Phase diagram and anomalous constant resistivity state of a magnetic organic superconducting alloy, λ-(BETS)₂Fe_xGa_1−xCl₄

Abstract

The combination of an organic superconductor, λ-(BETS)₂GaCl₄, and a field-induced organic superconductor, λ-(BETS)₂FeCl₄, provided unprecedented organic alloys, λ-(BETS)₂Fe_xGa_1−xCl₄, with the superconducting phase expanded by intruding into the adjacent antiferromagnetic insulating phase and an anomalous constant resistivity state located between the normal metallic and zero-resistivity states.

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In the last decade, magnetic organic metals and superconductors exhibiting distinct electromagnetic properties originating from the interactions between π conduction electrons of the organic donor molecules and localized 3d magnetic moments of the counter anions have been extensively investigated.^1,2 However, systems showing clear synergic actions of π and d electrons are still very rare. We have discovered unprecedented organic superconductors such as field-induced organic superconductors, antiferromagnetic organic superconductors and a system exhibiting a superconductor-to-insulator (SC–I) transition, which are composed of BETS (= bis(ethylenedithio)tetraselenafulvalene, C₁₀H₈S₄Se₄) molecules and MX₄⁻ (M = Fe, Ga; X = Cl, Br) anions.³ The crystal of λ-(BETS)₂FeCl₄ belongs to the triclinic system (Fig. 1).⁴ In contrast to the isostructural superconductor, λ-(BETS)₂GaCl₄ with non-magnetic GaCl₄⁻ anions, λ-(BETS)₂FeCl₄ has a π–d coupled antiferromagnetic insulating (AFI) ground state at ambient pressure³ and undergoes a field-induced insulator-to-metal transition at about 11 T, which can be regarded as a kind of colossal magnetoresistance (CMR) first discovered in organic systems.⁵ At about 17 T, λ-(BETS)₂FeCl₄ exhibits a field-induced superconducting (FISC) transition.^6,7

Fig. 1 (a) The crystal structure of λ-BETS₂FeCl₄ viewed along the c axis. The BETS molecules form the conduction layer parallel to the ac plane. (b) The anisotropic field (H) dependence of magnetization (M) of the oriented needle crystals of λ-BETS₂Fe_xGa_1−xCl₄ (x ≈ 0.47) at 2 K.¹²

Since the size of GaCl₄⁻ is approximately equal to that of FeCl₄⁻, the alloys λ-BETS₂Fe_xGa_1−xCl₄ can be prepared at arbitrary mixing ratios (x). As reported before, the crystal with x ≈ 0.4 exhibits successive superconducting (SC) and SC–I transitions with decreasing temperature.⁸ It is well known that in the phase diagrams of typical organic superconductors such as Bechgaard salts and κ-type BEDT-TTF (bis(ethylenedithio)tetrathiafulvalene) superconductors,^9,10 the SC phase tends to appear bordering on the antiferromagnetic insulating phase. But to the best of our knowledge, except for λ-(BETS)₂Fe_xGa_1−xCl₄, there is no conductor with the SC phase sandwiched by high-temperature metallic and low-temperature insulating phases.

About ten years ago, we reported the temperature–composition (T–x) phase diagram of λ-(BETS)₂Fe_xGa_1−xCl₄.¹¹ However, the number of data points used in the determination of the phase diagram was too small (only seven points apart from those of pure FeCl₄⁻ and GaCl₄⁻ salts). In this communication, we report the refined phase diagram and a newly discovered peculiar “constant resistivity state”.

The black needle crystals of λ-(BETS)₂Fe_xGa_1−xCl₄ were prepared electrochemically by using a mixed electrolyte of [(C₂H₅)₄N][FeCl₄] and [(C₂H₅)₄N][GaCl₄].⁴ The electrocrystallization was repeated with fine tuning of the mixing ratio of the electrolytes especially around x ≈ 0.4. The resistivity measurements were made by the four-probe method. Electrical contacts were achieved with gold wire (10 µm diameter) and gold paste. The following resistivity measurements were performed along the needle axes of the crystals (I//c): (1) resistivity measurements down to about 1.0 K at zero magnetic field (H = 0) to determine the superconducting, metal–insulator (MI) and SC–I transition temperatures (T_c, T_MI and T_SC-I), (2) resistivity measurements under a magnetic field of 15 T (or 10 T for x = 0.0) with rotating the crystal around the c axis at 1.4 K (H⊥c) to determine the directions parallel (//) and perpendicular (⊥) to the ac conduction plane, (3) resistivity measurements under magnetic fields (0 < H_//, H_⊥ < 15 T) at 1.0–8.0 K. The typical size of the crystal was about 0.22 × 0.05 × 0.02 mm³. The measurements (2) and (3) were made for the crystals with x < 0.7. The x value was determined by electron probe microanalysis (EPMA), which was made on the several points between the central two voltage terminals after all the four-probe resistivity measurements were finished. The error of the average value of x was about 2%. The x values of both ends of one needle crystal of about 5 mm length were found to be different by about 2%, which will be caused by the change of the electrolytic solution during the crystal growth (≈ 2 weeks).

