Pressure-Induced Superconductivity of the Quasi-One-Dimensional Organic Conductor (TMTTF)₂TaF₆

Abstract

We investigated the superconductivity of (TMTTF)₂TaF₆ (TMTTF: tetramethyl-tetrathiafulvalene) by conducting resistivity measurements under high pressure up to 8 GPa. A cubic anvil cell (CAC) pressure generator, which can produce hydrostatic high-pressure, was used for this study. Since the generalized temperature-pressure (T-P) diagram of (TMTCF)₂X (C = Se, S, X: monovalent anion) based on (TMTTF)₂PF₆ (T_CO = 70 K and spin-Peierls: SP, T_SP = 15 K) was proposed by Jérome, exploring superconductivity states using high-pressure measurement beyond 4 GPa has been required to confirm the universality of the electron-correlation variation under pressure in (TMTTF)₂X (TMTTF)₂TaF₆, which has the largest octahedral-symmetry counter anion TaF₆ in the (TMTTF)₂X series, possesses the highest charge-ordering (CO) transition temperature (T_CO = 175 K) in (TMTTF)₂X and demonstrates an anti-ferromagnetic transition (T_AF = 9 K) at ambient pressure. A superconducting state in (TMTTF)₂TaF₆ emerged after a metal-insulator transition was suppressed with increasing external pressure. We discovered a superconducting state in 5 ≤ P ≤ 6 GPa from T_c = 2.1 K to 2.8 K, whose pressure range is one-third narrower than that of X = SbF₆ (5.4 ≤ P ≤ 9 GPa). In addition, when the pressures with maximum SC temperatures are compared between the PF₆ and the TaF₆ salts, we found that (TMTTF)₂TaF₆ has a 0.75 GPa on the negative pressure side in the T-P phase diagram of (TMTTF)₂PF₆.

1. Introduction

Since the discovery of the first organic superconductivity in (TMTSF)₂PF₆ (tetramethyl-tetraselenafulvalene-hexafluorophosphate), quasi-one-dimensional (Q1D) organic conductors (TMTCF)₂X (C = Se and S, X = monovalent anion) have been extensively investigated because electronic-correlations related to spin, charge, and dimensionality generate various types of ground states [1,2,3,4,5]. In the (TMTCF)₂X crystal, face-to-face TMTCF molecules align perpendicularly along the a-axis. The hybridization of p-electrons on Se or S atoms in the TMTCF molecules leads to strong one-dimensional conductivity, and the 1D-TMTCF chain is well-separated by the monovalent anion X layer. The (TMTCF)₂X system has a 3/4 filling band structure [6]. Their flexible-molecular packing consequently produces multihued ground states, which change from AFM (anti-ferromagnetism) I-SP (spin-Peierls), AFM II (commensurate SDW), and incommensurate SDW (spin density wave) to an SC (superconductivity) phase at low temperatures, by controlling the superposed electron density in both inter-and intra-chains using chemical and the applied pressures [1]. For more than three decades, the generalized phase diagram has been extended by efforts in synthesizing TMTTF salts with centrosymmetric (cs) (X = Br, I, PF₆, AsF₆, SbF₆, NbF_6, and TaF₆) and non-centrosymmetric (ncs) anions (X = BF₄, ClO₄ and ReO₄). Simultaneously, many scientists have attempted to clarify the ground state changes of (TMTTF)₂X by conducting pressure measurements, and the validity of the temperature-pressure (T-P) diagram corresponding between the chemical pressure and the external pressure has been confirmed. In particular, the high-pressure investigation exceeding 4 GPa has revealed the existence of the superconductivity phase in the (TMTTF)₂X series [2,3,7,8,9,10].

The emergence of the superconducting phase in the (TMTTF)₂X series is understood as a crossing over anti-ferromagnetic fluctuation. (TMTTF)₂Br is the first superconductor in TMTTF series (T_C = 0.8 K@ 2.6 GPa) [11], whose ground state shifts from AFM II (T_AF = 15 K, C-SDW: commensurate) to SDW (I-SDW: incommensurate) by external pressure [12,13,14]. The SDW transition temperature decreases due to the imperfect nesting of Fermi surfaces by applying external pressure. The SDW phases observed in (TMTSF)₂MF₆ (M = P, As, Sb) were explained by the electron correlation and two-dimensionality with mean-field theory [15]. As it stands that the SC phase in (TMTCF)₂X always neighbors the SDW, there are many reports about the exotic superconductivity properties of (TMTCF)₂X, for instance, the anisotropic SC revealed by high magnetic field measurements [16,17] and by muon spin rotation [18].

