Introduction

The recent discovery of superconductivity in iron pnictide compounds1 has drawn significant attention in studying the unconventional superconductivity containing magnetic elements. Following the first report on the superconductivity in “1111” RFeAsO system, a number of pnictide families have been reported including “122” AeFe2As2 (Ae = Ca, Sr, Ba), “111” AFePn (A: Li, Na, Pn: As, P) and “11” FeSe types2,3,4. The parent compounds of the iron pnictide superconductors contain FeAs tetrahedral layers and exhibit a tetragonal to orthorhombic structural transition as well as a paramagnetic (PM) to antiferromagnetic (AFM) transition5,6. The AFM orthorhombic phase has been shown to be the parent phase of the pnictide superconductor forming the spin density wave (SDW) state in which superconductivity can be induced by suppressing the SDW state via chemical doping or applied pressure7,8. The structural and magnetic phase transitions of the pnictide parent compounds have been shown to play an important role in inducing superconductivity9. For example, previous studies have indicated that “122” SrFe2As2 compound undergoes the structural and magnetic transitions simultaneously at TS = 205 K at ambient pressure10,11, while its superconductivity (SC) occurs once the SDW state is suppressed at high pressures12. On the other hand, chemical substitutions with electron or hole doping have been shown to suppress the AFM state of SrFe2As2, resulting in the occurrence of superconductivity even at ambient pressure13,14. The correlation between the suppression of the long-range magnetic ordering and the simultaneous formation of the SC state indicates that the spin fluctuation of the Fe moments plays a key role in establishing the superconductive state. Compared to chemical doping where disorders can be inevitably introduced15,16, applied pressure introduces less lattice disorders than chemical doping and has been shown to be an effective tool in deciphering the intrinsic superconducting behaviors in Fe-based superconductors17,18. Indeed, applied pressure not only increases the TC in the LaFeAs(O1−xFx), FeSe, AFePn (A: Li, Na, Pn: As, P) system19,20,21,22,23, but it also induces superconductivity in the parent “122” compounds24,25,26,27. Superconductivity with high TC up to 12 K appears at pressures between 0.23 and 0.86 GPa in CaFe2As227. Similarly, pressure-induced superconductivity has been reported for BaFe2As2 and SrFe2As2 at approximately 3.0 GPa and 3.6 GPa, respectively24,28. Since the magnetic transition is strongly coupled with the structural distortion in the SrFe2As2 system at ambient pressure, studying its magnetic ordering, structural distortions and superconductivity at high pressures and low temperatures under controlled hydrostatic conditions can provide valuable insight into intrinsic underlying mechanism for the origin of superconductivity in the system. Here we have investigated the magnetic and structural transitions of SrFe2As2 using synchrotron Mössbauer spectoscopy (SMS) and x-ray diffraction (XRD) in a cryogenically-cooled high-pressure diamond anvil cell (DAC) having a relatively hydrostatic Ne pressure medium. Our results show that the magnetic and structural transitions of SrFe2As2 remain strongly coupled at extreme pressure-temperature environments. This sheds new light on the interplay of the lattice distortions and magnetism in the origin of superconductivity in the iron-based superconductors at high pressures and low temperatures.

Results

SMS spectra were collected up to 5.4 GPa and temperatures as low as 15 K, while XRD patterns were measured up to 8.2 GPa and 13 K (Figs. 1, 2). Fig. 1(a) shows representative pressure-dependent 57Fe SMS spectra of SrFe2As2 at 15 K. At 1.4 GPa and 15 K, the drastic appearance of quantum beats manifests the splitting of 57Fe nuclear level through hyperfine interaction, showing the AFM state. As pressure was increased to 4.3 GPa, the SMS spectrum changed significantly with the disappearance of the quantum beats, indicating that the magnetic phase had been suppressed via applied pressure at 15 K while the PM state started to appear. Since the spectrum could not be reasonably fitted using only paramagnetic or magnetic phases, both paramagnetic and magnetic phases were used to model the SMS spectrum at 4.3 GPa. Analyses of the modeled results showed that the magnetic phase accounts for approximately 42 vol.% of the two phases. At a higher pressure of approximately 5.4 GPa, the 57Fe nuclear level is characterized by flat spectral features without any splitting quantum beats, indicating the sole existence of the PM state with the completely suppressed magnetism by pressure. The derived hyperfine parameters show an abrupt increase in the strength of the magnetic fields as a function of temperature at a given pressure (Fig. 1(b)). For example, at 2.5 GPa the hyperfine magnetic field jumped to 6.7 T from zero as temperature was decreased to 160 K and then remains almost constant, indicating a PM to AFM transition. As pressure increases (Fig. 1(b)), the hyperfine magnetic field decreases and the magnetic transition region slightly broadens, implying suppressed magnetism by applied pressure; magnetism was totally suppressed at 5.1 GPa at each given low temperature as shown in Fig. 1(c).

