Iron isotope effect on the superconducting transition temperature and the crystal structure of FeSe_1-x

The Fe isotope effect (Fe-IE) on the transition temperature T_c and the crystal structure was studied in the Fe chalcogenide superconductor FeSe_1-x by means of magnetization and neutron powder diffraction (NPD). The substitution of natural Fe (containing \simeq 92% of ^{56}Fe) by its lighter ^{54}Fe isotope leads to a shift of T_c of 0.22(5)K corresponding to an Fe-IE exponent of \alpha_Fe=0.81(15). Simultaneously, a small structural change with isotope substitution is observed by NDP which may contribute to the total Fe isotope shift of T_c.

Historically, the isotope effect played a crucial role in elucidating the origin of the pairing interaction leading to the occurrence of superconductivity. The discovery of the isotope effect on the superconducting transition temperature T c in Hg [1] in 1950 provided the key experimental evidence for phonon-mediated pairing as formulated theoretically by BCS subsequently. The observation of unusually high T c 's in the newly discovered Fe-based superconductors immediately raised the question regarding the pairing glue and initiated isotope effect studies. Currently, we are aware of two papers on isotope experiments with, however, contradicting results. Liu et al. [2] showed that in SmFeAsO 0.85 F 0. 15 and Ba 0.6 K 0.4 Fe 2 As 2 the Fe isotope effect (Fe-IE) exponent, reaches values of α Fe ≃ 0.35 (M Fe is the Fe atomic mass), while Shirage et al. [3] found a negative Fe-IE exponent α Fe ≃ −0.18 in Ba 1−x K x Fe 2 As 2 . Note, that the only difference between the Ba 1−x K x Fe 2 As 2 samples studied in Refs. [2] and [3] was the preparation procedure (low-pressure synthesis in [2] vs. high-pressure synthesis in [3]), while the potassium doping (x ≃ 0.4) as well as the T c 's for the samples containing natural Fe (T c ≃ 37.3 K in [2] vs. T c ≃ 37.8 K in [3]) were almost the same.
In this paper we study the Fe-IE on T c and on the structural parameters (such as the lattice parameters a, b, and c, the lattice volume V , and the distance between the Se atom and Fe plane, Se height h Se ) for another representative of the Fe-based hightemperature superconductors (HTS), namely FeSe 1−x . The substitution of natural Fe (containing ≃ 92% of 56 Fe) by its lighter 54 Fe isotope leads to a shift of T c of 0.22(5) K corresponding to an Fe-IE exponent of α Fe = 0.81 (15).
The 54 FeSe 1−x / 56 FeSe 1−x samples (here after we denote natural Fe containing ≃ 92% of 56 Fe isotope as 56 Fe) with the nominal composition FeSe 0.98 were prepared by a solid state reaction made in two steps. Pieces of Fe (natural Fe: 99.97% minimum purity, average atomic mass M F e = 55.85 g/mol, or 54 Fe: 99.99% purity, 99.84% isotope enriched, M54 F e = 54.0 g/mol) and Se (99.999% purity) were first sealed in double walled quartz ampules, heated up to 1075 o C, annealed for 72 h at this temperature and 48 h at 420 o C, and then cooled down to room temperature at a rate of 100 o C/h. As a next step, the samples, taken out of the ampules, were powderised, pressed into pellets, sealed into new ampules and annealed first at 700 o C for 48 h and then at 400 o C for 36 h, followed by cooling to room temperature at a rate of 200 o C/h. Due to the extreme sensitivity of FeSe 1−x to oxygen [4], all the intermediate steps (grinding and pelletizing) as well as the preparation of the samples for the neutron powder diffraction and magnetization experiments were performed in a glove box under He atmosphere.
