Introduction

In most iron-based superconductors, superconductivity emerges on the verge of a long-range antiferromagnetically ordered state1, which is a common feature to many unconventional superconductors2,3 including the cuprates and heavy-fermion materials. It has been shown that the antiferromagnetic order in the iron-pnictide materials accompanies or follows the tetragonal-to-orthorhombic structural transition at Ts. In striking contrast, the structurally simplest FeSe exhibits a high Ts≈90 K but no magnetic order appears at lower temperatures4,5,6,7, and still its ground state is an unconventional superconducting state with Tc≈9 K (refs 8, 9, 10). This material is also intriguing in that in the form of one-unit-cell-thick films a very high Tc (up to 109 K) has been reported recently11,12,13, which is likely associated with a carrier-doping effect14,15 from the substrate. In bulk FeSe, a significant electronic anisotropy is found below Ts in the nonmagnetic orthorhombic phase, which is often called a nematic state9,10,16,17. In the nematic phase, very small Fermi surfaces with strong deviations from the first-principles calculations have been observed10,18,19, and the occurrence of superconductivity with such small Fermi energies is quite unusual, implying that the system is deep in the crossover regime between the weak-coupling Bardeen–Cooper–Schrieffer and strong-coupling Bose–Einstein–condensate limits10.

In addition to these distinct electronic characteristics of FeSe, remarkable properties have been reported under high pressure20,21,22,23,24,25,26,27. First of all, the initial study on powder samples has shown that the relatively low Tc≈9 K at ambient pressure can be enhanced by more than fourfold to ∼37 K under ∼8 GPa, pushing it into the class of high-Tc superconductors21. More recent studies under better hydrostatic pressure conditions revealed a complex temperature–pressure (T–P) phase diagram featured by a suppression of Ts around 2 GPa, a sudden development of static magnetic order above ∼1 GPa (ref. 23), and an enhancement of Tc in a three-plateau process24, that is, Tc∼10(2) K for 0–2 GPa, Tc∼20(5) K for 3–5 GPa, and Tc∼35(5) K for 6–8 GPa. The first jump of Tc from ∼10 to ∼20 K seems to coincide with the suppression of the nonmagnetic nematic state and the development of the long-range magnetic order at Tm evidenced by μSR measurements22. The observation that both Tc and Tm increase with pressure in the pressure range 1–2.5 GPa has been taken as evidence for the cooperative promotion of superconductivity by the static magnetic order22. Such a scenario, however, does not fit into the general scope of iron-based superconductors, in which the optimal superconductivity is realized when the long-range magnetic order is close to collapse1,28. This issue remains unclear unless the fate of magnetic order at Tm under higher pressures is sorted out. Due to the technical limitations of probing small-moment magnetic order above 3 GPa, this task only becomes possible very recently when a clear signature at Tm is visible in the resistivity23,25,26 of high-quality FeSe single crystals29. We also note that more recently the pressure-induced magnetic order in these single crystals has been confirmed below Tm by Mössbauer30 and nuclear magnetic resonance (NMR) measurements31.

Here by performing the high-pressure resistivity ρ(T) measurements up to ∼15 GPa on high-quality single crystals, we construct for bulk FeSe the most comprehensive T–P phase diagram mapping out the explicit evolutions with pressure of Ts, Tc and Tm. We uncover a previously unknown dome-shaped Tm(P), having two end points situated on the boundaries separating the three plateaus of Tc(P). Our results thus provide compelling evidence linking intimately the sudden enhancement of Tc to 38 K to the suppression of long-rang magnetic order. This highlights a competing nature between magnetic order and high-Tc superconductivity in the phase diagram of FeSe, which is a key material among the iron-based superconductors.