Though the insulating ground state of λ-BETS₂Fe_xGa_1−xCl₄ had been considered to be an antiferromagnetic state,³ there has been no report showing the anisotropy of the magnetic properties of the crystals with x = 0.3–0.5, where the characteristic SC–I transition was observed.³ Therefore, the magnetization curve of λ-BETS₂Fe_xGa_1−xCl₄ (x ≈0.47) measured at 2 K is presented in Fig. 1b.¹² The observed anisotropy of the magnetization showed that similar to the case of λ-BETS₂FeCl₄, the insulating ground state of λ-BETS₂Fe_xGa_1−xCl₄ is an antiferromagnetic state.^3,13 The spin-flop behavior observed for the field parallel to the c axis suggested the direction of the easy axis is almost unchanged by alloying. The spin-flop field (≈ 6.5 kOe) was about 60% of that of λ-BETS₂FeCl₄.¹⁴

The temperature dependences of the resistivities of λ-BETS₂Fe_xGa_1−xCl₄ are shown in Fig. 2a–c. The room temperature resistivity of λ-BETS₂Fe_xGa_1−xCl₄ was 20–40 S cm⁻¹. The T–x phase diagram is presented in Fig. 2d. Since the MI and SC–I transitions showed hystereses, the resistivity data obtained in the cooling processes were adopted to determine T_MI and T_SC-I. In the paper reporting the discovery of a SC transition of λ-(BETS)₂GaCl₄,¹⁵ we published an erroneously high T_c, because of the accidentally observed high onset temperature of the resistivity drop, probably due to “negative effective pressure” produced by bonding an anomalously large amount of gold paint to a very long thin needle crystal at that time. In order to avoid ambiguity in the determination of T_c, the temperature where the resistivity became 10 times smaller than the resistivity at the onset temperature of the SC transition was adopted as T_c (according to this definition, T_c of λ-(BETS)₂GaCl₄ derived from the data presented in Fig. 3 of ref. 15 becomes approximately equal to the value recently reported by Pratt and Blundell (T_c = 5.5 K)¹⁶).

Fig. 2 (a) Temperature dependence of the resistivity of λ-BETS₂Fe_xGa_1−xCl₄ (cooling process): (a) x < 0.43, (b) 0.46 < x < 0.51, (c) 0.52 < x < 1.0. The resistivity (ordinate) is that of crystal with the smallest x value in every group (a–c). Those of other crystals are shifted in order to show the temperature dependences of the resistivities. (d) The T–x phase diagram: M = metal, AFI = antiferromagnetic insulator, SC = superconductor.

In the previous paper,¹¹ we determined the phase diagram under the assumption that T_c decreases smoothly with increasing x and the “T_cvs. x curve” is terminated at the point where it meet with the “T_MI (or T_SC-I) vs. x curve” (see the dotted lines in Fig. 2d). It was also presumed that the T_SC-Ivs. x curve (x < 0.5) is smoothly connected to the T_MIvs. x curve (x > 0.5). However, it is not so easy to imagine how the T_cvs. x curve approaches the T_MI (or T_SC-I) vs. x curve around x ≈ 0.5 because the SC transition is a second order transition and the AFI transition of this system is a first order transition.⁵ The terminal point of the T_cvs. x curve will be a singular point in the T–x phase diagram.

As shown in Fig. 2d, T_c of small-x crystals (x < 0.25) decreased slightly with increasing x and T_MI of Fe-rich systems (x > 0.55) decreased with increasing Ga content. These results are in agreement with the previous ones.¹¹ But unexpected results were obtained at 0.3 < x < 0.5, where successive SC and SC–I transitions were observed. Fig. 2a and b showed that the SC temperature range sandwiched by high-temperature metallic and low-temperature insulating states did not decrease monotonously with increasing x. For example, the SC temperature range of the crystal with x = 0.46 (a in Fig. 2b) was wider than that of the crystal with x = 0.43 (f in Fig. 2a). As shown in Fig. 2d, similar results were obtained also in other crystals. The expansion of the SC temperature range will indicate the stabilization of the SC phase around x ≈0.45. An unexpected feature was also obtained in the x-dependence of T_SC-I. As seen from Fig. 2d, the SC temperature range was expanded also by the sharp depression of T_SC-I around x ≈ 0.5. These results suggest that the SC phase of λ-BETS₂Fe_xGa_1−xCl₄ is stabilized around the x-region where the SC phase neighbors on the AFI phase. This phase diagram will give a hint to clarifying the SC mechanism of λ-BETS₂Fe_xGa_1−xCl₄.