The charge-ordering (CO) state was observed in the (TMTTF)₂X series, except for (TMTTF)₂ClO₄, (TMTTF)₂SCN, and (TMTTF)₂I [19,20,21]. The CO transition of (TMTTF)₂X is called a structureless transition since only a small change in the dimer position was observed by X-ray diffraction measurement [22]. The spatial charge disproportion on TMTTF molecules affects the spin state at low temperatures. In the case of (TMTTF)₂X, which has an octahedron symmetry counter anion, the X = PF₆ and AsF₆ salts go into the SP phase from the CO phase, while the X = SbF_6, NbF₆ [23], and TaF₆ salts change to AFM I phase by cooling, depending on the CO pattern, dimensionality, and spin fluctuation [24,25]. Below 3 GPa pressure region, ¹³C NMR studies in X = SbF₆ have revealed that the ground states vary from AFM I → spin gap → AFM II (C-SDW) (Figure 1) [26,27]. The ground state change from SDW to SC became decisive through the high-pressure resistivity measurement up to 10 GPa using a cubic anvil cell (CAC); the superconducting phase of (TMTTF)₂SbF₆ was observed as an anomalously wide pressure range (5.4 < P < 9 GPa) under limited temperature above 1.8 K [9].

(TMTTF)₂TaF₆ has the largest cell volume in the (TMTCF)₂X series, with a cs anion. The one-dimensional character was confirmed by the result of the single-crystal X-ray diffraction analysis [28]. To understand the electron correlation, confirmations of the existence of the SC state and the pressure-dependent ground-state change toward the SC state in (TMTTF)₂TaF₆ are necessary. In this paper, we investigated the resistivity behaviors of (TMTTF)₂TaF₆ under high pressures up to 8 GPa and compared it to those for other TMTTF compounds (X = PF₆, AsF_6, and SbF₆).

Figure 1. Electronic temperature-pressure (T-P) diagram for quasi-one-dimensional (Q1D) organic conductors (TMTCF)₂X (C = S and Se), which start from the ground state of the (TMTTF)₂TaF₆ salt (CO state T_CO = 175 K and AFM T_AF = 9 K), suggested by Dressel et al. and Oka et al. This T-P diagram is depicted from the references [5,23,26,27,29,30,31,32]. The generalized T-P diagram (i.e., generalized electron correlation diagram) of (TMTCF)₂X was first established by D. Jérome and coworkers in 1991 [1]. The abbreviations for described states in the diagram are CO (charge-ordering state), CL (charge-localized state), SP (spin-Peierls state), AFM (anti-ferromagnet, I: commensurate state, II: commensurate SDW), SDW (spin density wave), and SC (superconducting state).

Figure 1. Electronic temperature-pressure (T-P) diagram for quasi-one-dimensional (Q1D) organic conductors (TMTCF)₂X (C = S and Se), which start from the ground state of the (TMTTF)₂TaF₆ salt (CO state T_CO = 175 K and AFM T_AF = 9 K), suggested by Dressel et al. and Oka et al. This T-P diagram is depicted from the references [5,23,26,27,29,30,31,32]. The generalized T-P diagram (i.e., generalized electron correlation diagram) of (TMTCF)₂X was first established by D. Jérome and coworkers in 1991 [1]. The abbreviations for described states in the diagram are CO (charge-ordering state), CL (charge-localized state), SP (spin-Peierls state), AFM (anti-ferromagnet, I: commensurate state, II: commensurate SDW), SDW (spin density wave), and SC (superconducting state).

