PHYSICAL REVIEW B 85, 184424 (2012)

NMR evidence for antiferromagnetic transition in the single-componentmolecular system [Cu(tmdt)2]

Rina Takagi, Kazuya Miyagawa, and Kazushi KanodaDepartment of Applied Physics, University of Tokyo, Bunkyo City, Tokyo, 113-8656, Japan

Biao Zhou, Akiko Kobayashi, and Hayao KobayashiDepartment of Chemistry, College of Humanities and Sciences, Nihon University, Setagaya City, Tokyo, 156-8550, Japan

(Received 19 January 2012; published 25 May 2012)

The magnetic state of the single-component molecular compound [Cu(tmdt)2], where tmdt indicatestetramethylene tetrathiafulvalene dithiolate, is investigated by means of 1H NMR. An abrupt spectral broadeningbelow 13 K and a sharp peak in the nuclear spin-lattice relaxation rate T −1

1 at 13 K are observed as clearmanifestations of a second-order antiferromagnetic transition, which is consistent with the previously reportedmagnetic susceptibility and electron paramagnetic resonance measurements. The ordered moment is estimatedat 0.22μB–0.45μB per molecule. The temperature dependence of T −1

1 above the transition temperature indicatesone-dimensional spin dynamics and supports the theory that the spins are on the central part of this molecule,unlike other isostructural compounds.

DOI: 10.1103/PhysRevB.85.184424 PACS number(s): 76.60.−k, 71.20.Rv, 75.50.Xx

I. INTRODUCTION

Most molecular conductors are charge transfer salts com-posed of donor and acceptor molecules, either or both of whichare responsible for electric conduction and magnetism. Theconduction band is of either the highest occupied molecularorbital or the lowest unoccupied molecular orbital withoutmixture because of their large energy separation. However, ithas been pointed out1 that single-component molecular con-ductors [M(tmdt)2] have quasidegenerate molecular orbitalsfrom first-principles band calculations,2 where M and tmdtstand for a metallic ion and trimethylene tetrathiafulvalenedithiolate, respectively. The frontier molecular orbitals arecomposed of π -type orbitals extending over the tmdt ligands(symmetric and asymmetric pπ orbitals) and a σ -type orbitallocalized around the metal d orbital (dpσ orbital). Theirenergy separation depends on the metallic ion M; that is, thehybridization of pπ and d orbitals is varied by the energylevel of the d orbital in M relative to the level of the pπ

orbital. Among various isostructural compounds [M(tmdt)2],the pπ and dpσ orbitals are energetically closer in M = Auand Cu compounds than in others such as [Ni(tmdt)2],2,3

where only the pπ orbitals in tmdt construct the conductionbands with three-dimensional Fermi surfaces confirmed byde Haas–van Alphen oscillations.4 The orbital degeneracy ispossibly responsible for the unique magnetic properties ofM = Au and Cu compoundsdescribed in the following.

[Au(tmdt)2] undergoes an antiferromagnetic phase transi-tion at TN = 110 K, as evidenced by susceptibility and nuclearmagnetic resonance (NMR) measurements,5,6 in spite of themetallic behavior in resistivity down to low temperatures. Afirst-principles calculation suggests a possible Fermi-surfaceinstability into a spin-density wave (SDW) in the tmdt conduc-tion band formed by the asymmetric pπ orbital and predicts anantiferromagnetic spin configuration between two tmdt ligandswithin a molecule.2 However, this SDW scenario has somedifficulties in explaining experimental facts. For example,there is no change in resistivity around the antiferromagnetictransition. In addition, assuming that the SDW moment is on

the tmdt ligand, the analysis of NMR spectra yields a sizableantiferromagnetic moment of 0.7μB–1.2μB per tmdt,6 whichis considerably larger than the value 0.08μB/tmdt, predictedin the SDW scenario.2 This disagreement seems to requirereconsideration of the electronic state in [Au(tmdt)2], takingthe multiorbital character into account.

