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Sci. Technol. Adv. Mater. 10 (2009) 024304 (12pp) doi:10.1088/1468-6996/10/2/024304

TOPICAL REVIEW

Variety of valence bond states formedof frustrated spins on triangular latticesbased on a two-level system Pd(dmit)2

Masafumi Tamura1 and Reizo Kato2

1 Department of Physics, Faculty of Science and Technology, Tokyo University of Science, Noda,Chiba 278-8510, Japan2 Condensed Molecular Materials Laboratory, RIKEN, Wako, Saitama 351-0198, Japan

E-mail: qra tam@ph.noda.tus.ac.jp

Received 18 October 2008Accepted for publication 4 November 2008Published 6 July 2009Online at stacks.iop.org/STAM/10/024304

AbstractRecent studies on the physical properties of the triangular system based on the Pd(dmit)2 salts(dmit = 1,3-dithiole-2-thione-4,5-dithiolate) are reviewed. Quantum chemical architectures ofthe Pd(dmit)2 molecule and its dimer are introduced with emphasis on the strong dimerizationof a two-level system, which provides unique physical properties of the salts. The magneticproperties are outlined in view of the magneto-structural correlation specific to the frustratedspin systems. Some newly discovered ground states and their origins are discussed, for whichthe valence bond formation plays a key role. Among them, the two-level structure is crucialfor the novel charge-separated state found in two salts. The valence bond ordering, similar tothe spin-Peierls transition, has been found in a two-dimensional frustrated spin system. Thephysical aspects and possible relation to the pressure-induced superconductivity are discussed.

Keywords: Pd(dmit)2 salts, triangular lattice, antiferromagnets, frustration, HOMO-LUMOinterplay, spin gap, superconductivity

1. Introduction

For a long time, the physics of frustrated quantum spinsystems has been a subject of active, mostly theoreticalresearch. Much attention has been paid to the possibility ofunconventional quantum states in frustrated systems, such asthe resonating valence bond state, particularly in connectionwith the high-Tc cuprate superconductors near the Mottcriticality. Following the extensive developments in 1980sand 1990s of materials with strongly correlated electrons, thesituation has noticeably changed in recent years, and a numberof such frustrated spin systems, including those based onorganic molecules, have become experimentally accessible.The strong electronic correlations in organic superconductorshave been reviewed in [1].

Specifically, two-dimensional (2D) triangularantiferromagnets, the prototypical frustrated system,are attained in some organic molecular systemshaving S = 1/2 Heisenberg spins. Two classes ofcompounds have been hitherto known to give 2Dtriangular antiferromagnets: the Z [Pd(dmit)2]2 salts [2](for a comprehensive review article see [3]) andκ-(BEDT–TTF)2 X salts [4] (for review see [5, 6]), whereBEDT–TTF = bis(ethylenedithio)tetrathiafulvalene, andZ and X are monovalent cation and anion, respectively(scheme 1 shows their chemical structures). Characteristicbehaviour of frustrated spins has been observed throughthe temperature dependence of magnetic susceptibilityχ in several Z [Pd(dmit)2]2 salts [2]. In the temperaturedependence of χ , a round maximum appears, indicatingthe onset of antiferromagnetic correlation over the

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Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

S

S

SS

Pd

S

S

S

SS

S

S

S

S

S

S

S

S

S

S

S

S

S

SNi

S

S

S

S

S

S

S

Pd(dmit)2

BEDT-TTF

Ni(tmdt)2

Scheme 1. Chemical structures of Pd(dmit)2, BEDT–TTF andNi(tmdt)2.

lattice, as usual in the low-dimensional quantum spinantiferromagnets, but the temperature of the χ maximum ismuch lower than the Weiss temperature inferred from thehigh-temperature tail of χ as a measure of the mean-fieldinteractions. This behaviour is explainable only by theeffect of frustration, which efficiently suppresses the growthof antiferromagnetic correlation. Similar behaviour hasbeen found in κ-(BEDT–TTF)2Cu2(CN)3 [4] and a fewother materials [7–9]. Most Z [Pd(dmit)2]2 salts exhibitantiferromagnetic ordering at lower temperatures [2],while no magnetic phase transition is detected inκ-(BEDT–TTF)2Cu2(CN)3 down to very low temperatures,which is viewed as the first evidence for a gapless spin-liquidstate realised in κ-(BEDT–TTF)2Cu2(CN)3 [4].

In both cases, the dimers of the featuring moleculesform 2D conduction layers in a nearly close-packed fashion.The conduction layers and the insulating layers comprisingclosed-shell counterions are alternatingly stacked in thecrystals. Each dimer has one charge carrier, so as to form aneffectively half-filled electron system. At ambient pressure,in fact, most Z [Pd(dmit)2]2 salts are Mott insulators havingone S = 1/2 spin localised on each dimer. Under a suitablepressure [10] or a uniaxial strain [11, 12], they exhibitmetallic conductivity, and superconductivity is found at lowtemperatures near the metal-insulator transition. The dimer[Pd(dmit)2]−2 is a radical anion, while (BEDT–TTF)+

2 isa cation. In addition to this apparent contrast, there areseveral significant differences between the two families. Forexample, the χ behaviour showing strong frustration effectis commonly observed in many Z [Pd(dmit)2]2 salts [2],whereas, among the κ-(BEDT–TTF)2 X salts, only theCu2(CN)3 salt exhibits such behaviour [4], the other κ-saltsbeing metals or paramagnetic insulators with significantantiferromagnetic correlation [5, 6]. In the Z [Pd(dmit)2]2

series, in contrast, a variety of unconventional valencebond states [13–17] appear around the spin-frustrated statedepending on the cation and pressure. For this reason, theZ [Pd(dmit)2]2 series occupy a unique position in molecularmaterials.

