Pressure-induced antiferromagnetic transition and phase diagram in FeSe

We report measurements of resistance and ac magnetic susceptibility on FeSe single crystals under high pressure up to 27.2 kbar. The structural phase transition is quickly suppressed with pressure, and the associated anomaly is not seen above $\sim$18 kbar. The superconducting transition temperature evolves nonmonotonically with pressure, showing a minimum at $\sim12$ kbar. We find another anomaly at 21.2 K at 11.6 kbar. This anomaly most likely corresponds to the antiferromagnetic phase transition found in $\mu$SR measurements [M. Bendele \textit{et al.}, Phys. Rev. Lett. \textbf{104}, 087003 (2010)]. The antiferromagnetic and superconducting transition temperatures both increase with pressure up to $\sim25$ kbar and then level off. The width of the superconducting transition anomalously broadens in the pressure range where the antiferromagnetism coexists.


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The superconductivity in FeSe has attracted growing attention since its discovery. 1 FeSe is unique among iron-based superconductors. In contrast to the iron-pnictide parent compounds such as LaFeAsO (Ref. 2) and BaFe 2 As 2 , 3 FeSe undergoes a structural transition at T s ∼ 90 K but no magnetic transition at ambient pressure. It becomes superconducting below T c ∼ 8 K. 1 The transition temperature can be enhanced substantially by the application of pressure, 4 the superconducting onset temperature reaching ∼ 37 K at P ∼ 89 kbar. 5 Moreover, single-layer FeSe films may have still higher transition temperatures. 6 Recent breakthroughs in the crystal growth (Refs. 7 and 8) have led to a flurry of research activities, revealing more and more peculiarities of FeSe. [9][10][11][12][13][14][15][16][17] Quantum oscillation and angleresolved photoemission spectroscopy (ARPES) measurements have found an unexpectedly shrunk Fermi surface. 9,12 Some other ARPES measurements have found a splitting of the d xz and d yz bands below ∼ T s , 10,15 suggesting that the structural transition is an electronic nematic order driven by orbital degrees of freedom, which is in accord with a conclusion from thermodynamic and NMR measurements. 8,14,16 Thermal conductivity measurements have found a phase transition within the superconducting phase. 13 It has also been argued that because of small Fermi energies the superconductivity in FeSe may be close to a Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein-condensation (BEC) crossover. 13 The absence of the antiferromagnetic order at ambient pressure may be at the heart of the FeSe enigma. Recent theoretical studies have suggested that the absence is due to the competition between spin fluctuations with different wave vectors. 18,19 Experimentally, a pressure-induced antiferromagnetic order was already suggested by early NMR measurements (Ref. 20) and has been confirmed by recent µSR measurements. 21,22 However, there is so far hardly any evidence from macroscopic measurements such as resistivity or magnetization under high pressure 4,5,23-28 : for the pressure range of the present study, only Ref. 24 observed kinks in the temperature dependence of resistivity of polycrystalline samples at pressures above 28.5 kbar and speculated that they might be of a magnetic origin.
In addition, to our knowledge, no previous studies observed both of the structural and antiferromagnetic transitions in the same sample under high pressure.
In this paper, we report resistance and ac magnetic susceptibility measurements on FeSe under high pressure up to P = 27.2 kbar. Our resistance measurements clearly show anomalies that are most likely associated with the antiferromagnetic transition. This corroborates the appearance of a static long-range order under high pressure. We construct a phase dia-gram composed of the three phase transitions, i.e., the superconducting, antiferromagnetic, and structural ones, which displays an intriguing interplay between those orders.
We performed four-contact electrical resistance measurements on high-quality single crystals of FeSe prepared by a chemical vapor transport method (Ref. 8) down to helium temperatures at pressures up to 27.2 kbar. The electrical contacts were spot-welded. The low-frequency ac current (f = 13 Hz) was applied in the ab plane. The current density was roughly in a range 6 -8 A/cm 2 . Piston-cylinder type pressure cells made of NiCrAl alloy (C&T Factory, Tokyo) were used. 29 The pressure transmitting medium was Daphne 7474 (Idemitsu Kosan, Tokyo), which remains liquid up to 37 kbar at room temperature and assures highly hydrostatic pressure generation in the investigated pressure range. 30 The pressure was determined from the resistance variation of calibrated manganin wires. We also performed ac magnetic susceptibility measurements under high pressure, where the ac excitation field (B ac ∼ 2 × 10 −5 T, f = 67 Hz) was applied approximately parallel to the ab plane. though the onset temperature still shows an increase. Resistance measurements performed on two more samples gave similar observations.  Fig. 2), which might serve as a better index of the bulk transition temperature. We note that the size of the diamagnetic signal remains nearly the same as pressure is applied, indicating bulk superconductivity up to the highest pressure of 25.0 kbar. We did not detect anomalies corresponding to T s or T u , most 6 likely because of the low sensitivity of the present setup. Figure 3 shows the high-pressure phase diagram of FeSe determined from the present measurements. The superconducting transition temperature initially increases, but decreases above ∼8 kbar and then increases again, resulting in a local minimum at ∼12 kbar. This is fully consistent with previous reports. 21,22,28 Furthermore, the observation that the superconducting volume fraction hardly changes in the investigated pressure range is also consistent with those reports. The structural transition temperature T s is quickly suppressed by the application of pressure. This is consistent with a previous report, 28 though the suppression rate observed in the present study is faster. The fate of the structural transition above P = 17.8 kbar is not clear and will be discussed later.
The resistance anomaly at T u probably corresponds to the antiferromagnetic order observed in the high-pressure µSR study. 21,22 According to Bendele et al., 21,22 a finite magnetic volume fraction appears at P = 8 kbar with T N = 17 K, but it does not reach 100% as T → 0 at this pressure. As pressure is increased above 8 kbar, the magnetic volume fraction and T N increase while T c decreases. At 12 kbar, the volume fraction reaches 100% (as T → 0) and scenarios, which assume that the superconducting dome is centered at the QCP, i.e., T c is 7 maximum at the QCP. It would be helpful to extend the pressure range to see how T c and T u evolve above 27 kbar. It would also be interesting to see how theories claiming competition between different spin fluctuations in FeSe could explain our observation. 18,19 The width of the superconducting transition considerably broadens as T Finally, we ask what is the fate of the structural transition T s above P = 17.8 kbar. Highpressure structural studies suggest that the low temperature structure remains orthorhombic up to ∼75 kbar. 25,34,35 One scenario compatible with this is as follows: The T s (P ) transition line merges with the T u (P ) line at some pressure, above which a stripe-type antiferromagnetic order and orthorhombic distortion occur simultaneously at T u , as is the case with BaFe 2 As 2 , for example. On the other hand, those structural data were obtained for mixed-phase samples and might not reflect the intrinsic phase diagram. 25,34,35 Thus the following scenario, among others, is also worthy of consideration: The structural transition temperature T s is suppressed down to zero (continuously or in a first-order fashion) at some pressure, above which the structure remains tetragonal as T → 0. We note that the T u (P ) line shows no clear kink marking the point where the T s and T u transition lines meet. This might suggest that the two orders are rather decoupled, as has been suggested by ambient-pressure studies, 8,14,16 and hence might support this scenario. In this case, the antiferromagnetic order would not be a stripe-type one but would have to be compatible with the tetragonal structure as has been suggested in Ref. 16