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
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