Fe-vacancy ordered Fe4Se5: The insulating parent phase of FeSe superconductor

We have carried out a detailed study to investigate the existence of an insulating parent phase for FeSe superconductor. The insulating Fe4Se5 with specific Fe-vacancy order shows a 3D-Mott variable range hopping behavior with a Verwey-like electronic correlation at around 45 K. The application of the RTA process at 450 celcius degree results in the destruction of Fe-vacancy order and induces more electron carriers by increasing the Fe3+ valence state. Superconductivity emerges with Tc ~ 8K without changing the chemical stoichiometry of the sample after the RTA process by resulting in the addition of extra carriers in favor of superconductivity.


Introduction
The FeAs-based [1] and FeSe-based [2] superconductors are among the most investigated materials in condensed matter physics since their discovery in 2008. The observation of a wide range of superconducting transition temperatures, with the highest confirmed Cooper pair formation temperature up to 75 K in monolayer FeSe film [3] provides a unique opportunity to gain more insight into the origin of high-temperature superconductivity. The multiple-orbital nature of the Fe-based materials, combined with spin and charge degrees of freedom, results in the observation of many intriguing phenomena such as structural distortion, magnetic or orbital ordering [4], and electronic nematicity [5,6]. There are suggestions that the orbital fluctuation may provide a new channel for realizing superconductivity [7,8].
The parent compounds of FeAs-based materials exhibit structural transitions from a hightemperature tetragonal phase to a low-temperature orthorhombic phase, which accompanies with an antiferromagnetic (AF) order [9,10]. Upon doping, both the orthorhombic structure and the AF phase are suppressed and superconductivity is induced. On the other hand, FeSe undergoes a tetragonal-toorthorhombic transition at ~ 90 K [2,11,12]. However, no magnetic order is formed at ambient pressure [12,13] and superconductivity below ∼8 K [2] is crucially related to this orthorhombic distortion. The nematic order coexists with superconductivity but not with long-range magnetic order has led to arguments that the origin of the nematicity in FeSe is not magnetically but likely orbitaldriven [14,15].
However, recent studies show that the nematic states in the FeSe systems are far more complex [16][17][18][19][20]. There exist strong high-energy spin fluctuations [20] which suggest that the nematicity and magnetism may be still intimately linked. It was also found that there are many interesting features in the band structures of the nematic state. More surprises came as one applied pressure to FeSe. The application of pressure leads to the suppression of structural transition, the appearance of a magnetically ordered phase at ∼1 GPa [13,21], and Tc increases to a maximum ~ 37 K [22][23][24][25][26][27] at ∼6 GPa. An even more dramatic enhancement of Tc was achieved on monolayer FeSe grown on SrTiO3 substrate [28][29][30][31] The above observations lead to questions that exist since the discovery of FeSe superconductor: what is the exact chemical stoichiometry of the compound, and what is the exact phase diagram for the FeSe system? Earlier studies showed that the superconducting property of FeSe is very sensitive to its stoichiometry [2,12,32]. The fact that higher superconducting transition temperature exists in monolayer FeSe on SrTiO3 substrate suggests that the commonly accepted phase diagram, derived from assuming that FeTe is the non-superconducting parent compound of FeSe [33], is questionable. Studies have observed the trace of the superconducting feature with Tc close to 40 K in samples of nano-dimensional form [34].
It has been a debate whether there exists an antiferromagnetic Mott insulating parent phase, similar to the cuprate superconductors, for FeSe superconductors [35,36,37]. Chen et al. first reported the existence of tetragonal β-Fe1-xSe with Fe vacancy orders, characterized by analytical transmission electron microscopy [38]. The authors further argued that the Fe4Se5 phase with √5 × √5 Fe-vacancy order to be the parent phase of FeSe superconductors [38]. The Fe vacancy order observed in the Fe4Se5 phase is identical to the Fe-vacancy order observed in the A2Fe4Se5 (A=K, Tl, Rb), which has been shown to be an antiferromagnetic [35,[39][40][41][42] and is the parent phase of the superconductor A2-xFe4+xSe5 [43,44]. The detailed studies of the Fe vacancy in K2Fe4+xSe5 reveal that its order/disorder is directly associated with superconductivity. A recent study shows that the Fe-vacancy ordered Fe4Se5 nanowire is the non-oxide material with the Verwey-like electronic correlation [45]. It suggests that a charge-ordered state emerges below T = 17 K. The question remains unanswered is whether this Fevacancy ordered phase is the parent compound of superconducting FeSe?
In this paper we present the results of structure, electrical transport, and magnetic measurements on the polycrystalline sample of Fe4Se5 treated by rapid-thermal-annealing (RTA) process at a proper temperature and time. After RTA treatment, the sample shows superconductivity with Tc ~ 8 K without changing its chemical stoichiometry. Our findings confirm that the Fe4Se5 with Fe-vacancy order is the parent compound of FeSe superconductors.