Another significant point that provides the Z [Pd(dmit)2]2

series with novel physical behaviour is the extraordinarilystrong dimerization in [Pd(dmit)2]2. It remarkably modifiesthe energy level structure of the dimer so as to givea unique quantum chemical effect, the HOMO–LUMOinterchange depicted in figure 2. (HOMO and LUMO are theabbreviations of the highest occupied and lowest unoccupiedmolecular orbitals, respectively.) This effect was pointedout by 1990 [18–23], and has been marked as a uniquecharacter of the Z [Pd(dmit)2]2 series. More sophisticatedcalculations support this conclusion [24–26]. A novel phasetransition is driven by this effect in some Z [Pd(dmit)2]2

salts [13–15]. Some of the observed phenomena [13–15]can never be expected for the single-level systems such asthe conventional TTF-based conductors. From a quantumchemical viewpoint, the HOMO–LUMO interchange is basednot only on the strong dimerization but also on thesymmetries of HOMO and LUMO, which are characteristicof the metal-dithiolene complexes [3]. The material designinspired by these features has been developed; it leads tothe single-component molecular metals based on Ni(tmdt)2

(tmdt = trimethylenetetrathiafulvalenedithiolate) [27]. In thiscase, the small HOMO–LUMO energy gap makes efficientHOMO–LUMO band crossing (hybridization) so as to formmultiple Fermi surfaces stabilising metallic state [28–30].On the other hand, in the dimer [Pd(dmit)2]2, the strongdimerization, owing to the Pd–Pd quasi-bonding, resultsin partial energetic transposition, rather than hybridization,of HOMO and LUMO. As a result, each dimer retainsquantum degrees of freedom, whose potential role in thesolid-state properties is an outstanding topic in the physics ofZ [Pd(dmit)2]2.

In this paper, we begin with qualitative discussions onthe molecular orbital characters of the Pd(dmit)2 moleculeand its dimer to explain the origin and evidence of theexotic HOMO–LUMO interplay effect in section 2. Inthe presence of the HOMO–LUMO interplay, the role ofthe MO characters is crucial even in the solid-state properties.Section 3 summarises the variation of the physical propertiesof the Z [Pd(dmit)2]2 series with Z . The effect of frustrationon the metal-insulator boundary in the phase diagram ispointed out. In section 4, common magnetic behaviour ofthe triangular frustrated spin system based on Z [Pd(dmit)2]2

is outlined. A possible spin-liquid state in Z [Pd(dmit)2]2,evidenced by recent experiments, is also mentioned. Section 5describes a novel charge separation phenomenon due tothe HOMO–LUMO interplay. In order to explain theobserved electron pairing, an idea of electron–hole compositesystem is introduced and applied to the dimer [Pd(dmit)2]2.Section 6 presents the discovery of spin-gapped groundstate and pressure-induced superconductivity in a frustratedspin system of Z [Pd(dmit)2]2. In this article, only typicalexperimental data are explicitly referred to. The structuraland electrical data for a wide range of related compoundscan be found in the comprehensive review [3] and referencestherein.

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Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

LUMO (5b2g)

HOMO (4b1u)

[Pd(dmit)2]2–[Pd(dmit)2]0

2|tA|

2|tA|

HOMO–LUMOseparation, ∆

x

y

a-HOMO

a-LUMO

b-HOMOb-LUMO

b

a

o b

a

oz = 0 z = c/2β′-type

Dimer (S = 1/2)[Pd(dmit)2]2–

tB

ts

t r

tA

[Pd(dmit)2]

(a)

(b)

Figure 1. (a) The HOMO–LUMO interchange caused by the strongdimerization. (b) A schematic display of the typical packing modeof the dimers in the β ′-type crystals, showing the solid-crossingstructure. The definition of the transfer integrals is also indicated.

2. Quantum chemical background: molecularcharacteristics of Pd(dmit)2 and its dimer

Prior to the solid-state properties, let us take a brief lookat the chemical characteristics of Pd(dmit)2 and its dimer.Figure 1(a) schematically shows the chemical structure andorbitals of Pd(dmit)2. The 4dxz orbital of Pd, which isasymmetric with respect to the x and z directions in terms ofthe assumed D2h symmetry, is relevant to the frontier levels.This leads a significantly different role from that of the centralC C unit in formation of HOMO of a TTF-based molecule;HOMO is usually π bonding over the central C C unit,i.e. symmetric with respect to x . The Pd(dmit)2 moleculemay be partitioned to the three units, the central Pd and thetwo wings, dmit π ligands. Therefore, three combinationsare possible with respect to the Pd–S coordination: bonding,anti-bonding and non-bonding. As a result of the x-asymmetryof the Pd 4dxz orbital, the Pd–S bonding and anti-bondingorbitals are x-asymmetric, and the x-symmetric orbital isnon-bonding with little contribution of Pd 4dxz . These arethe common features of the planar metal-dithiolene complexmolecules [3]. In contrast, the relevant molecular orbitals of aTTF-based molecule should be either bonding (x-symmetric)or anti-bonding (x-asymmetric) with respect to the centralC C unit. Therefore, HOMO of a TTF-based molecule(bonding molecular orbital) is energetically separated fromLUMO at least by the C–C π bonding energy. No suchrestriction operates in the case of the metal-dithiolene

complex; the metal-sulphur non-bonding molecular orbitalis purely on ligands, and it can have energy close to thatof one of the others [3, 28, 29]. This implies how tocontrol the HOMO–LUMO gap using a symmetric three-unitmolecule. In the case of Pd(dmit)2, the Pd–S bonding orbitallies far below the Fermi level, and the Pd–S anti-bondingorbital (LUMO) is slightly higher than the non-bondingorbital (HOMO). These two molecular orbitals have similarcharacters within a ligand, but HOMO is x-symmetric withlittle 4d contribution, while the pπ–dπ -hybridised LUMOis x-asymmetric [3]. These peculiar features in principleoriginate from the symmetric ligand-metal-ligand (L–M–L)three-unit structure of the metal-complex molecule.

For an isolated M(dmit)2 molecule (M = Ni, Pd),excess electrons are originally injected into LUMO. Thisassignment is retained even in the solid state of Ni(dmit)2;the conduction band of Ni(dmit)2 compounds comprisesLUMO [3]. For a face-to-face columnar arrangement ofNi(dmit)2 molecules, the asymmetric form of LUMO doesnot favour large intercolumnar overlapping, unlike the HOMOof BEDT–TTF. This appends quasi-one-dimensional (1D)conduction to each layer, although 2D character is built up bythe alternating stacking of the conduction layers with differentcolumn directions (the solid-crossing structure) in the crystals(figure 1(b)). An exception is found in some cases, whereonly the face-to-face-like overlapping modes, including thespanning overlap, form a honeycomb-like 2D network witha non-columnar arrangement [3, 31, 32].

