THE ROLE OF FRUSTRATION AND INHERENT DISORDER IN THE FORMATION OF

QUANTUM SPIN LIQUID: EVIDENCE FROM ELECTRONIC PROPERTIES OF

ORGANIC MOTT INSULATORS

Silvia Tomić

Institut za fiziku, Zagreb, Croatia

Quantum spin liquid – an intriguing phenomenon QSL in organic quasi-2D compounds with strong correlations Electronic properties and electrodynamic response• -(BEDT-TTF)2Cu2(CN)3

• -(BEDT-TTF)2Ag2(CN)3

• b´ – EtMe3Sb [Pd(dmit)2]2

Summary and Prospects

Outline

QSL: a highly correlated fluctuating quantum spin state

State in which quantum fluctuations are strong enough to preclude spin ordering

down to zero temperature

Expected to appear in geometrically frustrated systems

• Theoretically predicted more than 40 years ago as RVB – Anderson 1973

• Ground state of triangular lattice S=1/2 AF instead of conventional LR magnetic order

• Real materials with triangular lattice, no spontaneously broken symmetry and emergent

fractional excitations:

• Layered organics, approximate triangle Layered inorganics

• -(BEDT-TTF)2Cu2(CN)3 YbMgGaO4

• -(BEDT-TTF)2Ag2(CN)3 Sc2Ga2CuO7

• b´-EtMe3Sb [Pd(dmit)2]2 1T-TaS2 : perfect triangle

• -H3(Cat-EDT-TTF)2

• Inherent RandomnessAnderson , Mat.Res.Bull. (1973)

Klanjsek et al., Nat.Phys. (2017)Savary and Balents, Rep.Prog.Phys. (2017)

Zhou, Kanoda and Ng, Rev.Mod.Phys. (2017) Isono et al. , Phys.Rev.Lett. (2014)

Quasi-2D Organic Solids

• strong electronic correlations → charge localization

-Dimers of two molecules on a triangular lattice

-One hole/electron per organic dimer

• Under moderate pressure they become metallic with superconducting ground state

• Ambient pressure and low temperatures: AF ordering

• Frustration due to triangular arrangement of dimers

-t’/t ≈ 0.8-0.99

-Magnetic ordering suppressed despite strong AF exchange

-Ground state: quantum spin liquid

Kandpal et al. , PRL (2009)

Koretsune and Hotta, PRB (2014) Nakamura et al., PRB (2012)

Quasi-2D Organic Solids: Charge-transfer complexes

Organic layer

Ionic layer

Organic layer

Quasi-2D Organic Solids - QSL

• Organic dimers on a triangular lattice form layers which are separated by

the layers of the other ionic, non-magnetic and non-conducting, component

• 3 compounds - Mott insulators with different degree of electron correlations – QSL

• Magnetic and thermodinamic response with QSL signatures: T < 4 K

-no singular feature in the susceptibility, despite large J 250 K

-power-law behavior of T1 NMR relaxation time

-a finite linear term g in the specific heat vs T

-thermal conductivity: finite linear term in k/T vs T2 plots., or presence of tiny gap

• Close to the M-I transition spin-only description not sufficient!

• Exp: Charge response anomalous in dc, radio and terahertz range at T < 60 K

• Theory: spin-dipolar coupling in the presence of geometrical frustration

-exp confirmation for intra-dimer dipoles is missing

-frustrated triangular lattices cannot destroy magnetic order on their own

-mechanism relies on the Coulomb interactions within the organic sublattice only

Huse and Elser, PRL(1988)

Hotta PRB(2010), Crystals(2012)

Naka et Ishihara.,JPSJpn(2010, 2013)

Li et al., JPCM (2010)

Dayal et al., PRB (2011)

Shimizu et al., PRL(2003)

S.Yamashita et al., Nat.Phys.(2008)

M.Yamashita et al., Nat.Phys.(2008)

Shimizu et al., PRL(2016)

Itou et al., Phys.Rev.B(2008)

M.Yamashita, Science(2010)

Yamashita, Nat.Commun.(2011)

Electronic properties and electrodynamic response

• -(BEDT-TTF)2Cu2(CN)3

• -(BEDT-TTF)2Ag2(CN)3

• b’ – EtMe3Sb [Pd(dmit)2]2

DC transport: hopping

• Nearest neighbor hopping at high T: s exp(-D/T)

• 2D VRH at low T: s exp[-(T0/T)1/3]

• Crossover: -Cu: around 150 K; -Ag: close to RT

• Two distinct origins of the charge localization:

• Mott localization

• Anderson localization → Inherent randomness

• At hight T: nearest neighbor hopping

• at T < 100 K: s exp[-(T0/T)1/2]

• Efros-Shklovskii hopping

• Strong Coulomb interaction

• Soft gap

Efros and Shklovskii, J.Phys.C: SSP (1975)

Ge et al., PRB (2014)

Pinteric et al., Phys.Rev.B (2014)

Pinteric et al., Phys.Rev.B RC (2016)

Lazic et al., submitted (2017)

Dielectric response: Relaxor-like

Abdel-Jawad et al., Phys.Rev.B (2010)

Pinteric et al., Phys.Rev.B (2014)

Pinteric et al., Phys.Rev.B RC (2016)

Abdel-Jawad et al., Phys.Rev.B (2013)

Lazic et al., submitted (2017)

-ET2Ag2CN3-ET2Cu2CN3

in

in

out

out

Ferroelectric-like response

in the presence of disorder

Dielectric response: Relaxor-like

• Broad relaxation time spectrum

• Width increases on cooling

• Gradual freezing of the rel.time t0

Relaxor phenomenology• Polar domains of low-symmetry structure• Reorientation of dipole moments within domains• Motion of the interphase boundaries

t

-

D-1

01

1

iHF

Cooperative motion and glassy freezing in relaxor feroelectrics

Pinteric et al., Phys.Rev.B (2014)

Pinteric et al., Phys.Rev.B RC (2016)

Abdel-Jawad et al., Phys.Rev.B (2013)

Lazic et al., submitted (2017)

Is there any dipole?

