Charge disproportionation in the spin-liquid candidate $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ at 6 K revealed by $^{63}$Cu NQR measurements

The spin-liquid candidate $\kappa$-(ET)$_2$Cu$_2$(CN)$_3$ [ET: bis(ethylenedithio)tetrathiafulvalene] does not exhibit magnetic ordering down to a very low temperature, but shows a mysterious anomaly at 6 K. The origin of the so-called 6 K anomaly is still under debate. We carried out nuclear quadrupole resonance (NQR) measurements on the copper sites of the insulating layers, which are sensitive to the charge dynamics unlike the conventional spin-1/2 nuclear magnetic resonance (NMR). The main finding of this study is that the observation of a sharp peak behavior in the nuclear spin-lattice relaxation rate $T_1^{-1}$ of $^{63}$Cu NQR at 6 K while $T_1^{-1}$ of both $^{13}$C and $^{1}$H NMR show no clear anomaly. This behavior can be understood as a second-order phase transition related to charge disproportionation in the ET layers.

Quasi-two-dimensional organic charge transfer salts κ-(ET) 2 X [ET and X denote bis(ethylenedithio)tetrathiafulvalene and monovalent anion, respectively] possess half-filled band owing to strong dimeric structures of donor molecules. In the typical phase diagram, antiferromagnetic and superconducting phases are adjacent to each other and the phase transition between them has been discussed in terms of the bandwidth and on-site Coulomb repulsion [1], where the magnetic properties mainly originate from antiferromagnetic interaction between (ET) + 2 dimers with S=1/2. The role of the charge degree of freedom has also been pointed out to explore the recent observations of dielectric anomaly with antiferromagnetic ordering [2], charge order [3,4], and quantum dipole liquid [5].
Such complex physical properties related to spin and charge degrees of freedom have also been discussed in a representative spin-liquid candidate κ-(ET) 2 Cu 2 (CN) 3 . This material does not show long range magnetic ordering down to T =32 mK despite a large antiferromagnetic exchange interaction of ∼ 250 K [6], and therefore it has attracted much attention as the quantum spin liquid. κ-(ET) 2 Cu 2 (CN) 3 showed a relaxor-like dielectric response below 60 K, and intradimer charge disproportionation (CD) was proposed [7] although the mechanism is under debate [8][9][10]. It is also pointed out that the mysterious anomaly at 6 K could be related to charge properties. This anomaly was initially detected by the hump structure in the T dependence of specific heat whereby a crossover from a thermal disordered to a quantum spin liquid state was suggested [11]. On the other hand, the thermal expansion measurements indicate a phase transition, and the importance of charge degree of freedom was suggested [12]. Whereas many experimental and theoretical efforts have been devoted to elucidating the origin of the so-called "6 K anomaly" [13][14][15][16][17][18][19][20][21][22][23][24], it is not even clear whether it is a phase transition or a crossover phenomenon.
Nuclear magnetic resonance (NMR) is an effective technique for providing the microscopic evidences of charge and/or spin anomalies. Up to now, there have been several NMR reports using 13 C and 1 H nuclei with nuclear spin I=1/2. However, such NMR measurements cannot probe the charge directly because of no direct interaction between I=1/2 nucleus and charge, whereas one can obtain the information of the charge distributions through the change in hyperfine coupling constants [25]. Therefore NMR measurements using nuclei with I=1/2 are less sensitive to charge anomaly. In fact, no clear anomaly at 6 K has been observed in 1 H-and 13 C-NMR measurements, especially, in nuclear spin-lattice relaxation measurements [6,[26][27][28]. Here, we focus on the nuclear quadrupole resonance (NQR) technique, which is a charge-sensitive probe offering a new perspective. This is because the NQR technique directly detects the electric field gradient (EFG) through the nuclear quadrupole moment Q ( = 0 when I > 1/2). Until now, NQR method has attracted less attention in the field of organic conductors since there is no NQR-active nuclei in the ET molecule. In this Letter, we report the first NQR experiment in the ET-based charge transfer salts using copper nuclei located at the insulating layer in κ-(ET) 2 Cu 2 (CN) 3 . Our NQR results elucidate that the 6 K anomaly can be understood as a phase transition related to the charge degree of freedom in the molecular layers.