The Fe-IE on the structural properties was studied by neutron powder diffraction (NPD) experiments by using the high-resolution powder diffractometer HRPT (Paul Scherrer Institute, Switzerland) [5]. The experiments were carried out at a wavelength λ = 1.494Å. The 54 FeSe 1−x / 56 FeSe 1−x samples, placed into vanadium containers, were mounted into a He-4 cryostat in order to reach temperatures between 5 and 250 K. High statistics data were taken at 250 and 5 K. Data at 10 ≤ T ≤ 240 K were collected with intermediate statistics.   Table 1. The amount of the impurity phases and the Se content (1 − x), determined for the data sets taken at T = 250 K, were kept fixed during the refinement of the NPD spectra at lower temperatures. The mass fractions of impurity phases, the hexagonal FeSe (P 6 3 /mmc) and Fe (Im3m), were found to be 0.50(10)%, 0.31(4)% and 1.13(18)%, 1.06(7)% for 54 FeSe 1−x and 56 FeSe 1−x , respectively. Figure 2 shows the temperature dependence of the lattice parameters a, b, and c, the lattice volume V , and the Se height h Se of a representative 54 FeSe 1−x and a representative 56 FeSe 1−x sample (see Fig. 3). From Fig. 2a it is obvious that at T s ≃ 100 K a transition from a tetragonal to an orthorhombic structure takes place, analogous to that reported in [4,8]. The Fe-IE on the structural transition temperature T s could be estimated from the shift of the interception point of the linear fits to a(T ) and b(T ) in the vicinity of T s , as denoted by the arrows in the inset of Fig. 2a, which was found to be ∆T s = 0.2(2.5) K. Within the whole temperature range (5 K≤ T ≤250 K) the Table 1. Structural parameters of 54 FeSe 1−x and 56 FeSe 1−x at T = 250 and 5 K. Space group P 4/nmm (no. 129), origin choice 2: Fe in (2b) position (1/4, 3/4, 1/2); Se in (2c) position (1/4, 1/4, z). Space group Cmma (no. 67): Fe in (4b) position (1/4, 0, 1/2), Se in (4g) position (0, 3/4, z). The atomic displacement parameters (B) for Fe and Se were constrained to be the same. The Bragg R factor is given for the main phase; the other reliability factors are given for the whole refinement.
3.77036 (3) 3.76988 (5) 5.33523 (10)  lattice constants a and b are slightly larger for 54 FeSe 1−x than those for 56 FeSe 1−x (see Fig. 2a). This is in contrast to the lattice parameter c, which within the same range is marginally smaller for 54 FeSe 1−x than for 56 FeSe 1−x (Fig. 2b). The lattice volume remains, however, unchanged. Consequently, substitution of 56 Fe by 54 Fe leads to a small, but detectable enhancement of the lattice along the crystallographic a and b directions and a compression of it along the c−axis, resulting in a change of the shape of the Fe 4 Se pyramid, which is known to influence T c in Fe-based HTS [9,10,11]. This is shown in Fig. 2c where below 100 K the Se atom is located closer to the Fe plane in 54 FeSe 1−x than in 56 FeSe 1−x . The corresponding change of the Fe 4 Se pyramid is shown schematically in the inset of Fig. 2c. It is important to note that the observed Fe-IE's on the lattice parameters are intrinsic and not just a consequence of slightly different samples. As shown in Ref. [4], various samples of 56 FeSe 1−x with 1 − x ≃ 0.98 and T c ≃ 8.2 K indeed exhibit the same lattice parameters within experimental error. The Fe-IE on the transition temperature T c was studied by means of magnetization experiments.
Measurements were performed by using a SQUID magnetometer (Quantum Design MPMS-7) in a field of µ 0 H = 0.1 mT for temperatures ranging from 2 to 20 K. In order to avoid artifacts and systematic errors in the determination of the isotope shift of T c it is important to perform a statistical study: i.e. to investigate series of 54 FeSe 1−x / 56 FeSe 1−x samples synthesized exactly the same way (the same thermal history, the same amount of Se in the initial composition). The magnetization experiments were conducted for six 54 FeSe 1−x and seven 56 FeSe 1−x samples, respectively. The inset in Fig. 3 shows an example of zero-field cooled (ZFC) magnetization curves for a pair of 54 FeSe 1−x / 56 FeSe 1−x samples (M norm was obtained after subtracting the small paramagnetic offset M magn measured at T > T c and further normalization of the obtained curve to the value at T = 2 K, see Fig. 1 in Ref. [4] for details). The magnetization curve for 54 FeSe 1−x is shifted almost parallel to higher temperature, implying that T c of 54 FeSe 1−x is higher than that of 56 FeSe 1−x . The resulting transition temperatures determined from the intercept of the linearly extrapolated M norm (T ) curves with the M = 0 line for all samples investigated are summarized in Fig. 3. The T c 's for both sets of 54 FeSe 1−x / 56 FeSe 1−x samples fall into two distinct regions: 8.39 ≤ 54 T c ≤ 8.48 K and 8.15 ≤ 56 T c ≤ 8.31 K, respectively. The corresponding mean values are: 54 T c = 8.43(3) K and 56 T c = 8.21(4) K. Note, that one out of the seven 56 FeSe 1−x samples had T c ≃ 8.44 K which is by more than 5 standard deviations above the average calculated for the rest of the six samples. We have no explanation for this discrepancy, but decided to show this point for completeness of the data collected.