2. Experimental Section

The sample preparation of (TMTTF)₂TaF₆ was detailed in Ref. [28]. The single crystal (TMTTF)₂TaF₆ is a black needle type; the sample size used for resistivity measurement was 800 μm × 15 μm × 10 μm. The high-pressure resistivity measurement was performed by using a CAC apparatus at the Institute for Solid State Physics (ISSP), The University of Tokyo. The resistivity of (TMTTF)₂TaF₆ was measured along the a-axis (crystal growing direction) by a conventional four-probe method. The four Au electric terminals (ϕ 10 μm Au wire) were in contact with carbon paste on the sample surface and the ends of Au wires were relayed to ϕ 15 μm Pt wires with Au paste to avoid wire cutting during the application of high pressures. The four relayed Pt wires are fixed with a small piece of paper by using epoxide resin adhesives to prevent sample breaking by the shock when the high pressure was applied. The sample with electrodes was sealed in a small Teflon cell (ϕ 2.0 mm) with the pressure medium Fluorinert 70:77 (1:1) mixture and then wrapped with a cubic MgO gasket (6 mm squares), which also served as the second pressure medium. The four Pt electric leads outside of the Teflon cell were wired with thin Au ribbons on the MgO gasket. The MgO gasket was isotopically compressed up to 250 tons by Tungsten carbide anvils, which also play a role in four-wire electronic contact materials. The CAC can generate a high-quality steady hydrostatic pressure by controlling a constant load system up to 12 GPa. The temperature range for this measurement was from 1.8 K to 295 K and the resistance value of (TMTTF)₂TaF₆ was recorded upon heating. External pressure was applied on (TMTTF)₂TaF₆ between 0 GPa and 1.4 GPa; the resistance varied due to unsteady attachment between the gasket and CAC anvils. At 1.5 GPa, the MgO gasket was compressed enough to achieve steady resistance of the TaF₆ salt. Therefore, we did not measure the resistivity at 0 GPa; the measurement starts from 1.5 GPa. The resistivity along the a-axis was normalized by using the length and the surface values at room temperature.

3. Results and Discussion

At ambient pressure, the CO phase transition temperature (T_CO = 175 K) of X = TaF₆ is the highest in the TMTTF series with octahedron monovalent anion. The CO transition temperature increases with increasing the octahedron anion size, PF₆ (70 K), AsF₆ (102 K) SbF₆ (154 K), and NbF₆ (165 K) [23]. The stoichiometry-controlled salt (TMTTF)₂[AsF₆]_1-x[SbF₆]_x (x~0.3) has a higher T_CO of 120 K, which is between the temperatures of the AsF₆ and SbF₆ salts, and the characteristic SP magnetic susceptibility behavior is suppressed at a low temperature [33]. It was reported that the transition between SP and AFM I states occurs at x~0.5 chemical pressure [34], while the pressure experiment on (TMTTF)₂SbF₆ revealed that the AFM I state changed to a spin gap state due to the external pressure of 0.5 GPa, and the CO state becomes unclear above 0.5 GPa. [26]. (More details for the pressure effect on the CO state in X = AsF₆ and SbF₆ are in Ref [35]). The CO state in the TaF₆ salt has a -O-o-O-o- pattern (O: charge-rich site, o: charge-poor site) as in the SbF₆ salt, which coexists in the AFM I phase at ambient pressure [27,32]. The temperature-dependent magnetic susceptibility shows a characteristic one-dimensional decrease from 300 K to 50 K, and a rapid decrease was observed around 30 K. (TMTTF)₂TaF₆ undergoes an anti-ferromagnetic transition at 9 K [27].

Figure 2a shows the temperature-dependent resistivity of (TMTTF)₂TaF₆ in the a-axis direction under pressures from 1.5 GPa to 8 GPa. For the measurement, the initial temperature was set to around 1.8 K by cooling from room temperature, and then the temperature was gradually heated. Generally, the metallic conductivity of the TMTTF series becomes unstable due to the charge localization at T_𝜌 in the high-temperature region. For the TaF₆ salt, T_𝜌 is reported as ~200 K, which is quite close to T_CO = 175 K. The resistivity at room temperature is 0.1 Ω·cm [32]. In the case of our pressure measurement, the resistivity at 1.5 GPa was 0.35 Ω·cm at room temperature, whose value was two orders higher than that (0.005 Ω·cm) of (TMTTF)₂SbF₆ (Figure 2b). A possible cause of the high resistivity value at 1.5 GPa is considered as a partial remnant charge localization caused by interfering with smooth volume compression and/or exceeding the anisotropic crystal deformation by a large TaF₆ anion under low pressures.