Sample Preparation
Fe4Se5 nanosheets were prepared by a chemical co-precipitation method. First, 200 mL of ethylene glycol was mixed with NaOH and SeO2 powder and slowly heat up to 160 °C for mixing well.
The volume of 2.4 mL hydrazine hydrate was then added as the reducing agent. Then, at 160 °C, the Fe precursor solution was added and reacted for 12 hours in order to form Fe4Se5 nanosheets. The Fe precursor solution is made by dissolving the amount FeCl2 in ethylene glycol. The reaction was done under N2 gas purging to avoid the formation of oxide impurity. To clean the Fe4Se5 nanosheets, the reacted product .was dispersed in acetone with absolute ethanol, and high-speed centrifugation is applied to precipitate the nanosheets and remove the capping ligand dissolved in the above organic solvent. The nanosheets were finally dried in vacuum for 24 hours and collected. The process for the rapid thermal annealing (RTA) is: the as-grown Fe4Se5 nanosheets were heated at 450 o C for 10 minutes in a tube furnace with 1atm Ar gas inside to maintain a non-oxidation environment as a rapid thermal treatment process. After the rapid thermal treatment, an air-quenching process was taken by flowing room-temperature Ar gas through the tube. All the samples were stored in the oxygen-free glove box.

Analysis
The crystal structure observation of the Fe4Se5 samples was carried out by the high resolution transmission electron microscope (HRTEM, JEOL JEM-2100F) and 4-circle x-ray diffractometer with the incident beam (12.4 keV) of wavelength 0.82656 Å at beam-line BL13A and wavelength 0.61992 Å at beam-line TPS09A in NSRRC. The temperature-dependent structural information of Fe4Se5 samples was analyzed by the high resolution neutron powder diffraction (high resolution powder diffractometer Echidna with the wavelength of 2.4395 Å at ANSTO). The Fe4Se5 nanosheet powder was pressed into the pallet under 200 kg/cm 2 at 100 °C for 1 hour for the following measurements: To identify the stoichiometry, the energy-disperse X-ray spectrometer (EDS) setup with the SEM (JEOL JSM-7001F Field Emission Scanning Electron Microscope) was applied. To affirm the valence states of the Fe ions, the X-ray photoemission spectroscopy (XPS, VG Scientific ESCALAB 250) measurements for the samples were performed. For polycrystalline bulk samples, the resistance was measured by using the standard four-probe method with silver paste for electrical contact and the Hall measurement by a Hall-bar configuration was done by the Quantum Design Physical Properties Measurement System (PPMS, Model 6000). The magnetic property was measured by the Quantum Design Superconducting quantum interference device (SQUID, VSM).