The situation is altered for negatively charged Pd(dmit)2

in the solid state (figure 1(a)). The 4d orbital of Pd, which islarger than the Ni-3d orbital, promotes dimerization by Pd–Pdbond formation, as found in the x-ray structure analysesof most Pd(dmit)2 compounds. The effect is so strong thatthe dimerization splitting exceeds the small HOMO–LUMOenergy separation [3, 18–23]. Consequently, the bondingcombination (with respect to the two molecules in the dimer)combination of LUMOs (b-LUMO) has lower energy thanthe anti-bonding combination of HOMOs, which is occupiedby the excess electrons. In other words, the LUMO ofthe dimer [Pd(dmit)2]2 is the anti-bonding combination ofHOMOs (a-HOMO) of Pd(dmit)2. In what follows, we usethe labels HOMO and LUMO, irrespective to the dimerizationor valence, to specify the orbitals formed from the HOMOsand LUMOs of the isolated neutral Pd(dmit)2 molecules,respectively. The symmetry of the Pd(dmit)2 HOMO yieldsconsiderable side-by-side (intercolumnar) transfers of carriersbetween the dimers formed in this way. Like in theBEDT–TTF salts, a 2D band structure based on Pd(dmit)2

HOMO plays a significant role in the Z [Pd(dmit)2]2 series.The band calculations [3, 24–26] for them indicate 2Dhole-type Fermi surfaces based on Pd(dmit)2 HOMO, inspite of the negative charges of Pd(dmit)2 in the compounds.This specific aspect is called HOMO–LUMO inversion orHOMO–LUMO interchange.

Experimentally, this peculiar electronic structure of thedimers can be easily observed in the infrared (IR) spectraof Z [Pd(dmit)2]2 [14, 21–23]. For the light polarizationalong the dimerization direction, Z [Pd(dmit)2]2 exhibits a

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Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

remarkable absorption peak in the near-IR range (ca. 1.2 eV).No such absorption is observed in other molecular conductors.This absorption is attributed to the bonding–anti-bondingexcitation. In case of weak dimerization, only the LUMOelectron can be excited, which cannot account for thepeak intensity. The HOMO–LUMO interchange due tostrong dimerization enables the three electrons (two inLUMO and one in HOMO) to be excited in the dimer,which consistently explains the observed spectral features,giving direct evidence for the HOMO–LUMO interchangein Z [Pd(dmit)2]2 [14, 21–23]. It is also noticeable that thebonding–anti-bonding splitting of HOMOs and LUMOs arenearly the same. This means that the intermolecular overlapin the dimer is determined mainly by the ligand π orbitals,which are almost identical in the HOMO and LUMO. Thespectral evidence for the HOMO–LUMO interchange schemesuggests that the unit dimer [Pd(dmit)2]−2 is potentiallya multi-carrier system having two electrons in b-LUMOand one hole in a-HOMO levels [13]. The situation issomewhat similar to that in the single-component molecularmetal Ni(tmdt)2 having electron-like and hole-like Fermisurfaces [27–30], though the b-LUMO (filled band) electronsin Z [Pd(dmit)2]2 are completely paired in the dimer. InZ [Pd(dmit)2]2, only the a-HOMO hole band is partially filled.However, both levels are sensitive to dimerization strength,so that these charge carriers can couple to the structuraldeformation of the dimer [13]. This HOMO–LUMO interplayis never expected for the systems with weak dimerization(Ni(dmit)2 salts) and for the HOMO band systems of theTTF-based π donors. In the sense described here, thepeculiar properties of the Z [Pd(dmit)2]2 series and the firstsingle-component molecular metal Ni(tmdt)2 share the samequantum chemical origin. This provides a useful viewpointin understanding the molecular mechanism of the phasetransition as discussed in section 5.

For the Z [Pd(dmit)2]2 series, the average valence is−1 in terms of the dimer unit [Pd(dmit)2]2, which meansthe half-filling of the a-HOMO band. Therefore, the keyfactors in systematic understanding the physical states ofsuch a strongly correlated electron system are the interdimertransfer integrals t and the intradimer (on-site) electronrepulsion energy Udimer. The parameter Udimer is a function ofthe nearest-neighbour Coulomb repulsion Vintra and transferintegral tA [33], as in the case of the dimeric BEDT–TTFsalts [34]. As a result of the strong dimerization (large Vintra

and tA � t), the Z [Pd(dmit)2]2 series is characterised bylarge Udimer, which keeps the system near the Mott criticality(the metal-insulator boundary). A systematic change inthe physical behaviour is driven by the control of theinterdimer transfer integrals, as experimentally observed inthe dependence on cation type, pressure or uniaxial strain. Inthe presence of the HOMO–LUMO interchange, Udimer canbe drastically modified by an inhomogeneous distortion ofthe dimers [13]. This causes an effectively negative value ofUdimer, as observed in a spontaneous pairing of the electronsin a dimer with coupling to the lattice distortion [13].

3. Structural and magnetic classificationof Z[Pd(dmit)2]2

Most Z [Pd(dmit)2]2 salts are isostructural. The commoncrystal structure is called the β ′ structure (note that this is notthe same convention as used for the BEDT–TTF salts) withthe space group C2/c [3]. The crystal is formed by alternatingstacking of the Pd(dmit)2 anion layers and the insulatingcation layers. In a layer (the ab-plain), the dimers [Pd(dmit)2]2

are parallel and the structure is pseudo-columnar. In contrast,non-parallel packing of dimers is the main structural motifof the κ-(BEDT–TTF)2 X . Because of the considerableHOMO–HOMO overlapping between the columns, thesystem cannot be 1D, and a 2D triangular network is formedin the layer. Along the c-direction (perpendicular to thelayers), the crystallographically equivalent layers related bythe c-glide symmetry alternate with different orientations.This provides solid crossing of the pseudo-columns(figure 1(b)) [3]. The salts with Z = Etx Me4−x Y + (Et = C2H5,Me = CH3; x = 0, 2 for Y = P and x = 0, 1, 2 for Y = As,Sb) belong to this class and are Mott insulators at ambienttemperature and pressure. The Cs salt [35] also has theβ ′ structure. Unlike the others, this salt is metallic atambient condition and exhibits a metal-insulator transition at56.5 K [35].

The structures similar to, but not identical to, the β ′

structure are found in the EtMe3P salt [16, 17] and in theMe4N salts [36, 37]. At least two polymorphs are foundin the EtMe3P salt. The one with the space group P21/mhas triangular layers similar to those in the β ′ structure,but the layers are related by the mirror symmetry, so thatthe columns are orientated parallel in the whole crystal, andthe solid-crossing is lost [16, 17]. The other polymorph haslowered symmetry (space group, P 1̄) and no solid-crossingtoo; it undergoes two structural phase transitions accompaniedby doubled in-plain periodicity and charge disproportionationat low temperatures [38]. In spite of the structural similarityto the β ′ type salts, it does not show magnetically frustratedbehaviour specific to the 2D triangular systems, suggestingcharge fluctuations enhanced due to larger in-plain anisotropy.The Me4N salt exhibits polymorphs based on solid-crossingcolumns with subtle structural difference [36, 37]. Theβ-Me4N salt shows magnetic behaviour similar to thatof the β ′-type salts [37, 39]. Another sub-family basedon trialkylcharcogenide cations has been found, in whichsupramolecular cation-anion interactions play a significantrole in the crystal [3, 40, 41].

