Spin excitations in hole-overdoped iron-based superconductors

Understanding the overall features of magnetic excitation is essential for clarifying the mechanism of Cooper pair formation in iron-based superconductors. In particular, clarifying the relationship between magnetism and superconductivity is a central challenge because magnetism may play a key role in their exotic superconductivity. BaFe2As2 is one of ideal systems for such investigation because its superconductivity can be induced in several ways, allowing a comparative examination. Here we report a study on the spin fluctuations of the hole-overdoped iron-based superconductors Ba1-xKxFe2As2 (x = 0.5 and 1.0; Tc = 36 K and 3.4 K, respectively) over the entire Brillouin zone using inelastic neutron scattering. We find that their spin spectra consist of spin wave and chimney-like dispersions. The chimney-like dispersion can be attributed to the itinerant character of magnetism. The band width of the spin wave-like dispersion is almost constant from the non-doped to optimum-doped region, which is followed by a large reduction in the overdoped region. This suggests that the superconductivity is suppressed by the reduction of magnetic exchange couplings, indicating a strong relationship between magnetism and superconductivity in iron-based superconductors.

Scientific RepoRts | 6:33303 | DOI: 10.1038/srep33303 many calculations based on itinerant models have been proposed to explain the spin spectra [10][11][12] . Some models, for example based on the combination of density functional theory and dynamical mean-field theory, attempt to involve both itinerant and localized characters 13,14 . To establish a definitive model of magnetism, further examination of spin fluctuations is required.
Although systematic studies on spin fluctuations of electron-doped Ba(Fe,Ni) 2 As 2 have been reported 7,15 , the spin fluctuations of hole-overdoped samples over the entire Brillouin zone have not yet been established. In previous INS experiments on KFe 2 As 2 , spin fluctuations were observed up to E = 20 meV, which is halfway to the zone boundary 8,9 . In optimum-doped (Ba,K)Fe 2 As 2 , a conflict between INS and resonant x-ray inelastic scattering (RIXS) has been found. The spin dispersion is robust upon doping according to the results of INS 8 whereas softening has been observed in RIXS experiments 16 . To solve this problem, further study of the hole doping dependence is essential. We, thus, report the overall spectra of spin fluctuations in overdoped Ba 1-x K x Fe 2 As 2 obtained by the INS technique. Figure 1(a-e) show the observed two-dimensional constant-energy images of spin excitations in the case of Ba 0.5 K 0.5 Fe 2 As 2 . Figure 1(f-j) show the results of calculations with peak positions derived from the Gaussian fitting of constant-energy spectra. We describe the (H, K) plane with orthorhombic notation, even though superconducting Ba 1-x K x Fe 2 As 2 has a tetragonal crystal structure to facilitate comparison with non-doped BaFe 2 As 2 . Clear incommensurate peaks appeared around the (±1, 0) and (0, ±1) splitting along the longitudinal direction with a wave vector of (±2δ, 0) and (0, ±2δ), respectively, where δ = 0.06 at E = 13 meV. The (1 ± 2δ, 0) position corresponds to [π(1 ± 2δ, 0)] in the ab plane and (0.5 ± δ, 0.5 ± δ) in tetragonal notation. As the energy increases, spin excitations start to split along the transverse direction corresponding to (±1 ± 2δ, K) or (H, ±1 ± 2δ) and reach the magnetic zone boundary with merging signals from next zone boundaries. In contrast, magnetic excitations along the longitudinal direction corresponding to (±1 ± 2δ + H, 0) or (0, ±1 ± 2δ + K) are strongly damped, consistent with previous observations for the BaFe 2 As 2 system 17 . Figure 1(k,l) show the dispersion cuts along the transverse direction (1, K). A clear spin wave-like dispersion was observed up to E = 200 meV, where it reaches the zone boundary. Figure 2(a-j) show two-dimensional constant-energy images of spin excitations and the results of calculations for x = 1. Well-defined incommensurate peaks with incommensurability larger than that for x = 0.5 are observed at E = 5meV. With increasing energy, spin excitations split along the transverse direction, similarly to the case of x = 0.5. The dispersion cut along the transverse direction (0.68, K) shows that the spin excitations reach the zone boundary around E = 80 meV ( Fig. 2(k)). Nevertheless, magnetic signals exist even considerably above E = 80 meV with a vertical dispersion exhibiting a chimney-like structure ( Fig. 2(l,m)). The energy-constant cuts along the K direction clearly show that the magnetic signals extend up to E ~ 200 meV (Fig. 2(m)). Next, we overview the overall spin dispersion of Ba 1-x K x Fe 2 As 2 . Figure 3(a-c) show the spin excitation dispersions for x = 0.5 and 1 at T = 6 K derived from Gaussian fitting of the constant-energy spectra with those of the non-and underdoped samples. In x = 0.5, a spin wave dispersion is observed up to E = 200 meV, similarly to the cases of x = 0 and 0.33 (Fig. 3(a)). In x = 1, on the other hand, the dispersive spin excitations reach the zone boundary around E = 80 meV, which is considerably lower than the energy for x = 0.5 ( Fig. 3(b)). Instead, a vertical dispersion with a chimney-like structure was observed from E = 80 meV up to 200 meV. In x = 0.5, signals of the chimney-like structure can also be found above E = 200 meV, but they are less clear than those in x = 1 ( Fig. 1(m)). Figure 3(d) shows the energy dependence of the dynamical magnetic susceptibility ∫χ"(q, ω)dq for x = 0.5 and 1 at T = 6 K. ∫χ"(q, ω)dq for x = 0, 0.33 (T c = 38.5 K) and BaFe 2-y Ni y As 2 (y = 0.18, T c = 8 K) reported in 7,8,15 are also depicted for comparison. It can be seen that ∫χ"(q, ω)dq for x = 0.5 exhibits essentially equivalent behavior to that for x = 0.33. Compared with the case of x = 0, on the other hand, the signals in the high-energy region are much lower for x = 0.5, while the peak energy remains around E = 150~200 meV. For x = 1, ∫χ"(q, ω)dq above E = 100 meV is further low, with the peak energy decreasing to around E = 30 meV. The large reduction in the high-energy spin fluctuations with hole doping results in suppression of the total fluctuating moment, which has been estimated to be <m 2 > = 1.45 and 0.65 μ B 2 /Fe, for x = 0.5 and 1, respectively (Fig. 4). In contrast, ∫χ"(q, ω)dq in the low-energy region is almost independent of the doping level except for the sharp peak attributed to the spin resonance. Thus, the suppression of superconductivity in the hole-overdoped region cannot be due to a decrease in low-energy magnetic intensity as for electron-doped Ba(Fe,Ni) 2 As 2 7,8 .