Polycrystalline samples were prepared by the standard electrochemical reaction [29]. Zero-magnetic-field (ZF) NQR experiments of 63 Cu (I=3/2, Q=−0.21 barns) and 65 Cu (I=3/2, Q=−0.195 barns) were performed by using a home-made phase-coherent spin-echo pulse spectrometer. 63,65 Cu-NQR spectra were obtained in steps of frequency by measuring the intensity of the Hahn spin echo. The nuclear spin-lattice relaxation rate of 63 Cu, 63 T −1 where M (t) and M (∞) are the nuclear magnetization at time t after the saturation and the equilibrium nuclear magnetization at t → ∞, and β is the stretched exponent, respectively. The nuclear spin-echo decay rate T −1 2 was determined by the spin-echo signal M (2τ ) as a function of time 2τ , where τ is the interval between the first exciting and refocusing pulses. In the case of I=3/2, one expects a single NQR line at the resonance frequency of ν NQR =ν Q 1 + η 2 /3, where ν Q is nuclear quadrupole frequency defined by ν Q =eQV ZZ /2h. Here e, V ZZ , h, and η are elementary charge, the principal value of the EFG tensor, Planck's constant, and asymmetry parameter of EFG, respectively. Since there are two isotopes 63 Cu and 65 Cu, NQR spectrum must be a pair of lines with different intensities where the 63 Cu-NQR intensity is about double of the 65 Cu-NQR one due to the natural abundances of the two nuclei (viz, 63 Cu: 69%; 65 Cu: 31%). Therefore, the observation of four lines clearly indicates the existence of two Cu sites with slightly different environments. By taking the difference in Q between 63 Cu and 65 Cu into consideration, we can assign the two pairs (defined by Cu1 and Cu2 sites) as shown in Fig. 1(a).
In κ-(ET) 2 Cu 2 (CN) 3 , as shown in Fig. 1(b), there are three cyano groups around a Cu nucleus, and one of them is considered to be positionally disordered with a 50 % carbon and 50 % nitrogen distribution (depicted by black symbols) due to an inversion point at the center of the cyano groups [30,31]. Consequently, Cu + ions are expected to be trigonally coordinated with two carbons and one nitrogen, or with one carbon and two nitrogens, making two copper sites with slightly different environments (i.e., slightly different EFG) with equal probability. This is consistent with the observed NQR spectrum including the intensity ratio of 1:1 for Cu1 and Cu2. Although we do not know which one is which, our observation directly evidences the disorder of carbon and nitrogen ions due to the inversion symmetry in κ-(ET) 2 Cu 2 (CN) 3 .
It is noted that one cannot determine the values of ν Q and η for the Cu ions separately from only the NQR spectrum. A finite value of η, the lack of axial symmetry of EFG, is expected from the local symmetry at the Cu sites. With the help of NMR spectrum measurements described below, η is estimated to be ∼ 0.5, and thus the values of ν Q are estimated to be 36.2(37.3) MHz and 39.1(40.3) MHz for 65 Cu and 63 Cu, respectively, for the Cu1(Cu2) sites. The direction of V ZZ is considered to be parallel to the a * axis, perpendicular to the insulating layers.
As shown in Fig. 1(a), there is no significant difference in the spectra between 4.3 K and 10 K for the two Cu sites, hereafter, we show the T dependence of spectra and 63 T −1 1 measured at the peak at around 40.7 MHz ( 63 Cu ions at the Cu1 site). NQR experiments were able to be conducted between 1.5-120 K. Above 100 K, T −1 2 suddenly increases as shown in Fig. 1(c), and eventually the NQR signals disappeared above 130 K owing to the shortening of T 2 . This is probably due to the vibrational motion of ethylene end groups of ET molecule at high T [32]. NQR spectra suggesting no structural phase transition in the T range. The peak position is slightly shifted to lower frequency with increasing T , corresponding to the decrease in ν NQR as shown in Fig. 2(b). The T dependence of ν NQR is considered to be originated from thermal lattice expansion and can be described by the empirical formula [33,34], ν NQR =ν 0 exp(−αT 2 ). As shown by the curve in Fig. 2(b), the T dependence of ν NQR is well reproduced with the formula with ν 0 =40.68 MHz and α=3.58×10 −7 K −2 . Figure 2(c) shows the T dependence of linewidth (full width at half maximum, FWHM) determined by the fitting of the spectra with Gaussian function. With decreasing T , the linewidth increases from 0.3 MHz at 120 K to 0.36 MHz at around 60 K, and is nearly independent of T below 60 K. Figure 3 shows the T dependence of ZF 63 T −1 1 . For comparison, the T dependence of T −1 1 of 13 C, 13 T −1 1 , is also plotted [27]. Note that the values of 13  shows T 2 dependence above 60 K, below which it is proportional to T 1/2 coinciding with that of 13 T −1 1 . With further decreasing T below 10 K, 63 T −1 1 starts to increase and then shows a pronounced peak at 6 K, whereas 13 T −1 1 decreases monotonically. The exponent β deviates from unity below 6 K as shown in the inset of Fig. 3, indicating a development of inhomogeneity in 63 T 1 . A similar inhomogeneity below ∼ 6 K was also observed in 13 C-and 1 H-NMR measurements [6,27].