From now on, let us concentrate on the triangular systems(the β ′ type salts, the β-Me4N salt and the P21/m EtMe3Psalt), where the geometrical spin frustration operates. Basedon the χ behaviour and magnetic ground states, they can beclassified into the following types (see table 1):

(I) Antiferromagnetic ordering at ca. 40 K, (the Me4P andMe4As salts),

(II) Antiferromagnetic ordering in the 10–25 K range (theEt2Me2P, Et2Me2As, EtMe3As, Me4Sb and β-Me4Nsalts),

(III) No magnetic ordering (the EtMe3Sb salt),

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Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

Table 1. Classification of magnetic properties of the triangular Z [Pd(dmit)2]2.

Type Cation, Z Ground statesa Transition Referencestemperatures

(I) Me4P AF LRO TN = 40 K [2, 53, 55](I) Me4As AF LRO TN = 35 K [2, 55](II) Et2Me2P AF LRO TN = 14 K [2, 54, 55, 57](II) Me4Sb AF LRO TN = 18 K [2, 55](II) Et2Me2As AF LRO TN = 18 K [55](II) EtMe3As AF LRO TN = 23 K [16](II) Me4Nb AF LRO TN = 12 K [36, 37, 55](III) EtMe3Sb no LRO (spin liquid) – [60, 61, 63](IV) Et2Me2Sb charge separation TCS = 70 K [15, 67]– Csc charge separation TMI = 56.5 Kd [15, 35]

(V) EtMe3P valence bond order TVB = 25 Ke [16,17]

a AF LRO is antiferromagnetic long-range order.b The β-phase.c Metallic at room temperature (unfrustrated).d Metal-insulator transition.

(IV) A phase transition to a spin-singlet state with differentlycharged dimers (the Et2Me2Sb salt),

(V) A phase transition to a spin-singlet state with equivalentdimers (the P21/m EtMe3P salt).

Figure 2 shows typical temperature dependence of χ .Above the magnetic transition temperatures, the salts areparamagnetic insulators showing temperature dependence ofχ characteristic of a spin-1/2 Heisenberg antiferromagneton a triangular lattice [2]. The antiferromagnetic orderobserved for types (I) and (II) is a 2D Néel-like collinearorder, as that on a square lattice, with the easy axisperpendicular to the layer (see the next section). In addition,the Cs salt has the same ground state as the Et2Me2Sb saltbelow the metal-insulator transition temperature. Above thattemperature, it exhibits Pauli-like constant χ consistent withthe metallic behaviour. More details on types (I), (II) and(III) are described in section 4, and (IV) and (V) are treatedin sections 5 and 6, respectively. The variety of spin groundstates observed in the triangular Pd(dmit)2 salts is summarisedin figure 3.

This classification reflects in the conductivity behaviour.Type (I) salts are insulating at any pressure, but becomemetallic under specific uniaxial strain. Metallic behaviourappears in types (II) and (III) under hydrostatic pressurein the range 0.5–1 GPa, but those salts become insulatingagain at low temperatures under pressure above 1 GPa.X-ray analyses have shown that the high-pressureinsulating phase has different anion layers with loweredsymmetry [42]. Pressure-induced metallic phase is alsofound in types (IV) and (V). Bulk superconductivityappears around the insulator-metal boundary of type (V),while the spin-singlet insulator phase is predominant atlow temperatures in type (IV) (see sections 5 and 6).Although superconductivity has often been observed nearthe antiferromagnetic insulator-metal boundary in type (II)by resistivity measurements, it is efficiently suppressed bylarge current density and only weak diamagnetic shieldingcould be detected in the Et2Me2P and Me4Sb salts [43].Therefore, it has been concluded that the superconductivity

0 100 200 300

6

5

4

3

2

,ytilibitpecsus nip

S χ0

(1 –4

mc

3l

)o

m–1

T (K)

Me4As salt (type I)

Et2Me2P salt (type II)

TN

J/kB = 260 KJ/kB = 280 K

r

s

B

J = JB ≈ Js,J ′ = Jr,J ≥ J ′

JJ J ′

Figure 2. Typical temperature dependence of spin susceptibilitiesof the triangular Z [Pd(dmit)2]2 (Z = Me4As and Et2Me2P) showingstrongly frustrated features, together with the magnetic model (theanisotropic triangular lattice) defined for the real structure. Solidcurves indicate the χ values calculated on the basis of the spin-1/2Heisenberg isotropic (J ′

= J ) triangular lattice model.

by the antiferromagnetic insulator phase is usually not a bulkphenomenon [43], but a surface or an egde effect, whoseorigin has not been clarified yet. On the other hand, it isrecently found that the β-Me4N salt exhibits diamagneticresponse under pressure, indicating bulk superconductivity(Tc ∼ 5 K at P = 0.53 GPa) [44]. In the β-Me4N salt, ts isthe largest interdimer transfer, which is different from theother type (II) salts with the β ′-structure, where ts 6 tB. (Theindices A, B, s and r are denote the intermolecular relationdefined in figures 2 and 4(a).) This structral difference

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Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

Frustrated paramagnet (high temperature phase) (I) and (II): AF LRO

(IV): Et2Me2SbCharge separation

Dimer0

Dimer2–

(V): EtMe3P (P21/m)VB Order

InterdimerVB Pair

Figure 3. Variety of low-temperature spin states arising from thefrustrated spin system on the anisotropic triangular lattice ofZ [Pd(dmit)2]2. Depending on the spatial anisotropy and countercation (Z), unconventional valence bond (VB) states appear at lowtemperatures. AF LRO is antiferromagnetic long-range order.

presumably causes dissimilar superconducting behaviour ofthe type (II) salts.