Meanwhile, the recently synthesized [Cu(tmdt)2] is foundto have a new aspect in this family of single-componentmolecular conductors.7 According to first-principles calcula-tions, the Fermi level is in the conduction band formed bythe dpσ orbital. However, the conductivity is semiconductivedown to low temperatures and the magnetic susceptibilityexhibits the Bonner-Fisher type of temperature dependencewith exchange interaction J of 169 K.7 The dpσ orbital of[Cu(tmdt)2], localized around the central Cu ion coordinatedby four S atoms, is in contrast to the pπ orbital extended overthe tmdt ligands, and therefore the on-site Coulomb energyshould be greater in [Cu(tmdt)2] than in the other [M(tmdt)2]salts with pπ orbital conduction bands. Thus, the insulatingstate in [Cu(tmdt)2] is reasonably attributed to strong electroncorrelations. The intermolecular overlap integral of the dpσ

orbital along the a axis is one order of magnitude largerthan those in the other two directions.7 Thus, if the spins areon the dpσ orbital, they should form quasi-one-dimensionalS = 1/2 antiferromagnetic Heisenberg chains. The character-istic field dependence of the magnetic susceptibility and asudden decrease in the electron paramagnetic resonance signalintensity suggest an antiferromagnetic phase transition at12–13 K.7

To characterize the magnetic state of [Cu(tmdt)2] fromthe microscopic point of view, we have carried out NMRmeasurements at 1H sites in the planar Cu(tmdt)2 moleculeshown in Fig. 1. Here, we report on NMR evidence for asecond-order transition to an antiferromagnetic state at 13 Kwith a moment of 0.22μB–0.45μB per molecule and spindynamics suggesting a one-dimensional Heisenberg nature,which is consistent with the picture that the spins are on thedpσ orbital in [Cu(tmdt)2].

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RINA TAKAGI et al. PHYSICAL REVIEW B 85, 184424 (2012)

FIG. 1. Schematic of [Cu(tmdt)2].

II. EXPERIMENT

1H NMR measurements were performed for polycrystalsof [Cu(tmdt)2]. NMR spectra and the nuclear spin-latticerelaxation rate T −1

1 were measured under a magnetic fieldof 3.66 T in a temperature range from room temperaturedown to 1.9 K. The spectra were obtained by the fast Fouriertransformation of echo signals observed after the so-calledsolid-echo pulse sequence (π/2)x−(π/2)y .8 The typical pulsewidth was 1.2 μs. The spectra were much broadened below13 K, where we set the pulse width less than 1.0 μs in order tocover the whole spectral frequency. By examining the spectrawith varying radio frequency under a fixed magnetic field,we confirmed that the present pulse condition is sufficientfor getting the whole spectra properly even below 13 K.T −1

1 is obtained by the standard saturation-recovery method.The relaxation curves of nuclear magnetization deviated fromthe single-exponential function for reasons described later,so we define T −1

1 by fitting them to the so-called stretched-exponential function M(∞) − M(t)∝ exp[−(t/T1)β] in thewhole temperature region.

III. RESULTS AND DISCUSSION

The 1H NMR spectra are shown in Fig. 2. The spectralwidth characterized by the square root of the second momentis about 17 kHz at room temperature (see Fig. 3), whichis reasonably explained by nuclear-dipole interactions in atrimethylene group. Because of the small hyperfine couplingwith the conduction electrons, the Knight shift at proton sitesis too small to be resolved, which explains why the spectralposition is not changed during temperature variation, while thesusceptibility shows a clear temperature dependence.7 On theother hand, the spectra are broadened below 13 K and extendedover a frequency range as large as ±700 kHz at 1.9 K. Asshown in Fig. 3, the square root of the second moment exhibitsan abrupt but continuous increase below 13 K, indicating theappearance of internal fields due to magnetic order. The nuclearspin-lattice relaxation rate T −1

1 has a sharp peak, indicativeof critical slowing down toward a spin ordering at the sametemperature, as shown below. These two features provide clearmicroscopic evidence for a second-order antiferromagnetictransition at TN = 13 K.