The Fe-IE exponent α Fe was determined from the data presented in Fig. 3 using Eq. (1), where the relative Fe isotope shift of the quantity X is defined as ∆X/X = ( 54 X − 56 X)/ 56 X (this definition of ∆X/X is used throughout the paper). With 54 T c = 8.43(3) K, 56 T c = 8.21(4) K, M54 Fe = 54 g/mol, and M56 Fe = 55.85 g/mol one obtains α Fe = 0.81 (15). Two points should be emphasized: i) The positive sign of the Fe-IE exponent α Fe is similar to that observed in phonon mediated superconductors, such as elemental metals [1] and MgB 2 [12] as well as in cuprate HTS [13,14] where the pairing mechanism is still under debate. Bearing in mind that a positive Fe-IE exponent was also observed in SmFeAsO 0.85 F 0.15 and Ba 0.6 K 0.4 Fe 2 As 2 [2], we may conclude that at least for three compounds representing different families of Fe-based HTS (1111, 122, and 11) the sign of the Fe-IE on T c is conventional. This suggests that the lattice plays an essential role in the pairing mechanism in the Fe-based HTS. ii) The Fe-IE exponent α Fe = 0.81 (15) is larger than the BCS value α BCS = 0.5 as well as more than twice as large as α Fe ≃ 0.35 reported for SmFeAsO 0.85 F 0.15 and Ba 0.6 K 0.4 Fe 2 As 2 [2]. Note that an enhanced value of the oxygen isotope exponent (α O ≃ 1) was also observed in underdoped cuprate HTS [14] and was shown to be a consequence of the polaronic nature of the supercarriers in that class of materials [15]. Recently, Bussmann-Holder et al. [16] showed that in the framework of a two-band model polaronic coupling in the larger gap channel as well as in the interband interaction induce a T c (doping) dependent Fe-IE: α Fe increases strongly with reduced T c (doping), reaching α Fe ≃ 0.9 at T c ≃ 10 K. Note that a similar generic trend is observed in cuprate HTS [13,14].
However, our structural refined NPD data suggest that part of the large Fe-IE α Fe = 0.81 (15) may result from the tiny structural changes due to 54 Fe/ 56 Fe substitution. In the following we discuss a possible structural effect on the observed Fe-IE on T c . It is known that in FeSe 1−x a decrease of the Se height caused by compression of the Fe 4 Se pyramid leads to an increase of T c by ∆T h Se c /(∆h Se /h Se ) ≃ 3.4 K/% [11,17]. In contrast, an increase of the Se(Te)-Fe-Se(Te) angle in the FeSe 1−y Te y family (angle β in our notation [18], see the inset of Fig. 2c) results for y ≤ 0.5 in a decrease of T c by ∆T β c /(∆β/β) ≃ 2.9 K/% [10]. Based on the structural data presented in Fig. 2  In conclusion, from magnetization experiments the Fe-IE exponent of T c for the FeSe 1−x system was determined to be α Fe = 0.81 (15). The tiny changes of the structural parameters caused by isotope substitution may contribute to the total Fe-IE exponent, and may help to clarify or even be the origin of the previously reported controversial results [2,3]. However, more detailed and systematic structural investigations on Fe isotope substituted samples are required in order to draw definite conclusions. Our findings, on the other hand, clearly show that a conventional isotope effect on T c is present which highlights the role of the lattice in the pairing mechanism in this new material class.
We would like to thank A. Bussmann-Holder for fruitful discussions and for the critical reading of the manuscript. This work was partly performed at SINQ (Paul Scherrer Institute, Switzerland). The work of MB was supported by the Swiss National Science Foundation. The work of EP was supported by the NCCR program MaNEP.