At a glance, the cation size (or interlayer couplings)seems to control the magnetic and conduction behaviour.However, it turns out that the essential factor is thein-plain spatial anisotropy of the interdimer interactions.The stability of the insulating state is basically prescribedby the strength of electronic correlation Udimer/W , ifunfrustrated. For type (I) salts, this parameter is suppressedas a result of the larger tB and ts [3], in spite of therobust insulating state. This discrepancy is removed byconsidering the anisotropy parameter t ′/t = tr/tB ≈ tr/ts,which approaches 1 as the frustration is enhanced. Larger tBand ts (smaller t ′/t), with the spins less frustrated, favourthe Néel-like antiferromagnetic correlation growing on thesquare-like network of JB and Js, which provides the stabilityof antiferromagnetically ordered state and gives a highertransition temperature TN = 40 K. In the type (II) series, tBand ts are moderate and tr increases to enhance the t ′/tratio [3]. Consequently, Jr approaches JB and Js, so thatthe spins are more frustrated to reduce TN to 14 K in theEt2Me2P salt. And for the smallest anisotropy, t ′/t ≈ 1, theantiferromagnetic order finally disappears in the EtMe3Sbsalt (III) (see section 4), or is replaced by other spin-gappedphase (IV and V). The correlation parameter can be estimatedfrom the degree of dimerization tA/W . The magnetic andelectric behaviour of the system is primarily described bythe two parameters t ′/t and tA/W . A summary of thissystematic variation is schematically depicted in figures 4(b)and (c), on the basis of resistivity, magnetic and structuralstudies [45, 46], showing the relative stabilization of themetallic phase by the highly frustrated spins in the insulating

phase. In the most frustrated regime, the critical lines areclosely spaced, around which the novel ground states appearsas discussed below.

4. Frustrated paramagnetic state, antiferromagneticorder and a possible gapless spin liquid

As mentioned in the preceding sections, the commonmagnetic behaviour of the triangular Z [Pd(dmit)2]2 salts isthe weakly temperature dependent χ with a broad maximumat the temperature Tmax, which is much lower than θ =

z J/4kB (the mean-field Weiss temperature) [2, 17, 37],where z denotes the number of nearest-neighbour sites (z = 6for the triangular lattice), and the exchange coupling J isdefined by the spin Hamiltonian H =

∑(i, j) Ji jSi ·S j . For

an unfrustrated low-dimensional quantum antiferromagnet,Tmax ≈ θ is expected, with antiferromagnetic correlationgrowing over the lattice below Tmax. In the present cases,however, we obtain J/kB = 240–280 K and Tmax = 60–120 K,where kB is the Boltzmann constant. This indicates thatthe frustration prevents the antiferromagnetic correlationfrom growing out of the repeating unit, and the system isparamagnetic over a wide temperature range. The temperaturedependence was analysed in terms of the Padé approximantexpression [2] on the basis of high-temperature seriesexpansion of χ of the spin-1/2 Heisenberg model on thetriangular lattice [47]. It has been shown that the temperaturedependence is satisfactorily explained by this model near andabove Tmax, and the exchange parameters J are thus obtainedfor the triangular Z [Pd(dmit)2]2 salts [2, 48].

As temperature is lowered below Tmax, χ dropsexponentially until it changes the slope at TN in the (I) and(II) cases. The drop of χ indicates that antiferromagneticcorrelation rapidly spreads over the layer. As known forthe square-lattice antiferromagnets [49], such features arecharacteristics of an unfrustrated 2D system just above TN.This means that the frustration is released in this temperaturerange, which is a crossover from the high-temperaturefrustrated paramagnet to the antiferromagnetically correlatedstate [50, 51]. In other words, it is the interplay betweenthe short-ranged physics of frustration and the long-rangecorrelation, as found generally in quantum liquid systems. Thespatial anisotropy 1J = J − J ′, rather than J , should play akey role in this range. At higher temperatures, T � 1J/kB,the effect of 1J is negligible, so that the spins are frustrated.At low temperatures, 1J operates to release the frustration bymaking the system like a square-lattice-like antiferromagnetwith effective couplings of 1J .

Once the 2D antiferromagnetic correlation grows in thisway, even very weak interlayer couplings can implement thebulk antiferromagnetic ordering at TN. This is the reason forthe steeply varying χ just above TN. Similar change in χ(T )

slope at TN is found in other 2D quantum antiferromagneticsystems [52], though it is dissimilar to that in the conventional3D antiferromagnetic case. Below TN, χ becomes anisotropicto show that the easy axis is perpendicular to the plain [16], asexpected from the dipolar couplings in a 2D antiferromagnet.For the (I) and (II) types of the triangular Z [Pd(dmit)2]2 salts,

6

Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

T

FrustratedParamagnet

J ,U/

W

TN

oM

snarT tt

noitilateM

rotalusnI

P

AF LRO

SpatialAnisotropy

J – J ′

FrustrationJ ′/J

noit

alerr

oCW/

U

(c)(b)(a)

Type (I) Type (II) Types (III) and (V)

Figure 4. (a) The key parameters controlling the insulator-metal boundary. (b) Schematic phase diagram based on the structure andresistivity measurements under pressure or uniaxial strain. Solid arrows indicate simulated uniaxial effects with a 0.1 Å reduction in theinterdimer distance along the corresponding direction. For the Et2Me2P salt, dotted arrow indicates the reduction of about 0.2 Å along theb-axis under the hydrostatic pressure of 0.7 GPa. (Reprinted with permission from [45]. Copyright 2007 Royal Society of Chemistry.)(c) Schematic phase diagram taking account of the temperature dependence of the magnetic behaviour. The Mott transition line correspondsto the metal-insulator boundary in (b). The broken lines denote metal-insulator crossover. The critical point (the end-point of the first-ordermetal–insulator transition line) is expected to exist slightly above TN, as qualitatively indicated here. It is not well resolved yet, due toexperimental difficulty in fine control of pressure in this range. The magnetic susceptibility varies little through the metal-insulatortransition because of the strong correlation in the metallic phase [46], which made it difficult to detect the transition by magnetic study.

the rapid growth of antiferromagnetic correlation just aboveTN has been observed by the muon spin rotation/relaxation(µSR) technique, which probes slow dynamics of spins andthe internal field. The changes in the µSR time-spectraand relaxation rate towards the antiferromagnetic orderingcomplete within a narrow temperature range (0.8 K) in theMe4P salt (I) [53]. The change is not so acute in the Et2Me2Psalt (II) [54], indicating that the latter is more frustrated, asexpected. Electron spin resonance (ESR) and nuclear spinresonance (NMR) measurements have also been applied tocharacterise the antiferromagnetic ordering in the triangularZ [Pd(dmit)2]2 salts. An early ESR study [55] clarified thecation dependence of TN and pointed out the correlationbetween TN and strength of frustration that expected fromthe structural anisotropy of interdimer couplings. Thismagneto-structural correlation suggests the crucial role offrustration in the system. It should be emphasized here that TN

is scaled by the anisotropy 1J , rather than by J , in the presentfrustrated systems, unlike in the ordinary antiferromagnets.The NMR studies [56, 57], probing the fast dynamics, havereported the critical behaviour of the relaxation rate 1/T1

of the Me4P (I) and Et2Me2P (II) salts. The growth ofantiferromagnetic correlation, as noted by the critical slowingdown effect, is more evident in the Me4P salt: 1/T1 startsto increase even at temperature twice as high as TN. Thisdoes not contradict to the µSR experiments probing slowdynamics regime because both µSR and NMR results indicatelarger antiferromagnetic correlation and less frustrated natureof the Me4P salt. Pulsed ESR and antiferromagnetic resonanceexperiments using millimetre waves [58, 59] have beencarried out for the Et2Me2P salt. The results are explainableby the antiferromagnetically ordered spin system having theeasy axis perpendicular to the layer below TN [59].