Figure 3a shows the resistivity value at 290 K under several pressures for (TMTTF)₂X (X = PF₆, AsF₆, SbF_6, and TaF₆) by using the CAC pressure generator. The pressure-dependent resistivities of X = PF₆, AsF_6, and SbF₆ were plotted with the data in Refs. [7,8,9]. The resistivity rapidly decreases up to 5 GPa and the value becomes almost unchanged beyond 6 GPa, although the resistivities for (TMTTF)₂X (PF₆, AsF₆, and SbF₆) are almost suppressed below 2 GPa (Figure 3a inset). It should be noted that the resistivity of the SbF₆ salt is the lowest in the (TMTTF)₂X series from 1.5 GPa to 10 GPa.

For the resistivity of the TaF₆ salt at 1.5 GPa, we observed the drastic resistivity drop up to 100 K upon heating. After the temperature reached 100 K, the resistivity has a gradual incline (Figure 2b). The activation energies of Δ_𝜌 and Δ_S were obtained from a simple formula, $\log \rho \left(T\right)=\frac{\mathrm{\Delta }}{T}+\log {\rho }_0$. The inclination changes at a higher temperature and a second inclination change at a lower temperature correspond to T_𝜌 and T_S in Figure 2c, in $\log \rho \left(T\right)$-$\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$T$}\right.$ plot. Here, the sample size reduction caused by thermal expansion and pressure effects is not taken into account for the $\log \rho \left(T\right)$ calculation. Figure 3b,c show the pressure-dependent activation energies (Δ_𝜌 and Δ_S) for (TMTTF)₂X (X = PF₆, AsF₆, SbF₆ and TaF₆). It should be noted that the Δ_𝜌 value in Figure 3b includes both activation energies coming from CO and Mott localization. The CO gap ${\mathrm{\Delta }}_{\mathrm{CO}}$ has been discussed in several reports by resistivity measurements [20,32,33], using the formula ${\mathrm{\Delta }}_{\mathrm{CO}}=\sqrt{\mathrm{\Delta }{\left(T\right)}^2-{\mathrm{\Delta }}^2\left(T_{\mathrm{CO}}\right)}$ (here $\mathrm{\Delta }\left(T\right)=T\ln \rho$ in the CO state and ${\mathrm{\Delta }}^2\left(T_{\mathrm{CO}}\right)$ is the value above $T_{\mathrm{CO}}$). Each ${\mathrm{\Delta }}_{\mathrm{CO}}$ gap at ambient pressure is ~560 K for TaF₆, ~500 K for SbF₆, 430 K for [AsF₆]_1-x[SbF₆]_x (x ~0.3), ~315 K for AsF₆, and ~217 K for PF₆, which increases proportionally to T_CO [32,33]. ${\mathrm{\Delta }}_{\mathrm{CO}}$ values are less than half of the obtained Δ_𝜌 values at 0 GPa and the order of magnitude of (TMTTF)₂X is Δ_𝜌 (SbF₆) > Δ_𝜌 (AsF₆) > Δ_𝜌 (PF₆), which is different from Δ_co (TaF₆) > Δ_co (SbF₆) > Δ_co (AsF₆) > Δ_co (PF₆). For the obtained data of high-pressure measurements for the TaF₆ salt, the extraction of the ${\mathrm{\Delta }}_{\mathrm{CO}}$ value at around 1.5 GPa is already unresolved due to an unclear transition at T_CO.