Results

Low-pressure region

The tetragonal-orthorhombic structure transition at Ts≈90 K for bulk FeSe (blue square in Fig. 1) is manifested as a slight upturn in resistivity, which can be taken as a signature to track down the evolution of Ts with pressure. Our resistivity ρ(T) data measured with a self-clamped piston–cylinder cell (PCC) up to ∼1.9 GPa are shown in Fig. 2a. As can be seen, Ts is suppressed progressively to below 50 K at ∼1.5 GPa, above which the anomaly at Ts becomes poorly defined. Meanwhile, a second anomaly manifested as a more profound upturn in ρ(T) emerges at Tm∼20 K and moves up steadily with pressure. In light of the recent high-pressure μSR, Mössbauer, and NMR studies22,30,31, this anomaly at Tm corresponds to the development of long-range magnetic order. We also note that in this magetically ordered state below Tm, the orthorhombic structure similar to the one (space group Cmma) in the nematic phase has been reported recently30,31. Ts and Tm seem to cross around ∼2 GPa. In this pressure range, the superconducting transition temperature Tc (defined as the zero-resistivity temperature) first increases and then decreases slightly before rising again. This features a small dome-shaped Tc(P) peaked at ∼1.2 GPa (Fig. 1), which roughly coincides with the pressure where the long-range magnetic order at Tm starts to emerge. These results in this relatively low-pressure range are in general consistent with those reported previously23,25,26.

Figure 1: Temperature–pressure phase diagram of bulk FeSe.
figure 1

The structural (Ts, blue), magnetic (Tm, green), and superconducting transition temperatures (Tc, red and black) as a function of hydrostatic pressure in high-quality single crystals determined by anomalies in resistivity ρ(T) measured in the PCC (open circles), clamp-type CAC (closed circles), and constant-loading type CAC (closed squares). Tc values determined from the ac magnetic susceptibility (χ(T)) measurements in the clamp-type CAC are also shown (solid triangles). The magnetic phase is most likely a spin density wave (SDW) phase. Colour shades for the nematic, SDW, and superconducting (SC) states are guides to the eyes.

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Figure 2: Temperature dependence of resistivity in FeSe single crystals under high pressure.
figure 2

(a) ρ(T) curves below 100 K at different pressures up to ∼1.9 GPa measured in the self-clamped PCC. (b) Data up to ∼8.8 GPa measured in the self-clamped CAC. (c) Data up to ∼15 GPa measured in the smaller self-clamped CAC. (d) ρ(T) curves below 200 K up to 8 GPa measured in the constant-loading CAC. Except for (c) the data are vertically shifted for clarity. The resistive anomalies at transition temperatures Ts, Tm, and Tc are indicated by the arrows.

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High-pressure region

To further track down the evolution of Tm, we turn to ρ(T) measurements in cubic anvil cells (CACs) that can maintain a quite good hydrostaticity up to ∼15 GPa (refs 32, 33, 34). Figure 2b–d displays the ρ(T) data measured in two self-clamped CACs and one constant-loading CAC (see Methods for experimental details). In line with the results of PCC in Fig. 2a, the sudden upturn is clearly visible at Tm in both measurements in the pressure range up to ∼2.5 GPa (Figs 2b,d and 3a,b), above which the upturn anomaly disappears and instead a kink appears in ρ(T) followed by a gradual drop before reaching the superconducting transition (Figs 2b,d and 3c,d). Our self-clamped CAC enables us to measure ρ(T) under different magnetic fields32,33, which clearly resolves that this anomaly is of the same origin as the magnetic order at lower pressures. As seen in Fig. 4b, on the application of magnetic fields the resistivity kink at 2.8 GPa restores to the upturn anomaly and this anomaly shows little field dependence as that observed at 1.8 GPa (Fig. 4a). On further increasing pressures, Tm moves up gradually and reaches about 45 K at 4.8 GPa, where the resistivity kink becomes sharper (Fig. 2b). In striking contrast with the progressive enhancement of Tm in this pressure range of 2–5 GPa, Tc remains nearly unchanged at the second plateau of ∼20 K.

Figure 3: Determination of magnetic and superconducting transition temperatures from the resistivity curves under high pressure.
figure 3

(a–f) Temperature dependence of resistivity ρ(T) (left axis) and temperature derivative of resistivity dρ/dT(T) (right axis) at low temperatures. The temperature at the maximum slope of superconducting transition is defined as and the zero resistivity temperature as Tc. The magnetic transition temperature Tm is determined by the dip or peak in dρ/dT(T). At 6.3 GPa, the data at 9 T is also shown where Tm anomaly appears when the superconducting transition is suppressed to a lower temperature (e). At 8.8 GPa, the normal-state resistivity can be fitted to a T-linear dependence (dashed line in (f)).

