Papers in Physics, vol. 11, art. 110003 (2019) Received: 29 October 2018, Accepted: 30 April 2019 Edited by: A. Goñi, A. Cantarero, J. S. Reparaz Licence: Creative Commons Attribution 4.0 DOI: http://dx.doi.org/10.4279/PIP.110003 www.papersinphysics.org ISSN 1852-4249 Pressure-induced Lifshitz transition in FeSe0.88S0.12 probed via 77Se-NMR T. Kuwayama,1 K. Matsuura,2 Y. Mizukami,2 S. Kasahara,3 Y. Matsuda,3 T. Shibauchi,2 Y. Uwatoko,4 N. Fujiwara1∗ Recently, FeSe1−xSx systems have received much attention because of the unique pressure– temperature phase diagram. We performed 77Se-NMR measurements on a single crystal of FeSe0.88S0.12 to investigate its microscopic properties. The shift of 77Se spectra ex- hibits anomalous enhancement at 1.0 GPa, suggesting a topological change in the Fermi surfaces, the so-called Lifshitz transition, occurs at 1.0 GPa. The magnetic fluctuation simultaneously changes its properties, which implies a change in the dominant nesting vector. I. Introduction In contrast to most iron pnictides, FeSe under- goes nematic and superconducting (SC) transitions without any magnetism: in iron pnictides, such as the BaFe2As2 family, a SC phase emerges near an antiferromagnetic (AFM) phase, which accom- panies a tetragonal-to-orthorhombic transition so called a nematic transition [1]. The electronic state of FeSe dramatically changes under pres- sure [2]. The nematic transition temperature Ts is suppressed with increasing pressure and the AFM order is induced instead. These phases overlap each other in the pressure range of 1.2 GPa < P < 2.0 GPa. The SC transition temperature Tc exhibits double-dome structure and it reaches ∗Email: naoki@fujiwara.h.kyoto-u.ac.jp 1 Graduate School of Human and Environmental Studies, Kyoto University, 606-8501 Kyoto, Japan. 2 Graduate School of Frontier Sciences, University of Tokyo, 277-8581 Kashiwa, Japan. 3 Division of Physics and Astronomy, Graduate School of Science, Kyoto 606-8502 Kyoto, Japan. 4 Institute for Solid State Physics, University of Tokyo, 277-8581 Kashiwa, Japan. ∼ 37 K at 6.0 GPa. Such complicated pressure- temperature (P − T) phase diagram makes it diffi- cult to understand the origin of the high Tc. Recently, the detailed P − T phase diagram for S-substituted FeSe, FeSe1−xSx (0 < x < 0.17), has been obtained from the resistivity measurements [3]. Intriguingly, the nematic and AFM phases are completely separated in the intermediate S concen- tration (0.04 < x < 0.12). In these compositions, the SC dome appears in a moderate pressure region. Therefore, a bare SC phase is more easily attainable than pure FeSe. To understand the pairing mech- anism of FeSe systems, the 12%-S doped sample is preffered over the pure sample, because a high Tc over 25 K is attainable at low pressures (∼ 3 GPa), and it is free from complicated overlapping of the nematic, SC, and AFM states. II. Experimental Methods We performed 77Se-NMR measurements on a 12%- S doped single crystal, FeSe0.88S0.12, up to 3.0 GPa with a fixed field of 6.02 T applied parallel to the a axis. A single crystal with dimensions of about 1.0×1.0×0.5 mm3 was used for the measurements. We used a NiCrAl pressure cell [4] and Daphne oil 110003-1 Papers in Physics, vol. 11, art. 110003 (2019) / Kuwayama et al. !"# !$# Figure 1: The T dependence of the AC susceptibility at several pressures. (a) and (b) show the AC susceptibil- ities at zero field and 6.02 T, respectively. The dashed lines correspond to the linear fittings, and the inter- section points represent the superconducting transition points, Tcs. as pressure transmitting medium. The pressure was determined by Ruby fluorescence measurements [4]. We placed the crystal in the pressure cell so that the FeSe plane was parallel to the applied field. III. Experimental Results i. Determination of Tc Figure 1 shows the T dependence of the AC suscep- tibility at several pressures measured by the tank circuit of a NMR probe. To clarify the influence of the magnetic field on Tc, we measured the suscep- tibilities not only at zero field, but also at 6.02 T. A resonant frequency of the circuit f is expressed as follows: f = 1 2π √ L(1 + 4πχ)C (1) where L, C, and χ are the coil inductance, the ca- pacitance of the variable capacitor, and the AC sus- ceptibility, respectively. When a sample undergoes a SC transition, f diverges due to the Meissner ef- fect (χ = −1/4π). We determined Tc from the intersection point of linear fittings (Fig.1). Tc in- creases up to ∼ 27 K at 3.0 GPa from Tc ∼ 9 K at ambient pressure. We found that Tc at 1.0 GPa was 0.32 0.31 0.30 0.29 0.28 K ( % ) 1208040 T (K) K a K b 20 15 10 5 0 S p in E c h o I n te n si ty ( a rb .u .) 49.0449.0249.0048.9848.96 Frequensy (MHz) 40K 50K 60K 4K 10K 20K 65K 70K 80K 90K 100K 30K !"# !