Structural analysis of Fe4Se5
Figure 1(A) shows the X-ray diffraction (XRD) patterns of the as-grown Fe4Se5 sample at room temperature. The diffraction pattern, which exhibits superstructure peaks, is refined with a tetragonal P4 symmetry with √5×√5 Fe-vacancy order instead of the tetragonal P4/mmm symmetry as observed in FeSe [2]. The insets are the TEM image of as-grown Fe4Se5 nanocrystal and its TEM-SAED (selective area electron diffraction) patterns along the c-axis. The observation of extra diffraction points among the main diffraction points in the SAED pattern confirms the √5×√5 Fe-vacancy order in the as-grown Fe4Se5 nanocrystal [35]. After RTA treatment at 450 °C, the superstructure peaks observed in XRD and TEM-SAED due to the √5×√5 Fe-vacancy order disappears, as shown in Figure 1(B) and its inset. The refinement results, using the same P4 symmetry, reveal that the occupations of Fe at vacancy 4d sites and the originally occupied 16i sites are almost the same, indicating the Fe vacancies becoming disordered after RTA treatment. It is noted that the XRD patterns of the RTA treatment sample show nearly ten times smaller in the intensity response. This is due to the different synchrotron beamlines we used for our measurements. However, the difference does not affect the refined results.
It is noted that the FeSe4 tetrahedron in as-grown Fe4Se5 is highly distorted due to the existence of the Fe-vacancy order. As the Fe vacancies disordered by the RTA treatment, the FeSe4 tetrahedron becomes more symmetric. The refined structure parameters are tabulated in Supplementary Table 1 Figure 2. A transition temperature TV is marked as the onset temperarture of 3D-MVH behavior). The variable-range-hopping characteristic temperature T0 calculated is ~1400 K for the as-grown sample. The magnetic susceptibility of the same sample shows paramagnetic behavior as the sample cools down from 300K, and a sudden drop in susceptibility appears at about the same temperature as the resistance transition temperature (TV) ~45 K. The sharp resistive rise and the diamagnetic drop are the two signatures for the Verwey transition observed in Fe3O4, which occurs at 125K. These results are also in line with those reported results in the Fe4Se5 nanowire, which was recently demonstrated to exhibit the Verwey-like electronic correlation [45].  Figure 2(B). The lower-right inset is the magnetic susceptibility, which further demonstrates the superconducting transition with onset Tc ~ 7.9 K. The evolution to superconductivity in this RTA-treated sample is similar to that reported in the K2-xFe4+ySe5 system, where superconductivity appears after Fe vacancies becoming disordered through high temperature annealing and rapid quenching processes [43,44].

XPS and Hall measurement of Fe 4 Se 5
In order to gain more insight into the observed Verwey-like electronic correlation, XPS at room temperature and temperature-dependent Hall measurements on the samples were performed. Figure  3(A) is the observed XPS results for the as-grown Fe4Se5 sample. Figure 3(A) is the observed XPS results for the as-grown Fe4Se5 sample. The XPS spectrum clearly reveals two peaks showing the existence of mixed-valence states of Fe. The observed two peaks, at 708.5 eV and 711.5 eV can be associated with the Fe 2+ and Fe 3+ states, respectively. The best data fitting gives the ratio between Fe 2+ to Fe 3+ close to 1:1. This result is similar to that observed in the magnetite Fe3O4. After the RTA treatment, the Fe 3+ state becomes dominant. The extracted Fe 3+ ion to total Fe atoms ratio is 58.7% for 300 o C RTA-treated and 73.2% for 450 o C RTA-treated samples, respectively, indicating a substantial increase in electron carriers in these samples. It should be noted that the sample after 300 o C still exhibits temperature dependent behavior like semiconductor. No specific difference of Se 3d peak at 54.7 eV before and after the RTA process of the Fe4Se5 sample according to the XPS result, as shown in Supplementary Figure 3.
It is known that tetragonal FeSe is a metal with two-band based on the first-principles electronic structure calculation, for example, by T. Xiang et al., [46]. T. Xiang et. al., also reported the electronic structure of Fe4Se5 with √5 × √5 Fe-vacancy order is a pair checkboard antiferromagnetic insulator. The calculation shows the Fe-vacancy ordered Fe4Se5 has a single band structure with n-type carrier dominated and a band gap ~290 meV. Berlijn et al., [47] investigated the effect of disordered Fevacancies on the normal-state electronic structure of the alkali-intercalated FeSe system, where the KFe4Se5 exhibits exactly the same Fe-vacancy order as that in Fe4Se5. They found that the disorder of Fe-vacancy can effectively raise the chemical potential giving enlarged electron pockets without adding carriers to the system.
It is noted that as reported by Chen et al. [38], there exists a series of FexSey compounds with x/y = 1/2, 2/3, 3/4, 4/5, and etc. We have carried out a systematic study using the co-precipitation method to successfully prepare tetragonal Fe(1-x)Se with stoichiometry of Fe3Se4 and Fe4Se5. Based on the XPS results, the observed Fe 3+ /Fe 2+ ratio is 2 and 1 for tetragonal Fe3Se4 and Fe4Se5, respectively, as shown in Supplementary Figure 4 (A) and Figure 3 (A) . These data imply that Fe3Se4 would be hole-doped and Fe4Se5 be electron-doped if there are additional carriers based on the simple charge balance picture by considering Fe3Se4 to be the combination of Fe (2+) Se and Fe2 (3+) Se3, whereas Fe4Se5 is from 2(Fe (2+) Se) and Fe2 (3+) Se3. Indeed, our Hall measurement results show at 300 K a hole concentration of 1.20x10 19 /cm 3 for Fe3Se4 (Supplementary Figure 4(B)) and electron concentration of -6.52x10 17 /cm 3 for Fe4Se5.
Both of the as grown and RTA treated Fe4Se5 show a single-band behavior with n-type carrier from the Hall resistivity measurements, as shown in Supplementary Figure 5. The Hall coefficient of the as-grown sample at room temperature is -9.59 cm 3 /C, corresponding to the electron carrier concentration of 6.52 × 10 17 cm -3 , and the carrier concentration decreases by about a factor of 8 at the transition temperature TV, as shown in Figure 3(C).
After the Fe4Se5 sample is RTA-treated at 450 o C, the Fe 3+ /Fe 2+ ratio becomes close to 3:1, which means a large number of electrons are introduced, and subsequently induced superconductivity. Indeed, the Hall measurement results, as shown in Figure 3(D), show that the carrier concentration at 300 K increases to -3.34x10 21 /cm 3 (Hall coefficient -1.87x10 -3 cm 3 /C) for 450 o C RTA-treated sample. The electron carrier concentration is about four orders of magnitude increase comparing with the as-grown Fe4Se5. Obviously, the RTA treatment disrupts the Fe-vacancy long-range order and leads to the increase of electron carriers.