The T ∼2 dependence of 63 T −1 1 observed above 60 K can be explained by the thermal vibrations of the three nearest neighbor CN − ions with respect to Cu ion. A similar T dependence has been reported in other kinds of diamagnetic insulators [34][35][36], whose T de-pendence was explained by the quadrupolar relaxation due to the two-phonon Raman process [37]. In this case, the quadruple relaxation (T −1 1,Q ) is described as 2 Ω 0 e ω/kB T (e ω/kB T − 1) −2 (ω/Ω) 6 dω. Here, m, v, and Ω are the atomic mass of 63 Cu, sound velocity in the crystal, and cutoff frequency related to Debye temperature (Θ), respectively. F 2 is a parameter which can be approximated by 2πν Q [37,38]. Assuming v=10 3 m/s [39], and a typical value Θ = Ω/k B = 200 K for κ-(ET) 2 X [40,41], we have calculated the T dependence of T −1 1,Q . The dashed black curve is the calculated result without free parameter, which reproduces the experimental data very well by adding another contribution as described below.
From the calculated result of T −1 1,Q , 63 T −1 1 is expected to decrease drastically at low T due to the suppression of thermal vibrations. However, 63 T −1 1 gradually deviates from T −1 1,Q below ∼ 60 K and shows T 1/2 dependence between 10-40 K, which is the same as that of 13 T −1 1 [27]. Since 13 T −1 1 originates from the magnetic fluctuations from the π electrons of the ET layers [27,42], the similar T dependence of 63 T −1 1 indicates that the magnetic fluctuations become dominant at the Cu site. In fact, this interpretation can be confirmed by looking at the ratio of is proportional to the square of gyromagnetic ratio γ and hyperfine coupling constant A, the ratio of ( 63 γ 2 63 T 1 ) −1 /( 13 γ 2 13 T 1 ) −1 ∼ 0.02 should be proportional to | 63 A/ 13 A| 2 . To estimate the 63 A, we performed 63 Cu-NQR measurements on the antiferromagnet κ-(ET) 2 Cu[N(CN) 2 ]Cl (Néel temperature ∼22 K [43,44]) whose interlayer distance is close to the case of κ-(ET) 2 Cu 2 (CN) 3 [45]. We found the internal field at the 63 Cu site to be 63 H int ∼ 70 G [46]. According to 13 C-NMR measurement by Smith et al., the mean internal field at the 13 C site is estimated to be 13 H int ∼ 750 G [47]. Since the ratio of internal magnetic field (| 63 H int / 13 H int | ∼ 0.1) is considered to be proportional to the hyperfine coupling constant ratio, | 63 A/ 13 A| 2 is evaluated to be 0.01, which is in good agreement with ( 63 γ 2 63 T 1 ) −1 /( 13 γ 2 13 T 1 ) −1 ∼ 0.02. Therefore, the observed 63 T −1 1 between 10−40 K can be interpreted as the magnetic fluctuations originated from the π electrons on the ET layers. The red solid curve shown in Fig. 3 is the sum of the two contributions of the magnetic relaxation ( 63 T −1 1 ∝ T 1/2 ) and the quadruple relaxation T −1 1,Q : T −1 1 =aT 1/2 + T −1 1,Q (with a=0.055), which reproduces the experimental data quite well.
The most striking feature in the T dependence of 63 T −1 1 is the observation of the sharp peak around 6 K, indicating a second-order phase transition. We exclude the possibility of crossover phenomenon for the anomaly by measuring the resonance frequency dependence of 63 T −1 1 . In the case of crossover, we expect Bloembergen-Purcell-Pound-like behavior where frequency-dependent T −1 1 is expected [48]. Since one cannot change the resonance frequency in the NQR experiment, we have carried out NMR measurements. Figure 4(a) shows the field-swept 63,65 Cu-NMR spectrum measured at a fixed frequency 75 MHz at 1.7 K where a broad and complicated spectrum is observed. This is due to large ν NQR and a finite value of η as well as the superposition of four NMR lines ( 63,65 Cu ions for the two Cu sites). The red curve is the sum of the four calculated powder-pattern spectra [49]. As observed in the figure, the calculated spectrum well reproduces the characteristic shape of the observed spectrum. 63 T 1 was measured at the relatively sharp peak appeared at the lower magnetic field side of the main broad peak [around 6 T for 75 MHz in Fig. 4(a)] while changing the frequency [50]. As shown in Fig. 4(b), no obvious frequency dependence in 63 T 1 was observed within our experimental uncertainty, evidencing again that the anomaly at 6 K is not due to a crossover but to a phase transition with critical slowing down.
