Strong-coupling Spin-singlet Superconductivity with Multiple Full Gaps in Hole-doped BaKFeAs Probed by Fe-NMR
We present Fe-NMR measurements of the novel normal and superconducting-state characteristics of the iron-arsenide superconductor BaKFeAs ( = 38 K). In the normal state, the measured Knight shift and nuclear spin-lattice relaxation rate demonstrate the development of wave-number ()-dependent spin fluctuations, except at = 0, which may originate from the nesting across the disconnected Fermi surfaces. In the superconducting state, the spin component in the Fe-Knight shift decreases to almost zero at low temperatures, evidencing a spin-singlet superconducting state. The Fe- results are totally consistent with a -wave model with multiple full gaps, regardless of doping with either electrons or holes.
pacs:74.70.-b; 74.25.Ha; 74.25.Jb
The recent discovery of superconductivity (SC) in the iron (Fe)-based oxypnictide LaFeAsOF at the SC transition temperature K has provided a new route toward the realization of high- SC Kamihara (). The mother material, LaFeAsO, exhibits a structural phase transition from tetragonal (P4/nmm) to orthorhombic (Cmma) form at 155 K and then exhibits a striped antiferromagnetic (AFM) order with = (0, ) or (, 0) and 140 K Cruz (). The calculated Fermi surfaces (FSs) for undoped LaFeAsO consist of two small electron cylinders around the tetragonal M point and two hole cylinders, plus a heavy 3D hole pocket, around the point Singh (). Measurements of the nuclear spin-lattice relaxation rate () for the LaFeAsO system in the SC state revealed the lack of a coherence peak below and the presence of -like behavior, suggesting an unconventional SC nature with line-node gaps Nakai (); Grafe (); Mukuda (). However, some experiments to measure parameters such as penetration depth, together with studies using angle resolved photoemission spectroscopy (ARPES), have shown that the SC order parameter (OP) is of fully gapped -wave symmetry Luetkens (); Ding (); Hashimoto (); Kondo (). The theory was the first to propose -wave pairing symmetry as a promising candidate for the SC state in Fe-pnictide superconductors Mazin (); Kuroki ().
Another family of FeAs-based superconductors without oxygen has been reported in hole-doped BaKFeAs with K Rotter1 (). The mother material, BaFeAs, has a ThCrSi-type structure and consists of alternating layers comprising FeAs tetrahedra and Ba. BaFeAs also exhibits a structural phase transition from the tetragonal (I4/mmm) to orthorhombic (Fmmm) form, accompanied by a striped AFM order with = (, 0, ) at = 140 K Rotter2 (); Huang (). The previous As-NMR study on BaKFeAs reported that shows -like behavior well below Fukazawa (); MukudaPhysC (), which is in contrast to the fully gapped -wave symmetry of the SC OP, as revealed by ARPES on hole-doped BaKFeAs and electron-doped Ba(FeCo)As Ding (); Terashima (). Furthermore, ARPES results for BaKFeAs show that there are two SC gaps with different values: a large gap on the two, small, hole-like and electron-like FS sheets, and a small gap on the large, hole-like FS Ding (). This two-SC-gap phenomenon was suggested by NMR studies as well Kawasaki (); Matano (). In this letter, we report the results of microscopic Fe-NMR measurements on hole-doped BaKFeAs with K enriched with the isotope Fe to address its normal-state and SC characteristics.
A polycrystalline sample of Fe-enriched BaKFeAs was synthesized by the high-pressure synthesis technique, as described elsewhere Shirage (). Powder X-ray diffraction measurements indicated that the BaKFeAs sample almost completely consisted of a single phase with the lattice parameters = 3.9142 Åand = 13.305 Å. The sample was moderately crushed into powder for the NMR measurements, which were easily performed under a strong magnetic field along the direction including the plane. The Fe- and As-NMR measurements were performed on a phase coherent pulsed NMR spectrometer at respective magnetic fields of 11.966 and 5.12 T. was measured with a saturation recovery method.
Figure 1(a) shows the dependence of the Fe-NMR spectra at = 11.966 T parallel to the plane. The Knight shift stays almost constant above , followed by a steep increase upon cooling below , as shown in Fig. 1(b). The Knight shift comprises a spin component and an orbital component, denoted as and , respectively. Note that depends on , but does not. Here, is the hyperfine coupling constant and is the uniform spin susceptibility. Since is known to be negative due to the inner core-polarization effect, as in LaFeAsO Terasaki (), the increase in below (see Fig. 1(b)) indicates the decrease in , demonstrating the formation of a spin-singlet SC state, as in LaFeAsO. If we assume 1.38 % in this compound, goes down to zero at = 0, as displayed in Fig. 1(c).
Fe- was uniquely determined with a single component throughout the whole range. A large enhancement of Fe- is observed on cooling down to from the normal state, as also seen in the results for As- (Fig. 2). By contrast, note that , which is in proportion to , stays almost constant above . In general, is expressed as
where is the imaginary part of the dynamical susceptibility in a direction perpendicular to the applied magnetic field, is the NMR frequency, and is the nuclear gyromagnetic ratio. The difference in dependency between the Knight shift and points to the development of -dependent spin fluctuations, except at = 0, upon cooling. To unravel the characteristics of these spin fluctuations, compare the values at Fe and As sites; Fe-As- 0.68 and is almost constant in the range (= 38 K) – 100 K, as shown in the inset of Fig. 2. If ferromagnetic spin fluctuations are predominant around = 0, the ratio 0.038 is estimated using 1. This value is about one order of magnitude smaller than the experimental value, indicating that ferromagnetic spin fluctuations are not developed. Furthermore, according to the argument in the literature Terasaki (), spin fluctuations around are not responsible for the large enhancement in values at both the Fe and As sites. Given these facts, it is likely that the enhancement is the results of the spin fluctuations with and that would be expected from the interband nesting.