NMR reveals that TN is raised by pressure. For the Me4Psalt, TN increases up to 50 K at 0.7 GPa, and application of0.5 GPa enhances TN of the Et2Me2P salt up to 25 K [57].This pressure effect on TN has been confirmed by theχ measurements under pressure [46]. Similar results werereported for the β-Me4N salt [37, 39]. Taking accountof the P–T phase diagram inferred from the resistivitymeasurements, the insulating phase expands to higherpressures and temperatures by forming the antiferromagneticorder. The shape of the insulator-metal boundary is thereforeprescribed by the stability of the insulating phase. Since thefrustration diminishes the stability of the insulating phase,the correlation found between the transport and magneticproperties for the triangular Z [Pd(dmit)2]2 salts is understoodfrom this viewpoint. For example, the stiffness of theinsulating state of the Me4P salt is related to the less frustratednature, stronger antiferromagnetic correlation and higher TN,which arise from the spatial anisotropy of the interdimercouplings. These experimental results point out that not onlythe strength of electron correlation but also the frustration isthe controlling factor for the insulator-metal criticality [2, 3,45, 46]. The highly frustrated spins, giving high entropy in theinsulating state by breaking the antiferromagnetic long-rangeorder, provide relative stability of the metallic state, in whichentropy is released efficiently at low temperatures.

The χ of the EtMe3Sb salt (III) exhibits no signof magnetic ordering down to 10 K, and the temperaturedependence is approximately explained by the spin-1/2Heisenberg antiferromagnetic model on the triangular latticewith J/kB = 220–250 K [60, 61]. NMR study of this salt[61] has shown that neither magnetic long-range order norspin freezing occurs in this salt down to 1.37 K. Therefore,the ground state of this salt is assigned to a spin liquid

7

Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

with zero gap or very small gap (< 1% of J ). In thiscase, the high-temperature frustrated paramagnetic statecontinues to the ground state, possible gapless spin-liquidstate, without an apparent phase transition (or a symmetrybreaking). The appearance of the gapless non-magneticstate has been predicted by the path-integral renormalizationgroup calculations for the highly frustrated Hubbard modelon an anisotropic triangular lattice [62]. The temperaturedependence of the relaxation rate 1/T1 shows gradualgrowth of antiferromagnetic correlation below 200 K, butno critical enhancement down to 1.37 K. The NMR spectrashow inhomogeneous broadening due to static internalfield at low temperatures (<10 K). The origin of thisinhomogeneous broadening has not been clarified yet.Recently, the absence of magnetic order down to 19.4mK has been confirmed [63], and power-law temperaturedependence of 1/T1 has been observed below 1 K [64].Similar NMR features have been reported for anotherspin-liquid material, κ-(BEDT–TTF)2Cu2(CN)3 [4, 65]. Inthese cases, it is not easy to rule out the possible effectof the structural disorder [66]. Similar to the orientationallydisordered CN− anions in κ-(BEDT–TTF)2Cu2(CN)3, thenon-centrosymmetric cations EtMe3Sb+ are disordered in thepresent case. Further studies are still required to clarify theorigin and nature of these puzzling spin-liquid states.

5. A novel charge separation in the Et2Me2Sb salt

Similar to the spin-liquid EtMe3Sb salt, the Et2Me2Sb salt(IV) and the P21/m EtMe3P salt (V) belong to the mostfrustrated class among the triangular Z [Pd(dmit)2]2 salts,judging from the structure and χ results. However, thesetwo salts exhibit phase transitions to non-magnetic gappedground states. (In our earlier study [2], it was argued thatthe Et2Me2Sb salt has no phase transition. It turned out laterthat this is due to the suppression of the phase transitionby impurity [67].) Structural changes are involved in thesetransitions.

In a sufficiently pure sample of the Et2Me2Sb salt, asteep drop of χ appears at 70 K [67] (figure 5). This indicatesa first-order phase transition to a diamagnetic phase. Thediamagnetic nature is also found by µSR measurements [54],which show fast relaxation in the low-temperature phase.Correspondingly, resistivity is noticeably enhanced belowthis temperature. These changes are hysteretic with a widthof ca. 1 K. X-ray analyses [15] have revealed that thelow-temperature phase has a doubled periodicity along theb-axis as a result of alternating arrangement of two typesof dimers: contracting (strongly dimerised) and expanding(weakly dimerised) ones. The two Pd(dmit)2 moleculesforming a dimer remain equivalent. These structural featuressuggest non-uniform charge distribution over the dimers.

Extended Hubbard model calculations [13] have beencarried out of the unique electronic structure of the dimer[Pd(dmit)2]2 (see section 2). The dimer is modelled bya four-level system of b-HOMO, b-LUMO, a-HOMO anda-LUMO. Within the dimer, the intramolecular Coulombrepulsion U intermolecular Coulomb repulsion V and

6

4

2

00 100 200 300

[Pd(dmit)2]2–

[Pd(dmit)2]20

[Pd(dmit)2]22–

ytilibitpecsus nipS χ

0(1

–4

mc 3

l )

om

–1

T (K)

Et2Me2Sb

0

0

1000

6 8 10 12 14 16Wavenumber (103 cm )–1

σm

)

c(S

1–

σm

)

c(S

1–

100 K

50 K1000

2[Pd(dmit)2]2–

[Pd(dmit)2]22– [Pd(dmit)2]20

6 8 10 12 14 16

(a)

(b)

ytivitcudnoc lacitpO

a-LUMO

b-LUMO

a-HOMO

b-HOMO

Figure 5. (a) The spin susceptibility of the Et2Me2Sb salt showingthe transition at 70 K to the charge-separated phase. (b) The spectralchanges in the near-IR region, with the assignment of the splitpeaks.

intermolecular transfer integrals t are taken into account.The strength of dimerization is expressed by changing tand V ; a stronger dimer corresponds to the larger t andV . The effective repulsion on a dimer Udimer is evaluatedas the energy cost to cause charge disproportionation(separation) 2[Pd(dmit)2]−2 → [Pd(dmit)2]0