In the course of the examination of the x-dependence of the resistivity behavior at low temperature, an anomalous constant resistivity state was discovered when the magnetic field was applied parallel to the ac plane. The electrical resistances were measured under magnetic fields parallel (H_//) and perpendicular (H_⊥) to the ac conduction plane. The remarkable resistance behaviors were observed mainly for H_//. Fig. 3 shows typical results (x = 0.0, 0.20, 0.37, 0.52, 0.66).

Fig. 3 The magnetic-field dependence of the resistance (ρ) at various temperatures and the T–H_// phase diagrams (insets of b, c, d and e), where H_// and H_⊥ represent the magnetic field parallel and perpendicular to the ac conduction plane, respectively. (a) x = 0, ρ vs. H_// and ρ vs. H_⊥. The inset is T_cvs.H. a = 1.0 K, b = 2.1, c = 3.1, d = 2.5, e = 4.4, f = 5,2, g = 6,0, a′ = 1.0 K, b′ = 2.0, e′ = 5.2. (b) x = 0.2; a = 1.0 K, b = 1.4, c = 2.2, d = 2.5, e = 2.8, f = 3.1, g = 3.4, h = 3.8, i = 4.1. ρ_m and ρ_c and are the resistances of the metallic state and the constant resistivity state, respectively. (c) x = 0.37; a = 1.0 K, b = 1.8, c = 2.0, d = 2.5, e = 2.8, f = 3.2, g = 3.7, h = 4.1, i = 4.5. (c′) x = 0.37: the magnetic field dependences of ρ at 1 K measured with rotating the direction of the magnetic field (H). θ (degree) is the angle between the ac plane and the direction of H. The inset is the rotation angle dependence of the resistance at 15 T and 1.4 K. The needle crystal was rotated around the c axis. (d) x = 0.52; a = 1.0 K, b = 2.2, c = 2.6, d = 2.8, e = 3.0, f = 3.3, g = 3.8. (e) x = 0.66. a = 1.1 K, b = 2.1, c = 3.1, d = 3.6, e = 4.9, f = 5.3, g = 7.7.

Fig. 3a shows the resistance of pure GaCl₄⁻ (x = 0.0). λ-BETS₂GaCl₄ retained the SC state up to about 12.5 T for H_// and 3 T for H_⊥, which agrees well with the previous report.¹⁷ With increasing temperature (a → g, a′ → e′ (Fig. 3a)), the SC transition was smoothly shifted to lower field.

On the other hand, the Fe-rich system, λ-BETS₂Fe_xGa_1−xCl₄ (x = 0.66) with an insulating ground state at H = 0.0 showed successive insulator-to-metal and metal-to-superconducting transitions with increasing H_// (Fig. 3e). The T–H_// phase diagram is given in the inset of Fig. 3e. The MI transition was suppressed around 8 T, which is about 30% smaller than the corresponding critical magnetic field at x = 1.0 (11 T). The FISC phase appeared above 8 T. Needless to say, there is no FISC region for H_⊥. Only the AFI region and the metallic region appear.

With decreasing x, the AFI phase tended to be suppressed and the normal SC state began to appear behind the AFI phase around x ≈ 0.5. The temperature dependence of the resistance and the T–H_// phase diagram of the crystal with x = 0.52 are shown in Fig. 3d. A small region of normal SC phase appeared at H < 3T and T > 3 K. The resistance minimum around 13 T indicates the existence of a FISC phase around this field, which is consistent with the internal magnetic field on the BETS conduction layer obtained from the analyses of the global T–H phase diagram of λ-BETS₂Fe_xGa_1−xCl₄ by Uji et al (H_int ≈ 15 T at x ≈ 0.5).¹⁸ The round resistance maximum around 5 T suggests the existence of the boundary between the low-field normal SC region and the high-field FISC region.

Unexpectedly, the crystal with x = 0.20 exhibited a peculiar resistance behavior where the resistance was approximately independent of T and H_// (Fig. 3b). The “constant resistivity (ρ_c) state” was observed above 2 K (c–i). But this non-zero resistivity state appears to be inconsistent with the results shown in Fig. 2 because the crystal with x ≈ 0.2 showed a SC transition at 4.4 K (Fig. 2a). This discrepancy will be related to the difference in the measurement cycles. In the resistance measurements to determine the transition temperatures of T_c, T_MI and T_SC-I (measurement (1)), fresh crystals were used. But the resistance measurements under H_// and H_⊥ (measurement (3)) were carried out after measurement (2). Therefore, it might be possible that trapped magnetic flux remains in the crystal even at H_// = 0 in measurement (3), which will cause the non-zero resistivity. It should be also noted that the resistance tended to be zero at lower temperature (a, b). This will indicate that the trapped magnetic flux is fixed at lower temperature. The resistance change from the ρ_c state to the normal metal state (ρ_m state) was very sluggish around 3.8 K (h), which will be due to the merging of normal and field-induced superconducting phases around 6 T. The normal SC phase tends to disappear and the FISC phase tends to develop with increasing H around 6 T. Similar constant resistivity behavior was also observed in other crystals with x = 0.25–0.32.