Discussion
The present observations demonstrate that the energy scale of the dispersive spin wave is robust upon hole doping up to x = 0.5, which is followed by a rapid decrease up to x = 1 (Fig. 4). The decrease appears to be related to the appearance of the incommensurate spin structure. In fact, the band width is robust in electron-doped Ba(Fe,Co,Ni) 2 As 2 , which exhibits a commensurate spin structure except in the incommensurate AF state, which appears in a narrow doping range and has one-order smaller incommensurability than that of KFe 2 As 2 7,18 . The smaller band width of the spin wave leads to weaker effective magnetic exchange coupling J according to the Heisenberg model. The results, thus, suggest that J is correlated with the periodicity of spin fluctuations. The small value of J in KFe 2 As 2 is consistent with the fact that its electronic interaction strength U is quite large 19,20 .
The chimney-like structure can originate from particle-hole excitations, which define the itinerant character of spin fluctuations. Note that the chimney-like structure resembles the spin excitations in the itinerant AF metals Cr 21 , Cr 0.95 V 0.05 22 and Mn 2.8 Fe 0.2 Si 23 . The present results show that the band width decreases and the chimney-like dispersion appears with hole doping. This is qualitatively consistent with DFT + DMFT calculations 13,14 , which also supports the origin of the chimney-like dispersion to be particle-hole excitations.
The present observation of a large reduction in high-energy spin fluctuations upon hole doping is in contrast to the case of electron-doped Ba(Fe,Ni) 2 As 2 , where high-energy spin fluctuations are independent of doping 7 . Because hole-doped (Ba,K)Fe 2 As 2 exhibits a higher maximum T c of 38 K than electron-doped Ba(Fe,Ni) 2 As 2 (T c = 20 K) 2 even though (Ba,K)Fe 2 As 2 exhibits weaker spin fluctuations in the high-energy region, this reduction of the high-energy spin fluctuations does not appear to suppress T c . The suppression of T c in hole-overdoped (Ba,K)Fe 2 As 2 can rather be attributed to the reduction of J, which remains almost constant from non-doped to optimum-doped region and followed by rapid reduction in the overdoped region. The J dependence of the superconductivity has also been suggested in studies on spin resonance [24][25][26] . Stronger magnetic correlation leads to a larger energy split between the resonance and the superconducting gap energy. In fact, the resonance energy in overdoped (Ba,K)Fe 2 As 2 approaches the superconducting gap energy with doping up to x = 0.77 24 , which can result from the reduction of J. These results lead to the conclusion that there is a strong relationship between magnetism and superconductivity in Ba 1-x K x Fe 2 As 2 .

Method
Single crystals of Ba 0.5 K 0.5 Fe 2 As 2 (T c = 36 K) and KFe 2 As 2 (T c = 3.4 K) were grown by a KAs self-flux method 27,28 . The magnetic susceptibility was measured by a SQUID from Quantum Design.
The INS measurement was performed using the Fermi chopper spectrometer 4SEASONS in J-PARC 29 . We co-aligned 160 and 300 pieces of single crystal with x = 0.5 (~5 g) and x = 1 (~5 g), respectively. We employed the multi-E i method 30 with incident neutron energies of E i = 31, 65, 110, 202, 409, 720 meV for Ba 0.5 K 0.5 Fe 2 As 2 and E i = 30, 75, 149, 423 meV for KFe 2 As 2 . The incident beam was parallel to the c-axis. We converted signal intensities into absolute units using a vanadium standard. The data were processed by the "Utsusemi" visualization software developed at J-PARC 31 . Throughout this letter, wave vectors are specified in the orthorhombic reciprocal lattice.