The Δ_𝜌 and Δ_S at 1.5 GPa for (TMTTF)₂TaF₆ are 117 K (T_𝜌~90 K) and 116 K (T_S~20 K), respectively, which correspond to the values at about 2.1 GPa and 1.5 GPa for those of (TMTTF)₂SbF₆, respectively. The Δ_𝜌 becomes comparable to those of other (TMTTF)₂X salts near 2.0 GPa since the CO state of the TaF₆ salt already vanishes, then Δ_𝜌 values coincide with almost constant values in (TMTTF)₂X salts above 3 GPa. Meanwhile, activation energy Δ_S corresponds to a spin-related transition (SP, AFM II, and SDW), according to the similar analysis of (TMTTF)₂X [2,3,7,8,9]. With increasing applied pressures, high resistivity at low temperatures dramatically drops and the metallic behavior becomes dominant above 40 K upon heating (see Figure 2b). At 3 GPa, the resistivity at room temperature still shows a high value of 0.3565 Ω·cm; the minimum drop in the resistivity curve appears at around 20 K in the resistivity-temperature curve, written in both logarithmic axes. The respective activation energies Δ_S at 3 GPa and 4 GPa are 22 K (T_S = 13 K) and 10 K (T_S = 8 K), respectively, which correspond to the activation energies observed in the X = SbF₆ salt at ~4.6 GPa and 5.3 GPa, respectively (see Figure 3c). It should be noted that the AFM II (C-SDW) and SDW (I-SDW) transition temperatures are ~15 K (at 0 ≤ P < 0.3 GPa) and ~23 K (at 0.3 < P ≤ 0.75 GPa) in (TMTTF)₂Br [12]. Here, the resistivity of the TaF₆ salt between 200 K and 300 K at 4 GPa becomes almost equal to that of X = SbF₆ at room temperature (see Figure 2b).

At 5 GPa, the zero-resistivity is observed due to an occurrence of a pressure-induced superconductivity transition at 2.83 K. It should be noted that the value of resistivity (0.047 Ω cm) at 300 K is one order higher than that of the SbF₆ salt and the zero-resistivity was observed using the CAC apparatus in (TMTTF)₂X series except for the X = SbF₆ salt [7,8,9]. Figure 4 displays the temperature-dependent resistivity from 5 GPa to 8 GPa at low temperatures (between 1.8 K and 10 K). The superconductivity phase exists in a quite short pressure region of 5 ≤ P ≤ 6 GPa; the shape of the SC phase is completely different from the (TMTTF)₂SbF₆ salt (5.4 ≤ P ≤ 9 GPa). The maximum T_C is 2.8 K at 5 GPa, the superconducting temperature shifts to a slightly lower temperature with increasing pressure, and then the SC state almost disappears at 6 GPa. Above 7 GPa, only metallic behavior is observed. By estimating the power of temperature (T) with $\rho \left(T\right) ~ T^{\alpha }$ between 6 GPa and 8 GPa, the α increases linearly as pressure increases and reaches ~1.5 at 8 GPa.

The main physical parameters, maximum superconducting transition temperature T_C and the pressure P_C, activation energy Δ_S at 3 GPa, lattice parameters along the a-axis, volumes, and ground states at ambient pressure for (TMTTF)₂X (PF₆, AsF₆, SbF₆, and TaF₆) are listed in

Table 1. Physical properties of (TMTTF)₂X (X = PF₆, AsF₆ SbF₆, and TaF₆). T_CO, activation energies for Δ_S at 3 GPa, lattice parameters and volumes at ambient temperature, superconducting (SC) temperature T_C and the observed pressure, and ground states at low temperature (0 GPa). Δ_S, T_C, and pressure region for SC were obtained using resistivity measurements with the CAC pressure generator.

(TMTTF)2X	TCO	Activation Energy 3 GPa Δs [K]	Lattice Parameter a* [Å]	V [Å3] at Room Temperature *	Superconducting Temperature TC [K]	Pressure at Maximum TC [K] (Pressure Region for SC Phase) **	TSP [K]	TAF [K]
PF6	70	16	7.172(11)	676.6	2.5	4.3 (4.0 ≤ P ≤ 5.0 GPa)	15
AsF6	102	17	7.1662(4)	686.15	2.6	5.0 (4.5 ≤ P ≤ 5.0 GPa)	14
SbF6	154	57	7.1796(11)	702.93	2.8	6.0, 9.0 (5.4 ≤ P ≤ 9.0 GPa)		8
TaF6	175	22	7.1862(11)	706.52	2.8	5.0 (5.0 ≤ P ≤ 6.0 GPa)		9

* Lattice parameters and volumes refer to Ref. [28]. ** The temperature region for the resistivity measurement by the CAC was from 1.8 K to 300 K.