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Figure 4: Effects of magnetic fields on the magnetic and superconducting transitions under high pressure.
figure 4

(a–d, i–l) ρ(T) curves at different magnetic fields applied parallel to the c axis. The magnetic transition temperature Tm is field independent and marked by the green arrow (a–d). At 6.3 GPa, the Tm anomaly is only visible at high fields (i). (e–h, m–p) H-T phase diagrams. The zero resistivity is attained below Tc and the line (determined by the peak in dρ/dT(T)) is a lower bound of upper critical field Hc2. The sharp superconducting transitions under magnetic fields for P>6.3 GPa indicate narrowed regimes of the vortex liquid state.

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The situation changes markedly when further increasing pressure above ∼5 GPa. As shown in Figs 2b and 3d, ρ(T) at 5.8 GPa exhibits an abrupt drop at 38.5 K before reaching zero resistivity at Tc=27.5 K, and then at 6.3 GPa the abrupt drop develops into a very sharp superconducting transition at Tc=38.3 K with a transition width of only 0.4 K (Figs 2b and 3e). Thus, Tc is nearly doubled from ∼20 K at 4.8 GPa to 38.3 K at 6.3 GPa, and the abrupt drop at 38.5 K under 5.8 GPa corresponds to the onset of superconductivity rather than the magnetic order, which is supported by the large change under magnetic fields (Fig. 4d). Then, what is the fate of Tm? A closer inspection of the ρ(T) data at 5.8 GPa reveals an inflection point at the temperature slightly above the abrupt drop. This feature can be well resolved from the temperature derivative of resistivity dρ/dT in Fig. 3d. Here the small peak centred at 41 K corresponds to Tm, which is confirmed by the field independence (Fig. 4d). At 6.3 GPa, such a magnetic anomaly is absent in the dρ/dT(T) curve at zero field, but becomes visible under 9-T field when Tc is suppressed to lower temperatures, as shown in Figs 3e and 4i. On further increasing pressure, the superconducting transition remains very sharp and Tc moves down slowly to 33.2 K at 8.8 GPa. Due to the large upper critical field, Tm cannot be defined at P>6.3 GPa (Fig. 4j–l). These above findings are further confirmed by separate high-pressure resistivity measurements with a constant-loading CAC, as shown in Fig. 2d.

At higher pressures, the resistivity curves measured by using a small CAC (Fig. 2c) show a sudden change from metallic and superconducting behaviour to semiconducting and non-superconducting one at around 12 GPa. Indeed, the crystal structure studies of FeSe polycrystals at high pressures35,36 have shown that high pressures above ∼10 GPa will stabilize the collapsed three-dimensional orthorhombic Pbnm structure, which is non-superconducting. Therefore, we will focus our attention to the phase diagram at P<12 GPa, where the crystal structure symmetries should be the same as the ones in the ambient pressure.

The superconductivity is also checked by the ac susceptibility measurements under pressure using the self-clamped CAC (Fig. 5). The onset temperature of the diamagnetic signal is quantitatively consistent with the zero-resistivity Tc at each pressure (Fig. 1). Moreover, the magnitude of the diamagnetic signals at lowest temperatures does not show significant pressure dependence, suggesting the bulk superconducting nature in a wide pressure range covering the nematic, magnetic and nonmagnetic phases.

Figure 5: Temperature dependence of ac susceptibility χ under high pressure.
figure 5

The data are taken by using the clamp-type CAC. The onset temperatures of diamagnetic signals are marked by arrows.