What then is the origin of the phase transition? 13 T −1 1 measurements could not clearly detect the anomaly at 6 K [6,27], suggesting that the 6 K anomaly is not due to the magnetic fluctuation of the ET layers. Furthermore, magnetic fluctuations originated from the anion insulating layers are also unlikely because Cu + ion is nonmagnetic and also 1 T −1 1 performed on the ethylene end groups of the ET molecules near the anion layer, showed no clear anomaly [6]. Therefore, it is concluded that the peak in the T dependence of 63 T −1 1 originates from the EFG fluctuation. There are three possible scenarios: the first one is the charge fluctuations due to the disorder of C and N ions in the anion layers, the second one is structural phase transition, and the last one is due to CD in the ET layers.
Regarding the first one, since two Cu sites, Cu1 and Cu2, caused by the disorder of C and N ions in the anion layers were observed below and above 6 K, no change in the disorder is expected at 6 K. In addition, no change in ν NQR and linewidth at 6 K also will exclude the pos-sibility of structural phase transition at 6 K.
Hence, the most probable explanation is the CD in the ET layers. To check whether or not a CD on the conduction layers actually affects the EFG value at the Cu site, we have calculated the EFG while assuming a CD of ±0.1e on the ET molecules. From our simple point charge calculation, we found that the EFG at the Cu sites is modulated by 0.5 × 10 18 V/m 2 . The value is comparable to that from the thermal displacement of CN − ions which modulates the EFG by 2.2 × 10 18 V/m 2 at the Cu site [51]. Since we actually observed the T ∼2 dependence of 63 T −1 1 due to the thermal vibration of CN − ions at high T , we conclude that the critical slowing down of the CD on the ET molecules should be detected by 63 Cu NQR at low T when the lattice vibration is suppressed.
According to the previous 13 C-NMR studies, 13 C-NMR linewidth discontinuously increases below 6 K [26,27]. Since the linewidth relates to the distribution of charge density through the hyperfine couplings [26,27], the value of the discontinuous jump of the linewidth divided by the Knight shift (corresponding the mean value of charge density) will give an estimate of the degree of charge distribution. Using the data from Ref. [26], we estimate the charge distribution from the average valence of the ET molecules to be (0.5 ± 0.13)e [52]. The decrease in β both in 13 C NMR and 63 Cu NQR can also be understood by the CD due to the phase transition at 6 K. Therefore, it is quite reasonable that the charge degree of freedom in the ET layer is responsible for the observed phase transition. CD within dimers has been proposed experimentally [7,15] and theoretically [53][54][55][56][57], and the recent structural analysis also pointed out the possibility of CD between dimers [31]. On the other hand, powder transmission measurement detected no CD [8]. Further studies are required to clarify what kind of CD occurs.
Finally we comment on small humps around 3 K observed in 63 T −1 1 and β. The anomaly at the same temperature was also observed in such as thermal expansion, dielectric function, and µSR measurements, indicating it is intrinsic [12,14,58]. At present, we cannot conclude the origin of the hump behavior in 63 T −1 1 from our NQR experiments. Detailed low-T Cu-NQR measurements down to such as 0.1 K is interesting to shed the light on the physical properties of the compound at low T . This is a future work.
In conclusion, we performed the 63 Cu-NQR measurement on the quantum spin-liquid candidate κ-(ET) 2 Cu 2 (CN) 3 to investigate the charge dynamics. Two different Cu sites are observed in the 63,65 Cu NQR spectrum, which is direct evidence for the disorder of C and N atoms in the cyanide groups. 63 T −1 1 shows T 2 dependence indicating the EFG fluctuation due to the lattice vibration above 60 K, below which 63 T −1 1 changes from T 2 to T 1/2 dependence with the suppression of lattice vibration. The T 1/2 dependence of 63 T −1 1 observed in T =10 − 40 K was ascribed to the magnetic fluctuation of π electrons of the ET layers. Below 10 K, 63 T −1 1 increases and divergent behavior was observed at 6 K, evidencing a phase transition with critical slowing down derived from the EFG fluctuation. Based on our NQR data, we attributed the 6 K anomaly to the phase transition of CD originated from the π electrons in the ET layers. Our results require to reconsider the current interpretation of the low-T electronic state of κ-(ET) 2 Cu 2 (CN) 3 , which was thought to exhibit a paramagnetic spin state without the phase transition down to a very low T due to the spin frustration.