$# Figure 2: (a) The T evolution of 77Se spectrum at am- bient pressure. The black dashed line shows peak fre- quencies. (b) The 77Se shift at ambient pressure deter- mined from a single Gaussian fit. Ka and Kb reflect the high and low frequency peak, respectively. anomalously suppressed at 6.02 T, and the system has not undergone the SC transition above 4.2 K. In contrast, Tcs at 2.0 and 3.0 GPa are slightly de- creased by the field, as shown in Fig. 1. ii. 77Se-NMR spectra and 77Se shift We measured 77Se-NMR (I = 1/2, γ/2π = 8.118 MHz/T) spectra on FeSe0.88S0.12 with a fixed field of 6.02 T. Figure 2(a) shows the T evolution of the spectra at ambient pressure. A single 77Se signal in a tetragonal state (T > 60 K) becomes a double-peak structure below Ts ∼ 60 K, which is in good agreement with the structural transition tem- perature observed by the resistivity measurements [3]. Figures 2(b) and 3 show the T dependence of the 77Se shift at ambient pressure and the shift at several pressures, respectively. The average of the peaks below Ts is plotted for the data at ambient pressure in Fig. 3. The shift K is proportional to the density of states (DOS). In general, the DOS changes monotonically with increasing pressure due to a change in the bandwidth. In our sample, how- ever, the DOS is enhanced at 1.0 GPa, and then it reduces with increasing pressure. As discussed below, the origin of this anomalous P dependence of the DOS could be interpreted as a topological change in the Fermi surfaces, the so-called Lifshitz transition. 110003-2 Papers in Physics, vol. 11, art. 110003 (2019) / Kuwayama et al. 0.305 0.300 0.295 0.290 0.285 K a v ( % ) 3.02.01.00.0 P (GPa) 0.32 0.31 0.30 0.29 0.28 0.27 K ( % ) 120100806040 T (K) ambient 1.0 GPa 2.0 GPa 3.0 GPa Figure 3: The 77Se shift in the non-SC state at several pressures. The average of Ka and Kb is plotted below 60 K. The inset shows the 77Se shift at 70 K, reflecting the pressure dependence of the DOS. iii. The relaxation rate divided by temper- ature, 1/T1T Figure 4 shows the relaxation rate divided by tem- perature, 1/T1T . We measured the relaxation time T1 with the inversion-recovery method for 77Se. The relaxation rate provides a measure for the low- energy spin fluctuations. In general, an AFM fluc- tuation is enhanced when a system comes near an AFM phase. By contrast, the AFM fluctuation of FeSe0.88S0.12 is strongly suppressed at 1.0 GPa and is slightly enhanced above 2.0 GPa, although the AFM phase is induced above 3.0GPa. IV. Discussion From the results mentioned above, we suggest that the Lifshitz transition at around 1.0 GPa is cru- cial to understand the anomalies of FeSe0.88S0.12. Firstly, the DOS suggested from the 77Se shift shows that some kind of anomaly occurs at 1.0 GPa as mentioned above (see the inset of Fig. 3). Ac- cording to a recent theoretical investigation in FeSe, a Lifshitz transition may occur with reducing the lattice constants [5]. S-substitution is isovalent and S-substituted FeSe has smaller lattice constants than pure FeSe [6]. Furthermore, applying pressure also causes the lattice compression. In our sample, FeSe0.88S0.12, therefore, the Lifshitz transition may account for the anomaly in the DOS. Assuming that the Lifshitz transition occurs at around 1.0 GPa, the Fermi surfaces are recon- 100 80 60 40 20 0 T ( K ) 86420 P (GPa) !" #$% &'()*+, Figure 4: The T dependence of the relaxation rate di- vided by T , 1/T1T . The dashed lines are a guide to the eye. The inset shows the phase diagram of FeSe0.88S0.12 determined from the resistivity measurements [3]. structed, and the reconstruction of the Fermi sur- faces could induce a change in the dominant nesting vector. When the dominant nesting vector changes, it is possible that the AFM fluctuation at 3.0 GPa become weaker than that at ambient pressure, even though the AFM phase appears in a high pressure region. To clarify this scenario, it is necessary to determine the spin configuration of the pressure- induced AFM phase from the measurements in the higher pressure region. V. Conclusions We carried out 77Se-NMR measurements on FeSe0.88S0.12, and the 77Se shift suggests that the DOS exhibits an anomalous enhancement at 1.0 GPa. The Lifshitz transition, the change in topology of Fermi surface, could account for this anomaly. The Fermi surfaces are reconstructed due to the Lifshitz transition, resulting in a change of the dominant nesting vector. This is the reason why the AFM fluctuation at ambient pressure is stronger than that at 3.0 GPa despite the AFM order being induced above 3.0 GPa. Acknowledgements - The NMR work was supported by JSPS KAKENHI Grant Number 110003-3 Papers in Physics, vol. 11, art. 110003 (2019) / Kuwayama et al. JP18H01181 and a grant from Mitsubishi Founda- tion. We thank H. Kontani and P. Toulemonde for discussion. [1] R M Fernandes, A V Chubukov, J Schmalian, What drives nematic order in iron-based su- perconductor?, Nat. Phys. 10, 97 (2014). 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