Neutron diffraction of Fe4Se5
It is well known that the Verwey transition in magnetite exhibits a structural transition accompanying with the sharp resistive and magnetic susceptibility changes. To examine whether such a structural change exists for the as-grown Fe4Se5, we have carried out the neutron diffraction at low temperatures.
The detailed structural information of the as-grown Fe4Se5 sample measured by neutron diffraction at different temperatures is shown in Figure 4. At room temperature, the neutron data, consistent with XRD results, fit well with the P4-tetragonal symmetry. At low temperatures, a distortion appears at temperatures below 30K. The data at 5 K, with an evident peak emerge shown in the inset of Figure 4, indicates a possible structural change. This result further supports that the asgrown Fe4Se5 nanosheets, similar to the results observed in Fe4Se5 nanowire, shows the Verwey-like correlation. The Verwey-like transition temperature of ~45 K in nanosheets is higher than that observed in the nanowire, which was found to be ~30 K. This shows the size dependence of TV, which also noticed in Verwey transition [48][49][50]. Currently, we are waiting for the results of the detailed highresolution XRD at low temperatures using a synchrotron source to determine exactly the lowtemperature phase and the transition temperature.

Conclusions
We have carried out a detailed study to investigate whether there exists an insulating parent phase for FeSe superconductor. Our studies unambiguously show that: (1) the √5 × √5 Fe-vacancy ordered Fe4Se5 a Mott insulator with Verwey-like transition at low temperature; (2) Fe4Se5 is the parent compound of the FeSe superconductors. The application of the RTA process at 450 o C disrupts Fevacancy order and induces more electron carriers by increasing the Fe 3+ valence state. Superconductivity emerges with Tc ~ 8 K without changing the chemical stoichiometry of the sample after the RTA process. Consistent with the observations in K2Fe4+xSe5, superconductivity is directly related to the disappearance of Fe-vacancy long-range order. In the Fe4Se5 case, no extra Fe doping is required as the random occupation of Fe atom in the vacancy sites, resulting in the addition of extra carriers in favor of superconductivity. More detailed evolution of superconductivity by varying the RTA temperature and time is currently underway in order to gain more insight into the exact phase diagram of the FeSe superconductors.