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Discussion

When the obtained Tm(P) and Tc(P) data are plotted in Fig. 1, we uncover a previously unknown dome-shaped magnetic order with two ends situated near the boundaries separating the three-plateau Tc(P). This observation suggests that the superconductivity in FeSe is intimately correlated with the magnetism. Despite the absence of static magnetic order within the nematic phase at ambient pressure5,6,7, strong spin fluctuations with an in-plane wave vector q=(π, 0) have been identified recently37. Recent theoretical studies38 have attributed the absence of static magnetic order to unusual magnetic frustration among multiple competing magnetic orders with q=(π, ξ) with 0≤ξ≤π/2. According to the calculations, this magnetic frustration can be removed under pressure, and gives way to a long-range magnetic order with q=(π, 0). Indeed, the stabilization of static magnetic order at Tm is concomitant with the destruction of nematic order as seen in Fig. 1, thus highlighting the competing nature between nematic and magnetic order. The q≠0 nature of the pressure-induced magnetic phase is supported by the Fermi surface reconstruction recently reported from quantum oscillations25, and also consistent with the field independence of Tm found in the present study (Fig. 4a–d). Thus the pressure-induced order that supersedes the nematic order above ∼2 GPa is most likely a spin density wave (SDW), although the previous neutron scattering experiment was unsuccessful due to the small magnetic moment22. The most recent NMR study as well as the orthorhombicity found below Tm also support the stripe-type SDW order with q=(π, 0)30,31. Most importantly, our results reveal unambiguously that the sudden jump of Tc around 6 GPa comes concomitantly with the suppression of magnetic order, demonstrating another competition between the SDW order and high-Tc superconductivity at high pressures. The peak temperature (≈45 K) of the Tm(P) dome is quite close to the maximum Tc(=38.3 K), indicating that these competing orders have very similar energy scales. This is different from other iron-based superconductors where the antiferromagnetic transition temperatures in the mother materials are significantly higher than the maximum Tc values of the derived superconducting phases1,28. We note that the non-monotonic dependence of Tc(P) is somewhat akin to the two-dome shape of Tc(x) recently found in LaFeAsO1−xHx (refs 1, 39). However, the complete dome shape of Tm(P) with two ends in a single-phase diagram of FeSe without changing of carrier balance is distinctly different from the case of LaFeAsO1−xHx, in which two different antiferromagnetic orders exist near the opposite doping ends of the superconducting phase. Altogether with the presence of competing nematic order at low pressures, this phase diagram of FeSe thus exhibits unique features among iron-based superconductors. It should be noted that a phase diagram bearing some resemblance has been recently found in hole-doped cuprate superconductors, where the high-Tc superconducting dome is partially suppressed by the presence of dome-shaped charge density wave (CDW) order3.

It is also intriguing to point out that above the SDW dome, the resistivity curves in the pressure range of ∼3–6 GPa show anomalous sub-linear (convex) temperature dependence (Fig. 2b,d), which mimics the suppression of the quasiparticle scattering by the pseudogap formation above the CDW phase of underdoped cuprates. At higher pressures, this convex anomaly in the temperature dependence of resistivity becomes less pronounced. At 8.8 GPa, ρ(T) displays a perfect linear-in-T dependence in a wide temperature range of the normal state (Figs 2b and 3f), which is a hallmark of non-Fermi-liquid behaviour. The observation of the non-Fermi-liquid behaviour at high pressures where the magnetic order is vanishing is an indication of the presence of strong critical fluctuations. Similar T-linear ρ(T) above Tc has been observed near a quantum critical point (QCP) at x≈0.3 in the BaFe2(As1−xPx)2 system28. In that system, the critical fields near the QCP show anomalous features pointing to an enhancement of the energy of superconducting vortices possibly due to a microscopic mixing of antiferromagnetism and superconductivity40. The analysis of the upper critical field Hc2, which is related to the effective mass m* in a simple picture by (ref. 41), has been shown to be much less sensitive to the mass enhancement observed in other techniques near the QCP. In our similar analysis (Fig. 6) we also find a rather flat behaviour at high pressure. This suggests that the vortex state of FeSe at high pressures is also nontrivial.

Figure 6: Mass analysis from H–T curves under high pressure.
figure 6

The pressure dependence of the square root of the initial slope of the line divided by , which corresponds to the effective mass in a simple picture. For comparison, the low-pressure data from ref. 26 are also indicated (blue squares).

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We also note that the unusually strong vortex pinning has been found in clean films of BaFe2(As1−xPx)2 near the QCP42. Our H-T phase diagrams at different pressures indicate that the vortex-liquid region between the width of transition (Tc and ) shows a dramatic narrowing when the SDW is suppressed below the superconducting transition (Fig. 4e–h, m–n), which can also be accounted for by the enhanced pinning near the QCP. However, a peculiar feature here is that the optimal Tc takes place at the point where Tm just crosses Tc, rather than the possible QCP at > ~ 8 GPa where Tm completely vanishes. This is again rather similar to the case of hole-doped cuprate superconductors in a sense that a putative QCP is located at the slightly overdoped side3.