According to molecular-orbital calculations,7 the dpσ or-bital is localized around the central Cu ion and the surroundingfour S atoms. The tmdt ligand contains six protons availablefor NMR. The dipolar fields at each proton site are estimated,assuming that S = 1/2 spins are located at the central partof the molecule. Since the tmdt ligand has an elongatedstructure, the distance of the proton sites from Cu within aCu(tmdt)2 molecule is about 11.5–13.3 A. It is much longerthan the distances from Cu in the adjacent molecules in the

FIG. 2. Temperature dependence of 1H NMR spectra of polycrys-talline [Cu(tmdt)2].

crystal, which are about 2.7–4.9 A at minimum. Since thedipolar field is proportional to ∼1/r3, where r is the distancebetween a proton and the Cu atom, the main contribution tothe local field at the proton sites is from the dpσ spins in thesix nearest-neighbor molecules [see Figs. 4(a) and 4(b)]. Inwhat follows, we estimate the antiferromagnetic moment fromthe observed spectra, using the atomic parameters obtainedby an x-ray diffraction study.9 As the dpσ spins form aquasi-one-dimensional antiferromagnetic chain along the a

axis, we assume an antiferromagnetic spin configuration inthis direction, as indicated by red lines in Figs. 4(a) and4(b). With respect to the interchain coupling along the b axis,

FIG. 3. Square root of the second moment as a function oftemperature.

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FIG. 4. (Color online) Two possible antiferromagnetic spin configurations with respect to the interchain coupling along the b axis:(a) ferromagnetic and (b) antiferromagnetic coupling. Antiferromagnetic chains along the a axis are indicated by bold solid lines. (c),(d)Absolute value of dipole field parallel to the external field at one proton site, for the spin configuration patterns (a) and (b), respectively. Theseare the summations of six Cu sites, illustrated by arrows in (a) and (b).

ferromagnetic or antiferromagnetic coupling is conceivableas shown in Figs. 4(a) and 4(b), respectively. Note that thespin arrangements along the c axis make no difference in theestimation of the local field at the proton sites. Assuming thata moment of 1μB is located on the Cu site, we calculatedthe dipole fields from six Cu spins, illustrated by arrows inFigs. 4(a) and 4(b), and then summed them up to get the totallocal field at each proton site. In the present experiment witha powdered sample, the direction of the external magneticfield against the crystal axes is different from grain to grain inthe sample. In addition, the present field of 3.66 T is higherthan the spin-flop field but the easy axis is unknown.5 Takingthese facts into consideration, we set the moment directionarbitrarily, keeping the spin configuration as mentioned above,and calculated the component perpendicular to the localmoment aligned normal to the external field due to the spinflop. Note that NMR line measures the local field parallel tothe external field and perpendicular to the antiferromagneticmoment. The calculation was performed for all the momentdirections at the six proton sites. Because the distance anddirection from the nearest Cu spin are dependent on the protonsites in a tmdt molecule, the local field is quite different fromproton site to site. However, what we need for the estimationof an antiferromagnetic moment is only the maximum valueof the local field in the six protons, which corresponds tothe spectral edge. As an example, the calculated dipole fieldat one proton site is shown in Figs. 4(c) and 4(d), for thespin configuration patterns (a) and (b), respectively. Themaximum value is about 680 G in pattern (a) and 740 G inpattern (b). The observed spectral edge of 700 kHz at 1.9 K,which is equivalent to 160 G in the local field, points to thelocal moments of 0.24μB/molecule and 0.22μB/molecule,

respectively. We also performed similar calculations, assumingthat the spins are distributed only on four S atoms aroundthe Cu ions, which gave, as the maximum value of the localfield, 420 G in pattern (a) and 360 G in pattern (b). Thesevalues correspond to local moments of 0.40μB/molecule and0.45μB/molecule, respectively. Because the real dpσ orbitalspreads over the Cu and S ions, the antiferromagnetic momentof [Cu(tmdt)2] should be in between the estimates in thetwo extreme cases; namely, 0.22μB–0.45μB per molecule.The value, much smaller than the classical moment of 1μB,is understood as spin contraction due to enhanced quantumfluctuations in low dimensions.

The fitting exponent β for the nuclear relaxation curve,which measures the spatial distribution of T −1

1 , is shown inthe inset of Fig. 5. β is almost constant, around 0.9, for a widetemperature range from room temperature down to TN. Thesix protons in a molecule have different hyperfine couplingtensors against the external magnetic field, and the field isdirected randomly against the microcrystal axes in a powderedsample. This explains the small but finite deviation of β fromunity even above TN. A sudden decrease in β below 13 K isa clear signature of the additional inhomogeneous local fieldgenerated by the magnetic ordering.