Figure 1
figure 1

(a) Representative pressure dependent SMS spectra of SrFe2As2 at 15 K in Ne medium. Open circles: experimental data; red solid lines: modeled spectra using CONUSS program. Quantum beats in the spectra represent the occurrence of the magnetic field and hence the AFM state, whereas the absence of the beats (flat spectral feature) is indicative of the PM state. (b) Derived hyperfine magnetic fields of the AFM SrFe2As2 as a function of temperature at representative high pressures. Appearance and disappearance of the magnetic fields are used to construct the magnetic PM-AFM transition as a function of P-T. Filled symbol: AFM state; open symbol: PM state. (c) Derived hyperfine magnetic fields of SrFe2As2 as a function pressure at 15 K.

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Figure 2
figure 2

(a) Representative synchrotron angle-dispersive x-ray diffraction of SrFe2As2 as a function of pressure at 13 K. Splitting of the 220 reflection to 400/040 is indicative of the tetragonal to orthorhombic transition at high pressures. Ort: orthorhombic phase; Tet: tetragonal phase. At 4.7 GPa, the orthorhombic and tetragonal phases coexist at 13 K. (b) Variation of lattice parameters with pressure at 13 K. (c) Volume fraction of the orthorhombic phase as a function of pressure at 13 K.

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In order to clarify the relationship between the structural and magnetic transitions, we have also performed XRD experiments under high pressures and low temperatures (Figs. 2). Analyses of the high-pressure XRD spectra showed that the (220) reflection of the tetragonal phase splits to (400) and (040) reflections that are characteristic of the tetragonal to orthorhombic structural transition in SrFe2As2 with decreasing temperature at a given pressure11. Similar to the magnetic transition, this structural transition is strongly suppressed by pressure (Fig. 2(a)). At a constant temperature of 13 K, derived lattices parameters in Fig. 2(b) show the existence of the orthorhombic phase (space group: Fmmm) below 4 GPa and the tetragonal phase (space group: I4/mmm) above 6 GPa, respectively, whereas there is a P-T region between 4 GPa and 6 GPa, in which the tetragonal and orthorhombic phases coexist. With increasing pressure, the orthorhombic phase observed in the region is suppressed while the abundance of the tetragonal phase is enhanced (Fig. 2(c)).

Combining our synchrotron SMS and XRD results (Figs. 1–2) with literature high Tc studies, we have constructed the structural, magnetic and superconducting phase diagram of SrFe2As2 under high pressures and low temperatures (Fig. 3). The magnetic transition temperature (TN) was defined as the mid-point between the first appearance of the hyperfine magnetic field and the last appearance of the paramagnetic phase, while the structural transition temperature (TS) was defined as the mid-point from the pure tetragonal to the pure orthorhombic structural phase transition; for the co-existence of the tetragonal and orthorhombic phases at 13 K, the TS is defined as the point of disappearance for the orthorhombic phase. At ambient pressure, previous studies showed that the structural transition concurs with the magnetic transition10,11. Our results here further show that, within experimental uncertainties, these two transitions are strongly coupled at high pressures and low temperatures (Fig. 3), except the P-T region overlap starting with the Tc dome where an extended P-T region of the two-phase coexistence was observed (see further details in Discussions). These transition temperatures decrease with increasing pressures up to approximately 4.6 GPa, but are drastically suppressed to zero at a quantum critical pressure (PC) of 4.8 GPa.

Figure 3
figure 3

Magnetic and structural transition diagram of SrFe2As2 at high pressures and low temperatures. XRD data: blue diamond symbols (λ = 0.4047 Å) and blue square symbols (λ = 0.3737 Å); SMS data: red circle symbols. TS (blue dash line) and TN (red dash line) are extracted from analyses of the data in order to define the structural and magnetic transition conditions. The superconducting transition temperature TC with grey solid line for filamentary SC, as well as TS with darker grey solid line for the structural transition is taken from Ref. 25 using single crystals in a cubic anvil having glycerin pressure medium, that were similar to our experimental conditions. A quantum critical phase transition at a Pc of 4.8 GPa is suggested. Tet: tetragonal structure; Ort: orthorhombic structure; AFM: antiferromagnetic; PM: paramagnetic. The half-filled red circles represent for the coexistence of PM and AFM phases, while the half-filled blue squares represent for the coexistence of Ort and Tet phases. The filled purple region represents for the coexistence of filamentary superconductivity, AFM Ort and PM Tet phases. Pressure uncertainties are smaller to the symbols, whereas temperature uncertainties are less than 5 K.