To summarize, by using high pressure as a clean tuning knob, we have clarified in bulk FeSe the interplay of three competing orders, that is, nematic, magnetic and superconductivity, and elucidated how the high-Tc superconducting phase is achieved. The relatively low Tc at ambient pressure should be attributed to the presence of competing nematic order; the application of high pressure initially suppresses gradually the nematic order so as to enhance superconductivity. At the same time, the suppression of nematic order also relieves the magnetic frustration so as to stabilize the magnetic order, which then competes again with superconductivity, leading to a local maximum of Tc(P) around 1 GPa. Then, a complete elimination of nematic order around 2 GPa gives rise to a more profound enhancement of Tc to the second plateau of ∼20 K; the opposite effects on Tc imposed by the strong fluctuations of nematic order and the long-range SDW order produce the local minimum of Tc(P) around 1.5 GPa. Above ∼2 GPa, only the static SDW order is present and competes with superconductivity so that Tc keeps nearly unchanged while Tm rises until ∼5 GPa, where the magnetic order at Tm eventually becomes destabilized by pressure. Then, the suppression of magnetic order leads to a great enhancement of Tc to 38 K. In such a way, FeSe exhibits a unique phase diagram with three competing orders, nematic, SDW and high-Tc superconductivity; the latter two of which have very close energy scales. This newly constructed diagram, which shares some similarities to that of cuprates, may offer important clues for discussing the unconventional origins of the high-Tc superconductivity in this class of materials.

Methods

Sample preparation and characterization

High-quality FeSe single crystals used in the present study have been grown by two different methods: the chemical vapour transport technique29 (Kyoto University) and the flux method43 (Oak Ridge National Laboratory). These two methods yield FeSe single crystals with similar quality in terms of the phase transition temperatures (Ts=87–90 K and Tc=8.5–9 K) and the residual resistivity ratio RRR ∼40. However, the flux method produces much larger (up to ∼10 mm) and thicker (∼1 mm) crystals and thus we cleaved and cut these samples to fit in the pressure cells. The crystals are well characterized by means of X-ray diffraction, energy dispersive spectroscopy, magnetic and transport properties under ambient pressure.

High-pressure measurements

High-pressure resistivity ρ(T, P) measurements have been performed under hydrostatic pressures up to ∼2 GPa with a PCC and up to ∼15 GPa with CACs, respectively. For the crystals grown with the flux method, ρ(T, P, H) data under high pressures and magnetic fields were measured in the Institute of Physics, Chinese Academy of Sciences, by using the self-clamped type CACs and PCC. The data up to 9 GPa have been taken by a 4-mm CAC, in which we also measured ac susceptibility by a conventional mutual inductance technique. Higher-pressure data up to 15 GPa were taken by a 2.5-mm CAC. The high-pressure resistivity of crystals grown with the chemical vapour transfer method was measured in the Institute for Solid State Physics, University of Tokyo with a constant-loading type CAC, which can maintain a nearly constant pressure over the whole temperature range from 300 to 2 K. The pressure value inside the PCC was determined by monitoring the shift of superconducting transition of lead (Pb), while those of CACs were calibrated at room temperature by observing the characteristic transitions of bismuth (Bi). (It should be noted that for the self-clamped pressure cells, both PCC and CAC, the pressure value at room temperature is slightly different from that at low temperature due to the solidification of liquid pressure transmitting medium and the different thermal contraction of cell components. Therefore, some corrections have been made in comparison with the data obtained from the constant-loading CAC). For all these high-pressure resistivity measurements, we employed glycerol as the pressure transmitting medium. All resistivity measurements were performed with the conventional four-terminal method with current applied within the ab plane and magnetic field perpendicular to the ab plane.

Data availability

The data that support the findings of this study are available on request from the corresponding authors (J.-Q.Y., J.-G.C., or T.S.).

Additional information

How to cite this article: Sun, J. P. et al. Dome-shaped magnetic order competing with high-temperature superconductivity at high pressures in FeSe. Nat. Commun. 7:12146 doi: 10.1038/ncomms12146 (2016).