The nuclear spin-lattice relaxation rate T −11 above TN gives

information on the spin dynamics. The room temperaturevalue is 11–13 s−1, which is four times larger than thevalue of the analogous single-component molecular conductor[Au(tmdt)2], exhibiting a magnetic transition at 110 K. The[Au(tmdt)2] salt remains metallic even below TN; so the originof the magnetic phase transition has been argued in the contextof the imperfect nesting of Fermi surfaces, which is suggestedby band-structure calculations.2 T −1

1 is proportional to the

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RINA TAKAGI et al. PHYSICAL REVIEW B 85, 184424 (2012)

FIG. 5. (Color online) Temperature dependence of T −11 obtained

by fitting to stretched-exponential functions of the relaxation curves.T −1

1 can be fitted to a linear function of temperature in the range60 < T < 160 K (solid line) and a temperature-independent function(constant) in the range 20 < T < 40 K (dashed line). The inset showsthe temperature dependence of the exponent β, obtained as a fittingparameter.

square of the fluctuations of local magnetic fields at nuclearsites. As the spin fluctuations in localized-spin systems are ingeneral enhanced compared to those in the degenerate metallicstate, it is reasonable that T −1

1 of [Cu(tmdt)2] is larger than thatof [Au(tmdt)2].

In the limit of T � J/kB (kB is the Boltzmann constant),10

T −11 of a powdered sample with localized spins is given by

T −11 =

√8πg2γ 2

N

3ωeS(S + 1)

∑

i

B2i , (1)

where

ω2e = 8zJ 2S(S + 1)

3h2 .

Here g is the electron g factor, γN is the gyromagnetic ratio ofthe 1H nuclei, J is the exchange interaction between spins S, zis the coordination number, and B2

i is the solid-angle average ofthe dipole hyperfine coupling constant between the 1H nuclearspin and the Cu spin labeled by i (i = 1–6). If the dpσ spinsare solely on the Cu ions, Bi is given by Bi =μB/r3

i , where μB

is the Bohr magneton and ri is the distance between the protonand the ith Cu spin. At a given proton site, the dipole fields fromthe six nearest Cu spins are calculated and then the squaredvalues B2

i are summed over i. The measured relaxation rateis the averaged value over the six proton sites, 〈T −1

1 〉. (Notethat the relaxation rates from different Cu spins should besummed up at a given proton site whereas the relaxation ratesat different proton sites should be averaged.) The substitution

of the values of 〈∑i B2i 〉 = 7.5 × 104 (Oe/μB)2, g = 2.048,

J = 169 K, and z = 2 into Eq. (1) yields 〈T −11 〉 of 6.4 s−1. If the

spins are on four S atoms around Cu, 〈∑i B2i 〉 is estimated at

2.0 × 104 (Oe/μB)2, which yields T −11 of 1.7 s−1. In reality, the

dpσ spins are distributed on Cu and S atoms and thereforethe high-temperature limit of 〈T −1

1 〉 is expected to be betweenthe two. This gives a reasonable explanation for the experimen-tal value of 12 s−1, considering the ambiguity in estimatingBi and averaging the calculated values over the nonequivalentproton sites, and a possible contribution to 〈T −1

1 〉 from theisotropic hyperfine coupling through the bonding electronswithin a molecule.

T −11 is a measure of the dynamic part of the spin sus-

ceptibility, and its temperature dependence is often useful inelucidating the nature of the spin system in question. Generally,low-dimensional spin systems do not show a magnetic orderingeven at T ∼ J/kB. The transition, if any, occurs at a lowertemperature far below J/kB as in the present case. [Cu(tmdt)2]is regarded as a quasi-one-dimensional spin system with J

of 169 K. In the close vicinity of TN of 13 K, T −11 shows

a steep variation due to the critical fluctuations; however,the temperature dependence features temperature insensitivityfor 20 < T < 40 K, and a crossover to a temperature-linearvariation for 60 < T < 160 K (Fig. 5). This behavior isconsistent with the scaling theory for the S = 1/2 Heisen-berg chain model.11 It predicts that staggered susceptibility,which gives a constant T −1