2 + [Pd(dmit)2]2−

2for a two-dimer set. It has been shown that the two-dimersystem with the uniform valence is unstable against thisdisproportionation when the non-equivalent distortions ofthe dimers are assumed [13]. A large energy gain stemsfrom the bonding and resonating energies in the contractedneutral dimer [Pd(dmit)2]0

2, in which all the electronsoccupy the bonding levels (b-HOMO and b-LUMO), andthe cost of V is cancelled because of zero net charge. Thebond strengthening (contraction) and reduction of electronrepulsion are cooperative in the neutral dimer. This efficientlycompensates the energy cost arising from the pairing ofa-HOMO electrons in [Pd(dmit)2]2−

2 , so that the total costcan be negative at a certain condition. The electron pairing

8

Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

(intradimer valence bond formation) and the inhomogeneousdistortions of the dimers are thus coupled. The origin ofthe charge separation is thus assigned to the HOMO–LUMOinterplay in the dimer [13]. The x-ray analyses report the bondlengths in the molecules. The changes in the bond lengthsat the transition agree with the valence change assumedhere [15]. The in-plain arrangement of the charged and neutraldimers coincides with one of the predicted patterns fromMadelung calculations [67].

The calculations predict 1 : 2 splitting of thebonding-antibonding photo-excitation appearing in thenear-IR region [14]. In fact, the reflectivity spectraexhibit the expected splitting of the near-IR peak at lowtemperatures [14]. All spectral features in the near-IRrange are consistently explained by the above model, fromwhich the energy levels of the dimers are evaluated (figure 5).A similar splitting was reported for the low-temperature phaseof the Cs salt [21, 23, 35], which exhibits a second-ordermetal-insulator transition at 56.5 K. The x-ray analyses [15]have shown that the low-temperature phase has the structureidentical to that of the Et2Me2Sb salt below 70 K. Therefore,the metal-insulator transition in the Cs salt has been concludedto have the same origin as based on the HOMO–LUMOinterplay in the strongly dimerised structure, though it waspreviously considered to result from the nesting of quasilD Fermi surfaces [35]. Fast photo-response (relaxationwithin a few picoseconds) has been observed for the near-IRreflectivity spectra of the low-temperature phase of theEt2Me2Sb salt using the pump-probe technique, whichshowed photo-induced melting of the charge-separatedstate [68]. The pumping power dependence suggests thephoto-excitation causes a cooperative phenomenon, i.e.,a photo-induced phase transition to a state similar to thehigh-temperature phase [68].

The x-ray analyses suggest that the first-order nature ofthe transition in the Et2Me2Sb salt is due to the conformationalchange of the cations [15], which can accommodate andbefit the distortion in the Pd(dmit)2 layers to latch thetransition. The transition temperature of the Et2Me2Sb saltis significantly suppressed by cation impurities [45], whichalso suggests the role of the cation conformation. SimpleCs cation cannot act in such a way. According to thesusceptibility [69] and specific heat [70] measurements forthe Et2Me2Sb salt under pressure, the first-order nature ofthe transition is retained even at high pressures, where thehigh-temperature phase is metallic. Therefore, it is concludedthat the difference in the high-temperature phases of the twosalts, i.e., a frustrated paramagnetic insulator vs. metal, doesnot concern the order of the transition. Although it is not fullyunderstood why the charge separation appears only in the twosalts, the above results suggest that it is related to the dynamicsof the lattice distortion such as the cation conformationalchange.

Since the low-temperature phase of the Et2Me2Sb saltis diamagnetic, the value of spin susceptibility just abovethe first-order transition temperature is easily found as asharp rise of χ upon heating. This is useful, particularlyin the pressure experiments, which often suffer from the

magnetic background signals. The transition temperature andχ of the high-temperature phase along the phase boundaryare thus measured as a function of pressure [69]. Thetransition temperature takes a maximum value ca. 100 K,which is consistent with the resistivity results. Along thephase boundary, χ continuously decreases with pressure untilit becomes pressure independent for the high-temperaturemetallic state appearing above ca. 0.6 GPa [69]. This isconsistent with the crossover nature of the Mott boundary athigh temperatures above the critical point [46].

It is worth noting that, as well as b-LUMO electrons, holeinjection into the a-HOMO level (removal of anti-bondingelectrons) provides intermolecular bonding energy in thedimer. In this sense, it is convenient to treat the dimer at theaverage valence [Pd(dmit)2]−2 as a system of one unpairedhole (a-HOMO) and an electron pair (b-LUMO) [13].It follows naturally that the holes acting in the anionicbackground attract each other by cancelling the negativecharges of the b-LUMO electrons. This results in the holepairing (removal of a-HOMO electrons) to cause a neutraldimer having doubled intradimer valence bond correspondingto the hole and electron pairs. In this system with theHOMO–LUMO interchange, the neutral dimer is not anempty object but a composite of two electrons and twoholes. Since the spin degree of freedom is held by a-HOMOand the net negative charge comes from b-LUMO at theaverage valence, a kind of spin-charge separation (oppositedistributions of the spin and negative charge densities) isexpected to favour less charged spin-singlet valence bondpairs. When this pairing completes within a dimer, thecharge reduction processes to the limit of a neutral dimer(a complete charge separation). This two-level electron-holecomposite scenario cannot be applied to the HOMO-basedsystems such as the BEDT–TTF salts. On the other hand, themolecular origin (the HOMO–LUMO interplay) is in closeconnection with the single-component metal Ni(tmdt)2, inwhich electrons and holes coexist and hybridise with eachother [28–30].

6. Valence bond ordering and pressure-inducedsuperconductivity in the P21/m EtMe3P salt

The P21/m EtMe3P salt (type V) undergoes a second-orderphase transition at 25 K, where χ shows a bend [16, 17](figure 6). Above this temperature, χ shows typicaltemperature dependence of the frustrated paramagnet ofthe triangular Pd(dmit)2 salts (J/kB = 250 K), while χ

exponentially approaches zero as T is lowered from 25 K.NMR spectra indicate the absence of long-range magneticorder at low temperatures [61]. X-ray analyses show thatall the dimers are still crystallographically equivalent in thelow-temperature phase, but the intermolecular interactions aremodulated along the column direction to give the doubledperiodicity [17] (figure 6). Since the spin-1/2 unit is thedimers in this case, it is concluded that interdimer spin-singletpairs (valence bonds) are formed along the column in thelow-temperature phase. Note that this salt has parallel columnstructure [16], unlike the other triangular [Pd(dmit)2]2 salts

9

Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

0

2

4

6

0 100 200 300T (K)

ytilibitpecsus nipS χ

0(1

4–

mc 3

lom

1– ) J/kB

= 250 K

EtMe3P (P21/m)

20 25 30

5

4

3

2

(a)

ao

c

ao

c

T < 25 K

(b)

Figure 6. (a) The valence bond ordering as detected by the χ -slopeanomaly at 25 K. The discontinuity seen at 30 K has no physicalmeaning; it is an experimental artefact due to zero-crossing of theraw magnetization signal. (b) Doubled periodicity accompanyingthe valence bond ordering.

having solid-crossing columns. The crystal slightly expandsto the intercolumnar directions through the transition to thespin-gapped states [17]. The analysis of the temperaturedependence of χ [17] and ESR study [71] of this materialconsistently give the spin-gap value of ca. 35 K in the T = 0limit.