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Discussions

As discussed in the previous studies of the “122” system, differential stress can strongly affect the critical pressure in the BaFe2As2 and SrFe2As2 compounds29,30,31. In order to draw a more direct, meaningful comparison with literature results, our structural and magnetic results are plotted on top of the superconducting transition from Ref. 25, which reported electrical resistivity and ac magnetic susceptibility measurements using a relatively hydrostatic glycerin medium that is similar in hydrostaticity to Ne medium used in our experiments. Comparisons of these results show that filamentary superconductivity with zero resistivity emerges with the occurrence of the tetragonal phase co-existing with the orthorhombic phase in the AFM state at around 4.2 GPa and 13 K. Our results also imply that filamentary superconductivity can only coexist with the partial magnetism in the mixed tetragonal and orthorhombic region in the SrFe2As2 at temperatures below 28 K and pressures between 4.2 and 4.8 GPa as shown in the filled purple region in Fig. 3. Furthermore, bulk superconductivity, as observed by an anomaly in the field cooling (FC) magnetic susceptibility, only appears in the P-T region with the tetragonal phase in the PM state, where the TS and TN transitions are fully suppressed. Based on both diffraction and Mössbauer results, the volume fraction of the AFM orthorhombic phase as a function of pressure appears to be inversely proportional to the high Tc (Figs. 2 and 3), further supporting the notion that the superconductivity is partially suppressed by the existence of magnetism in the AFM orthorhombic phase. Thus we assume the presence of an AFM quantum critical point (QCP) near the AFM phase boundary. Previous NMR experiments indicate an antiferromagnetic fluctuation associated with QCP has strong correlation with the high-Tc superconductivity in chemically-doped BaFe2As2 compounds32,33. These results indicate that the QCP is likely to connect with the superconductivity in the iron based compound.

Methods

Single-crystal SrFe2As2 samples with 20 at.% 57Fe enrichment were grown using the FeAs self-flux method34. XRD analyses of the synthesized samples showed lattice parameters of a = 3.9234(3) Å and c = 12.371(2) Å at ambient conditions. A sample measuring 15 μm thick and 70 μm big was loaded into a symmetric DAC using Ne as the pressure medium, together with three ruby spheres for pressure calibration at low temperatures. The pressure of the sample chamber was controlled using a membrane diaphragm. A helium flow cold-finger cryostat was used to cool down the DAC to as low as 10 K; temperatures of the DAC were equilibrated after each cooling and were measured using two thermocouples attached to each side of the DAC. Temperature uncertainties were less than 5 K. SMS measurements with a resonant energy (E0) of 14.4125 keV for 57Fe were performed at the undulator beamline 16-IDD of the Advanced Photon Source (APS), Argonne National Laboratory (ANL). The energy band-width of the undulator beam was monochromotized to approximately 2 meV bandwidth using a water-cooled diamond (1 1 1) double crystal monochromator and a high resolution monochromator consisting of 2 channel cut silicon crystals (Si(4 4 0) and Si(9 7 5)). A pair of KB mirrors was used to focus the x-ray beam to approximately 50 μm at the sample position in the DAC. SMS spectra were collected using an avalanche photodiode detector at the nuclear forward scattering geometry with a collection time of 1–2 hours. SMS spectra were collected in the form of the intensity of the 57Fe nuclear decay as a function of time. When the nuclei in the sample are excited by the synchrotron radiation pulse of 14.4125 meV with a bandwidth of +1 meV, the coherent decay of the excited ensemble of nuclei phases with time. Through analyses of the time-resolved intensity of the SMS spectra, hyperfine parameters, including hyperfine magnetic fields, containing structural and electronic information of the resonating nucleus can be derived. The high resolution (ΔE/E ~ 1*10−7) of the SMS technique enables us to detect the AFM to PM phase transition of SrFe2As2 at high pressures. The spectra were fitted using the CONUSS program35 to derive hyperfine parameters including hyperfine magnetic fields of the Fe ions.

Angle-dispersive XRD measurements were performed on powder samples at the 16-IDB beamline of the APS, ANL. The powder samples were gently ground from the same batch of the 57Fe-enriched single crystals used for SMS experiments and loaded into the same symmetric DAC using Ne pressure medium and ruby pressure calibrate. XRD measurements of the starting sample showed consistent lattice parameters to the single crystals. To avoid systematic errors, care was taken to ensure that experimental conditions between SMS and XRD experiments were consistent: the same cryostat with the same temperature thermocouples and membrane controller were used in both experiments. Two types of XRD experiments were conducted: decreasing temperatures at a constant pressure with an x-ray wavelength of 0.4072 Å; increasing pressures at a constant temperature of 50 K or 13 K with an x-ray wavelength of 0.3737 Å. Diffraction patterns were collected by a MAR345 detector and processed using the FIT2D software. Rietveld refinements of the patterns were performed using the GSAS package36.