Comparison with Theory 6/13

The Experiment : Main Result

Introduction + Motivation The Experiment Comparison with Theory 7/13

Result 1: First Phase Transition

Field scan at T = 120mK :

No magnetic moments belowµ0Hc = 14mT

For H > Hc magnetic momentsdevelop... Field induced quantumphase transition.

Be ∝ (H − Hc)β where

β = 0.39(2) taken over

µ0H ∈ [0, 0.4]T .

Introduction + Motivation The Experiment Comparison with Theory 8/13

Result 2: Detailed Phase Boundary

Position of Hc(T ) for T ∈ [0.02, 8]K

Fitted to Tc ∝ (H − Hc)φ to

obtain φ = 0.94(1)

Fit to 2D BEC Tc gives similarvalue.

Interpolation: H0 = Hc(T = 0)

• Scaling: µ0H0 = 5.2(3) mT

• 2D BEC : µ0H0 = 5.2(2) mT

Spin Gap:

∆s [= gS(µbµ0/kB)H0] = 3.5(1) mK [ ref: J ∼ 250 K .]

Introduction + Motivation The Experiment Comparison with Theory 9/13

Result 3: Crossovers

Temperature scan at H = 0:

Spin fluctuation rate:Γ(T ) ∝ Tw

1st crossover(T = ∆v ∼ 0.5 K ):w ≈ 0→ w = 2.27(5)

2nd crossover (T = TP):w = 2.27(5)→ wavg ∼ 0

For T > 100 K , w = 1.

Introduction + Motivation The Experiment Comparison with Theory 10/13

Result 4: Second Phase Transition

Field scan at T = 0.8 K :

Scaling Law: Be ∝ (H − Hc)β

‘Crossover’: βL = 0.36(4)→βH = 0.83(4)

Fits model of field-induceddeconfinement transition:S = 1 spin waves → S = 1

2spinons.

Introduction + Motivation The Experiment Comparison with Theory 11/13

Comparison with Theory

Ref.[17] : Kaul, R. K. & Sachdev, S. PRB 77, 155105 (2008).

Ref.[22] : Ballasteros, H. G. et. al. Phys. Lett. B 387, 125131 (1996).

Ref.[23] : Isakov, S. V., Senthil, T., &. Kim,Y. B., PRB 72, 174417 (2005).

Introduction + Motivation The Experiment Comparison with Theory 12/13

The Experiment : Main Result

Introduction + Motivation The Experiment Comparison with Theory 13/13