Too small charge imbalance:

±0.05e

Charge imbalance cannot

be determined

Pinteric et al., Phys.Rev.B RC (2016) Pustogow, Dressel, unpublished (2016)

Sedlmeier et al., PRB (2012)

C

C

C

CAndrej Pustogow

Is there any dipole?

Charge imbalance cannot

be determinedLazic et al., submitted (2017)

Dimeric

mode

Molecular

mode

Andrej Pustogow

b’ – EtMe3Sb [Pd(dmit)2]2

Where is disorder?Any domains of low-symmetry?

• Cu (Ag) ions triangularly coordinated to CN in the anions

• c1 and c2 reside on an inversion center inherent disorder in global P21/c

• Four possible configurations

• Structural refinements: P21/c is broken

• Domains with lower symmetry

Lazic et al., submitted to PRL(2017)

Pinteric et al., Phys.Rev.B (2014)

Pinteric et al., Phys.Rev.B RC (2016)

Dressel et al., Phys.Rev.B RC (2016)

Pinteric et al., PRB, RC (2016)

• EtMe3Sb reside on a 2-fold axis

• Et (CH2-CH3): 2 different equally probable orientations

inherent disorder in global C2/c

• Eight possible configurations

Foury-Leylekian et al.

DFT calculations of relaxed structure of minimum energy

Results• Energy difference between 4 / 8 configurations is extremely small• -Cu and -Ag: 5-25 meV; b’-EtMe3Sb-dmit: 28-146 meV

• Symmetry: lower than the global symmetry

• Ground state: electronic states quasi-degenerate in energy →• Randomly distributed domains of local order with reduced symmetry• Disorder lower in -Ag (P21) than in k-Cu (P1) and in b’-EtMe3Sb-dmit (P1)

• Nb of H-bonds between ionic and organic dimer sublattice

Dressel et al., PRB RC (2016)

Pinteric et al., PRB, RC (2016)

Lazic et al., submitted to PRL(2017)

Predrag Lazic

Procedure

• Atomic coordinates: x-ray data to construct possible configurations

• Entire system relaxes with the atomic positions and the unit cell parameters

Low-energy excitations: charged domain walls

• Domains of local order/reduced symmetry are already formed at RT

• Disorder whose origin is in the ionic sublattice causes charge redistribution within

organic dimer layers

• Charge defects within anti-phase boundaries between domains respond to ac electric

field

• As T decreases → domains become more “visible” and nb of domain walls increases

and the motion of domain wall pairs become increasingly correlated.

Van der Waals interaction: dmit versus BEDT-TTF

b’-EtMe3Sb-dmit: Van der Waals interaction important for the cohesion of the crystal

BEDT-TTF:

Structure dominantly determined

by the networks of Cu2(CN)3 and

Ag2(CN)3 anions

Dressel et al., PRB RC (2016)

Pinteric et al., PRB, RC (2016)

Lazic et al., submitted to PRL(2017)

• Semi-local DFT ie. no vdW: the cell parameters were

unrealistically large: 22% larger unit cell than found

experimentally

• Non-local vdW-DF: the relaxed unit cell meets

the experimental one to within 4%

• Largest changes in the a and b parameters

• Dimers in the (a,b) plane are held together by vdW

Summary and Prospects

• Frustration due to triangular arrangement of organic dimers

• Triangular lattices on their own unable to destroy LR magnetic order?

• Real materials: Inherent disorder - randomness - in ionic sublattice

• Ground state: a manifold of electronic states with reduced symmetry and

charge redistribution

• Hopping dc transport

• Relaxor dielectric response due to cooperative motion of charged DWs

• Role of dimer-spin coupling not clear

• No experimental evidence for electric intra-dimer dipoles• Global symmetry broken locally or at global scale? Foury-Leylekian et al.

• Existing inorganic QSL real materials contain additional inherent disorder

outside of the triangular or kagome lattices:

-ZnCu3(OH)6Cl2 – herbertsmithite….: defects coupled to kagome spins, global symmetry reduction Zorko et al. PRL (2017)

-1T-TaS2 : disorder in inter-layer coupling Klanjsek et al., Nat.Phys. (2017)

Inherent randomness in QSL real materials may be of critical importance for the prevalence of QSL over AF ordering

Research in collaboration with

Single crystals prepared by

K.Kanoda, K.Miyagawa, Uni Tokyo

J.A.Schlueter, Argonne NL

G.Saito, T.Hiramatsu, Y.Yoshida, Uni Nagoya

R.Kato, RIKEN

Zagreb

Marko Pinterić

Predrag Lazić

Tomislav Ivek

Matija Čulo

Bojana Hamzić

Ognjen Milat

Branko Gumhalter

Nadja Došlić

David Rivas Gongora

Marko Kuveždić

Mario Basletić

Emil Tafra

Amir Hamzić

University Stuttgart

Andrej Pustogow

Martin Dressel

Paris, Orsay

Vita Ilakovac

Pascale Foury

Jean-Paul Pouget