These features are similar to those found in thespin-Peierls case. The spin-gapped ground states with thespontaneously broken translational symmetry of exchangecouplings are commonly formed in both cases. However, theP21/m EtMe3P salt is a 2D system, for which an occurrenceof a spin-Peierls transition has not been reported so far. ANéel type antiferromagnetic ordering is more preferred in anordinary 2D system. In the present case, the highly frustratednature suppressed the antiferromagnetic ordering, so that thespin-gapped state can appear instead, in order to reduce thehigh entropy of the frustrated spins. The appearance of such adimer order has been predicted by a theoretical study [72] ofthe spin-1/2 Heisenberg antiferromagnets on an anisotropictriangular lattice without symmetry breaking. The predictedcolumnar arrangement of valence bonds [72] is consistentwith that found in the P21/m EtMe3P salt. The spin-gappedphase discovered in the 2D triangular Pd(dmit)2 salts shouldbe distinguished from the conventional spin-Peierls phaserelated originally to the one-dimensionality. Here, we callthis new phenomenon valence bond order, to discriminateit from the valence bond solid used mainly to specify thespin-gapped state without translational symmetry breaking(e.g., the Haldane systems). For the appearance of the valencebond order, suppression of the antiferromagnetic order by

frustration is required. The lattice structures—the parallelcolumns and the discrete counterion layers—can assist thevalence bond ordering. In addition, the effective hole-holeattraction (a kind of spin-charge separation), operating inthe HOMO–LUMO interchanging system as pointed out inthe preceding section, can contribute to reduce the energycost of the interdimer valence bond pairing by makinginhomogeneous site charges in the dimer. Therefore, it wouldbe worth examining how this mechanism contributes to thevalence bond formation by experimental evaluation of the sitecharge distribution.

Pressure-induced superconductivity has been found inthe P21/m EtMe3P salt by resistivity measurements, whichalso show complicated insulator-metal phase boundary atlow temperatures, as noted by re-entrant behaviour [16].Static magnetization measurements have been carriedout to examine the bulk properties under the in situcalibrated pressure. Bulk superconductivity appears aroundthe insulator-metal critical pressure [73], with Tc = 4.8 Kat 0.18 GPa, 5.5 K at 0.2 GPa, and 0.3 K at 0.44 GPa. Itis the first report of bulk Meissner signals (figure 7)detected in the Z [Pd(dmit)2]2 series. Taking account ofthe resistivity results [16, 74], the P–T phase diagram isinferred from the magnetic experiments [73] (figure 7).An outstanding point is that the superconducting phaseadjoins the spin-gapped insulating phase. This suggests aclose connection of the superconducting pairing and thevalence bond pairing. These features remind us of the x–Tphase diagram (x denotes hole concentration) for the high-Tc

superconductors, in which the so-called pseudo-gap phase iscontiguous to the superconducting phase in the under-dopedregime. It is suggestive but not simple to relate these twosystems because the Pd(dmit)2 salts can be examined onlyby pressure control, and the frustration, lattice distortionand symmetry breaking play more significant roles in thePd(dmit)2 salts. Several theories have been proposed for thepossible novel pairing symmetry in the superconductivityon the triangular lattice [1, 75–79]. In order to test thepossibilities, microscopic and dynamical information on thispressure-induced superconductivity should be explored.

The valence bond ordering temperature graduallydecreases with pressure [46, 73], as is expected fromthe volume expansion in the valence bond ordering. Theexpansion is presumably related to the columnar arrangementof the valence bond pairs. The valence-bond order disappearsat about 0.2 GPa, where it is replaced by the metallic phase.Unlike the insulating phase stabilised by antiferromagneticordering in the (I) and (II) cases, the first-order phaseboundary between the frustrated paramagnetic insulator(low-pressure phase) and the metal (high-pressure phase) haspositive slope in the low-temperature part of the P–T phasediagram. This corresponds to the insulator-metal transitionobserved on cooling. The large entropy contained in thefrustrated phase explains the positive slope. The systemre-enters into the valence bond ordered state on furthercooling at the pressures close to the boundary. This meansthat the stability of the insulating phase is attained by thespin-gap formation at lower temperatures. The stability is

10

Sci. Technol. Adv. Mater. 10 (2009) 024304 Topical Review

ParamagneticInsulator

VB ordering Metallic

Superconductor

Spin-gappedinsulator

EtMe3P (P21/m)

Figure 7. Upper panel: the P–T magnetic phase diagram, in whichthe pressure-induced superconductivity appears adjoining theinsulating phase with the valence bond order. Lower panel:Superconducting diamagnetic signals of the single crystal of theP21/m EtMe3P[Pd(dmit)2]2 [73].

diminished by application of high magnetic field as to breakthe valence bond pairs. The field-induced insulator–metaltransition is in fact observed by the resistivity measurementsin the 4–8 T range at the pressure just near the insulator-metalboundary [74]. As expected for the valence bond relatedsuperconductivity, the highest Tc 5.5 K is attained at theinsulator-metal boundary.

7. Conclusion

In the Z [Pd(dmit)2]2 system, the two unique characteristicsare shown to lead particular physical properties, in additionto the Mott physics, which is common to the other stronglycorrelated molecular systems with half-filling. First, thefrustration, stemming from the 2D triangular arrangementof the spin-1/2 units, affords suppressed antiferromagneticordering, for which a magneto-structural correlation specificto frustrated systems is found. Second, the HOMO–LUMOinterchange operating in the dimer [Pd(dmit)2]2, as clearlyindicated by the spectroscopic studies and the chargeseparation phenomena, provides an electron–hole compositepicture, which is useful in understanding the valence bondrelated magnetic properties. The finding of the valence bondorder and the pressure-induced superconductivity in thisfrustrated triangular system would contribute to the physicsof strongly correlated electron systems.

Acknowledgment

This work is supported by Grants-in-Aid for ScientificResearch (nos 16GS0219 and 18043024) from the Ministry ofEducation, Culture, Sports, Science and Technology, Japan.

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