Here, we remark that on the basis of the fluctuation-exchange approximation (FLEX) on an effective five-band Hubbard model, the recent theoretical work Ikeda () appears to explain qualitatively the evolution of magnetic characteristics from that in electron-doped systems to that in hole-doped systems: in electron-doped systems, and spin susceptibility decrease significantly upon cooling, producing a pseudogap behavior that originates from the band-structure effect, i.e., the existence of a high density of states just below the Fermi level. In hole-doped systems, is enhanced upon cooling due to the nesting across the disconnected FSs, but the Knight shift is not. In this model, it was suggested that the dominant contribution to the pairing interaction for -wave SC comes from an interplay between spin-dipole and spin-quadrupole and not from striped AFM spin fluctuations at and .
Next, we discuss the SC characteristics of BaKFeAs through the dependence of Fe-, as shown in Fig. 3. In the SC state, Fe- steeply decreases upon cooling, without a coherence peak just below , pointing to the unconventional SC nature of this compound and electron-doped LaFeAsO systems Terasaki (). On the other hand, ARPES revealed nearly isotropic and nodeless SC gaps with different values on three electron and hole FSs Ding (). Motivated by these seemingly incompatible experimental results, an extended -wave model with a sign reversal of the OP among the FSs has been proposed Mazin (); Kuroki (); Nagai (); Ikeda (). Note that the dependence of Fe- below cannot be simulated with either a simple -wave SC model( with ) or an isotropic -wave model() with no coherence effect, as shown in the inset of Fig. 3. Therefore, we have applied a multiple SC gap model to interpret the dependence of Fe- below .
|parameters||= 38 K||= 28 K|
First, we proceed with an analysis of by applying an anisotropic two-full-gap -wave model in which one of the gaps is anisotropic and the other isotropic, denoted as Model A. This was proposed to explain the behavior of observed in LaFeAsO on the basis of the effective five-band model Nagai (). For simplification, we assume that there are two FSs (FS1 and FS2) dominated by an isotropic full gap and an anisotropic full gap in the SC state, respectively, and neglect the coherence factor. These gap functions are given by and . Here gives rise to an anisotropy in a full gap function, as described in Ref. Nagai (). According to Nagai et al., when we assume a fraction of the density of states (DOS) at FS1, = 0.4, the experiment becomes consistent with a calculation using the parameters = 0.25 , = 9.2, and the smearing factor = 0.015 for the DOS (to compensate for impurity scattering), as shown by solid line in Fig. 4(a). Here, and are the respective DOSs at FS1 and FS2. We state that this model reproduced the result for LaFeAsO using parameters = 0.25 , = 4.6, and = 0.05 , which is also shown by the dashed curve in Fig. 4(a). The = 9.2 in BaKFeAs is twice that in LaFeAsO (4.6), which reveals that a strong-coupling SC state is realized in BaKFeAs, thus increasing . The fact that in BaKFeAs is smaller than that in LaFeAsO ( 0.3) implies that the SC in BaKFeAs is more robust to impurity scattering because of the larger SC gap . In Table 1, we have summarized the experimentally obtained parameters for BaKFeAs and LaFeAsO. The important outcome is that the respective results for BaKFeAs and LaFeAsO, which seemingly follow a - and a - like behaviors below , are consistently explained in terms of Model A only by changing the size of the SC gap .
Next, since the ARPES experiment on BaKFeAs revealed that the anisotropy of the gap is small in every FS sheet Ding (), we tentatively apply an isotropic two-full-gap -wave model in which both gaps are isotropic, denoted as Model B. Assuming that the large () and small () isotopic full gaps open on FS1 and FS2, respectively, a good fitting to the experiment is possible as shown by the solid line in Fig. 4(b) using parameters , = 0.35, = 0.7, and = 0.015 . However, the experiment does not replicate the slight step-wise behavior predicted by the calculation. Remarkably, the simulated result for the gap ratio = 0.35 is comparable to the value estimated by ARPES (0.44) Ding (). As for LaFeAsO, we note that the data are also reproduced as shown by the dashed line in Fig. 4(b), using a smaller gap = 4.4 and a larger = 0.05 than those in BaKFeAs. In this context, we cannot rule out at the present stage that Model B also explains both the experimental results in BaKFeAs and LaFeAsO. In order to shed light on the differences between the two models, the quasiparticle DOSs in the SC state are shown in Figs. 4(c) and 4(d), respectively. To identify the more appropriate model, further precise measurements are required on the hole-doped systems, involving systematic variation in the hole-doping level.
In conclusion, Fe-NMR studies on the hole-doped BaKFeAs with K have unraveled novel normal- and SC-state characteristics. Spin fluctuations with finite -vectors develop upon cooling down to ; they may originate from the nesting across the disconnected FSs with = (, 0) and (0, ). The Fe- results have revealed that Model A is consistently applicable not only to hole-doped BaKFeAs with = 38 K but also to electron-doped LaFeAsO with = 24 K. But Model B cannot be ruled out in understanding the present Fe-NMR results. In any case, the value of BaKFeAs is almost twice that of LaFeAsO, which reveals that a strong coupling SC state is realized in BaKFeAs. We suggest that the pairing mechanism of the unconventional SC with multiple fully gapped -wave symmetry may be universal to the Fe-based superconductors.
This work was supported by a Grant-in-Aid for Specially Promoted Research (20001004) and partially supported by the Global COE Program (Core Research and Engineering of Advanced Materials-Interdisciplinary Education Center for Materials Science) from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. M. Y. was supported by a Grant-in-Aid for Young Scientists (B) of MEXT (20740175).
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