1 , dominates the low-temperaturebehavior at T J/kB whereas at higher temperature (butbelow J/kB), T −1

1 is dominated by uniform susceptibility,leading to temperature-linear behavior. Quantum Monte Carlocalculations also suggest the characteristic crossover betweenthe two behaviors (Fig. 3 in Ref. 12). The predicted low-temperature regime is seen in the temperature-insensitiveCu NMR T −1

1 in the conventional one-dimensional systemSr2CuO3 with J = 2200 ± 200 K and TN = 5 K,13,14 andthe overall crossover behavior is seen in the 31P NMR T −1

1of another one-dimensional spin system BaCuP2O7 withJ = 108 ± 3 K and TN = 0.85 K;15 that is, T −1

1 is nearlytemperature independent below kBT/J ∼ 0.12 and linear withtemperature above that temperature, quite similar to the presentresults. According to Ref. 12, the crossover temperaturedepends on the nonlocality of the form factor in the hyperfinecoupling constant. Anyway, the data in Fig. 5 corroborate thatthe spins form a one-dimensional system as suggested earlier.

As described in the Introduction, molecular orbital calcu-lations indicate that the pπ and dpσ orbitals are energeticallyclose in the present system. This suggests another possibility,that the localized spins are on the pπ orbital. In what follows,we argue this case. In an isolated Cu(tmdt)2 molecule, the(symmetric or asymmetric) pπ orbital is constructed witha weak coupling (bonding or antibonding) of the two tmdtpπ orbitals on both sides of Cu. In the crystal, the tmdt pπ

orbitals overlap with those in adjacent molecules as well.Referring to first-principles calculations and their reductionto the tight-binding model on the isostructural [Au(tmdt)2],16

the largest intermolecular transfer integral between the tmdtligands is 208 meV, which is four times the intramolecularone (54 meV). This means that the entity accommodating thespin is the intermolecular (tmdt)2 instead of the intramolecular

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NMR EVIDENCE FOR ANTIFERROMAGNETIC TRANSITION . . . PHYSICAL REVIEW B 85, 184424 (2012)

(tmdt)2. Taking other transfer integrals available in Ref. 16into account, the spins on (tmdt)2 would form an anisotropicthree-dimensional lattice with transfer integrals of 50 meV inthe ab plane and half that in the c direction. A qualitativelysimilar situation is expected in [Cu(tmdt)2]. If the spinswere on tmdt ligands, one would have three-dimensionalspin dynamics. This consequence is inconsistent with theone-dimensional nature of the spin dynamics in the presentobservation. Therefore, the observed behavior of T −1

1 givesexperimental support for the picture that the electron spins areon the dpσ orbital in [Cu(tmdt)2].

IV. CONCLUSION

We have performed 1H NMR experiments for the single-component molecular system [Cu(tmdt)2]. The observation ofa NMR line broadening and a divergent peak with temperatureprovides clear microscopic evidence for an antiferromagnetictransition at 13 K. The analysis of the broadened spectra belowthe transition temperature gives a moment of 0.22μB–0.45μB

per molecule. The temperature dependence of the NMRrelaxation rate above the transition temperature points tospin dynamics of a one-dimensional nature, which stronglysuggests that the spins are on the dpσ orbital in [Cu(tmdt)2],unlike other members of the [M(tmdt)2] family. This con-sequence shows a potential richness of electronic phases in[M(tmdt)2].

ACKNOWLEDGMENTS

The authors thank H. Seo, S. Ishibashi, and H. Fukuyamafor valuable discussions. This work was supported by MEXTGrants-in-Aid for Scientific Research on Innovative Area(New Frontier of Materials Science Opened by Molecular De-grees of Freedom; Grants No. 20110002 and No. 20110003),JSPS Grants-in-Aid for Scientific Research (A) (Grant No.20244055), (C) (Grant No. 20540346), and (B) (Grant No.20350069), and the MEXT Global COE Program at theUniversity of Tokyo (Global Center of Excellence for thePhysical Sciences Frontier; Grant No. G04).

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