The most characteristic features were observed at x ≈ 0.4. The resistance behavior of λ-BETS₂Fe_xGa_1−xCl₄ (x ≈ 0.37) is shown in Fig. 3c. As seen from Fig. 2a, the crystal with x = 0.37 exhibited a SC transition at about 4.6 K and a SC–I transition at 2.2 K (cooling process). At 1.0 K (a), the crystal was of course in the insulating state at H_// ≈ 0.0. But with increasing H_//, the I–SC transition was observed around 2 T. Then the zero resistivity state (ρ_o state) was broken at 3.3 T where the resistance was increased very sharply. But the increase of the resistance was stopped at ρ = ρ_c and the constant resistivity state (ρ_c state) was continued up to 15 T. The transition between ρ_o and ρ_c states showed a hysteresis, indicating the ρ_o–ρ_c transition to be a first order transition. At 2.5 K (d), the crystal is in the SC state at H_// ≈ 0.0. But the ρ_o–ρ_c transition took place at 2 T and the ρ_c state was retained up to about15 T, where an indication of a very slight resistance increase from the ρ_c state was observed. At 2.8 K (e), similar behavior was observed but around 14 T a resistance increase began to appear. At 3.2 K (f), the resistance at H_// ≈ 0.0 took a non-zero value (ρ_o < ρ < ρ_c) and increased to ρ_c around 1 T. Then the ρ_c state was retained up to about 12 T. Similar to the case of the crystal with x = 0.20 (Fig. 3b), non-zero resistance at H = 0.0 (f–i) will be related to the magnetic flux trapped in the crystal. On the other hand, the existence of ρ_o state below 3 T (a–e) will indicate that at H_// = 0, the magnetic flux is expelled from the crystal in the insulating state (a–c) or fixed in the SC state at sufficiently low temperature (d, e). At 3.5–4.5 K (g–i), the crystal took the ρ_c state at H_// = 0.0. At 3.7 K (g), a very sluggish ρ_c–ρ_m transition was observed around 10 T. In contrast to the discontinuous ρ_o–ρ_c transition, the ρ_c–ρ_m transition showed no hysteresis. The ratio of ρ_c and ρ_m was about 6.0 (ρ_m/ρ_c ≈ 6.0). As shown in the inset of Fig. 3c, the T–H_// phase diagram shows the existence of a wide ρ_c region where the resistivity is independent of T and H_// (ρ = ρ_c). Fig. 3c′ showed the field-dependence of the resistance of the crystal with x = 0.37 at 1 K measured for various directions of the magnetic field in the a*b* plane. The ρ_c state was observable for θ < 15°, where θ is the angle between the ac plane and the direction of the magnetic field. That is, similar to the FISC state, the two-dimensionality of the system seems to be essential for the ρ_c state. But compared with FISC state observed only for θ < 0.3°,⁶ the limitation on θ is very loose for the ρ_c state. It should be also noted that in contrast to the smooth resistance increase in the ρ_c–ρ_m transition observed for H_//, a stepwise resistance increase was observed for H_⊥ (f, θ = 90°).

In order to confirm that the constant resistance behavior is not an accidental phenomenon, the resistance measurements were repeated on crystals with x = 0.37–0.41 exhibiting a SC–I transition at zero-magnetic field (measurement (1)). All the crystals (several crystals) whose resistance measurements were successfully made under H_// and H_⊥, exhibited similar resistance behavior though the ρ_c-values were fairly scattered (ρ_m/ρ_c = 6–12). Anyway, it can be said that the ρ_c state surely exists in λ-BETS₂Fe_xGa_1−xCl₄, though the reason for its appearance is not clear at present.

In summary, the precise examination of the T–x phase diagram of λ-BETS₂Fe_xGa_1−xCl₄ revealed that the system has the superconducting phase expanded by intruding into the adjacent antiferromagnetic insulating phase. Furthermore, an unprecedented constant resistivity state was discovered between the zero-resistivity state and the normal metallic state, where the resistance was independent of temperature and magnetic field. To clarify the origin of the “constant resistivity state”, further examination (for example, the examination of the current density dependence of ρ_c and role of Fe³⁺ concentration) will be needed, which remains for future studies.

We thank Drs A. Sato and K. Takahashi and Mr Y. Okano for their help in the preparation of figures. We are also very grateful to Prof. H. Fukuyama for his warm encouragement.

Notes and references

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