. The T-P diagram of (TMTTF)₂TaF₆ based on the result of this resistivity measurement is described in Figure 5, in which the electron-correlation change is referred to in the data of (TMTTF)₂PF₆. This phase diagram is obtained by adjusting both pressure points of TaF₆ and the PF₆, where the maximum SC transition temperatures (T_C (PF₆) and T_C (TaF₆)) were recorded. The ground states of the TaF₆ salt vary in CO/AFM I -(SP)- SDW (C-SDW: commensurate spin density wave and I-SDW: incommensurate spin density wave) and SC as referred to in reports [1,2] and the previous studies [7,8,9]. In this case, the chemical pressure between the PF₆ and TaF₆ salts is roughly estimated as 0.75 GPa. Due to the fact that the ground state change at a lower pressure in the TaF₆ salt has not yet been proven, the pressure range on the lower pressure side of Figure 1 differs from that of this T-P phase diagram.

The emergence of the SC phase in the narrow pressure region for the TaF₆ salt is similar to those observed in the PF₆ and AsF₆ salts; however, the SC phase of the SbF₆ salt is observed over a wide pressure range (see Figure 5b). The reason is probably attributed to the difference in structural compression sensitivity corresponding to the dimensionality by applied pressure and thermal expansion upon cooling. The structural investigation and the DFT calculations indicated that pressure (~2.7 GPa) and a lower temperature increase two-dimensionality in X = PF₆ and SbF₆ [36,37]. It was reported that, in the structure of (TMTTF)₂PF₆ under high pressure, the space group $P\overline{1}$ remains up to 8 GPa and a pressure-induced structural transition (triclinic → monoclinic phase transition) occurs above 8.5 GPa [38]. The lattice a is dramatically compressed to approximately 12.5% and then the total unit cell volume shrinks by about 27.5% by external pressure up to 8 GPa. At the SC-appearing pressure (~4.3 GPa), the compressed lattice and volume where the SC can be observed are a(PF₆) ~ 6.44 Å and V(PF₆) ~ 540 ų, which are approximately 90% and 80% of the values at ambient pressure, respectively (see Table 1). Considering a simple estimation, since the actual pressure of the TaF₆ salt shifts by 1 GPa to the negative pressure side of that of the PF₆ salt, the volume of TaF₆ would be compressed to approximately 22.5% by V(TaF₆) ~ 547 ų to appear in the SC phase. Unfortunately, the bulk modulus and thermal expansion of X = SbF₆ and TaF₆ under high pressure are unknown. High pressure structural investigations in X = SbF₆ and TaF₆ are necessary to understand not only the origin of the high resistivity of TaF₆ but also the narrower SC phase compared to that of the SbF₆ salt.

4. Conclusions

We measured resistivity for (TMTTF)₂TaF₆ under high pressure (up to 8 GPa) using a CAC pressure apparatus that can generate hydrostatic pressure. (TMTTF)₂TaF₆ has charge-ordering (T_CO = 175 K) and anti-ferromagnetic (T_AF = 9 K) states at ambient pressure. At 3 and 4 GPa, the growth of resistivity was observed at low temperatures due to spin-related transition; SDW (C-SDW and/or I-SDW) is predicted from our T-P phase diagram, as observed in (TMTTF)₂X (X = PF₆, AsF₆, and SbF₆). With increasing applied pressure, a superconducting (SC) state appears at 5 GPa. The T_C of (TMTTF)₂TaF₆ records the highest SC temperature of 2.8 K (at 5 GPa) in the (TMTTF)₂X series. However, the SC phase is observed in the short pressure region between 5 GPa and 6 GPa above ~2 K. From the results of high-pressure resistivity measurements with the CAC pressure generator for the Q1D organic conductor (TMTTF)₂X (X = PF₆, AsF₆, SbF_6, and TaF₆), the generalized TMTCF T-P diagram could be extended by confirming the SC phase in TaF₆ salt with a negative offset pressure of ΔP~0.75 GPa when the pressures at maximum SC temperature were compared between the PF₆ and the TaF₆ salts. High-pressure X-ray structural measurement is future work required to reveal the different appearances of SC phase shapes between TaF₆ and SbF₆ salts under high pressure.