Pressure-induced Lifshitz transition in FeSe_0.88S_0.12 probed via ⁷⁷Se-NMR

 

T. Kuwayama,¹² K. Matsuura,³ Y. Mizukami,³ S. Kasahara,⁴ Y. Matsuda,⁴ T. Shibauchi,³ Y. Uwatoko,⁵ N. Fujiwara²*

¹* Email: naoki@fujiwara.h.kyoto-u.ac.jp
²Graduate School of Human and Environmental Studies, Kyoto University, 606-8501 Kyoto, Japan.
³Graduate School of Frontier Sciences, University of Tokyo, 277-8581 Kashiwa, Japan.
⁴Division of Physics and Astronomy, Graduate School of Science, Kyoto 606-8502 Kyoto, Japan.
⁵Institute for Solid State Physics, University of Tokyo, 277-8581 Kashiwa, Japan.

Received: 29 October 2018, Accepted: 30 April 2019 DOI: http://dx.doi.org/10.4279/PIP.110003

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Abstract

Recently, FeSe_1-xS_x 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 exhibits anomalous enhancement at 1.0 GPa, suggesting a topological change in the Fermi surfaces, the socalled Lifshitz transition, occurs at 1.0 GPa. The magnetic fluctuation simultaneously changes its properties, which implies a change in the dominant nesting vector.

Keywords: NMR, Superconductor, Strongly correlated electron system, Iron superconductor

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I. Introduction

In contrast to most iron pnictides, FeSe undergoes 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 accompanies 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 T_s 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 T_c exhibits double-dome structure and it reaches ~ 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 T_c.

Recently, the detailed P — T phase diagram for S-substituted FeSe, FeSe_1-xS_x (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 concentration (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 mechanism of FeSe systems, the 12%-S doped sample is preffered over the pure sample, because a high T_c 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 x 1.0 x 0.5 mm⁴ was used for the measurements. We used a NiCrAl pressure cell 4 and Daphne oil as pressure transmitting médium. 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 T_c

Figure 1 shows the T dependence of the AC susceptibility at several pressures measured by the tank circuit of a NMR probe. To clarify the influence of the magnetic field on T_c, 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:

2n /L(1 + 4nx)C where L, C, and x are the coil inductance, the capacitance of the variable capacitor, and the AC susceptibility, respectively. When a sample undergoes a SC transition, f diverges due to the Meissner effect (x = — 1/4n). We determined T_c from the intersection point of linear fittings (Fig.1). T_c increases up to ^ 27 K at 3.0 GPa from T_c ^ 9 K at ambient pressure. We found that T_c at 1.0 GPa was anomalously suppressed at 6.02 T, and the system has not undergone the SC transition above 4.2 K. In contrast, T_cs at 2.0 and 3.0 GPa are slightly decreased by the field, as shown in Fig. 1.

ii. ⁷⁷Se-NMR spectra and ⁷⁷Se shift

We measured ⁷⁷Se-NMR (I = 1/2, y/2n = 8.118 MHz/T) spectra on FeSeo.ssSo.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 T_s ^ 60 K, which is in good agreement with the structural transition temperature observed by the resistivity measurements 3. Figures 2(b) and 3 show the T dependence of the ⁷⁷ Se shift at ambient pressure and the shift at several pressures, respectively. The average of the peaks below T_s 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 socalled Lifshitz transition.

 

 

iii. The relaxation rate divided by temperature, 1/Ti T

Figure 4 shows the relaxation rate divided by temperature, 1/TiT. We measured the relaxation time Ti with the inversion-recovery method for ⁷⁷Se. The relaxation rate provides a measure for the low-energy spin fluctuations. In general, an AFM fluctuation is enhanced when a system comes near an AFM phase. By contrast, the AFM fluctuation of FeSeo.ssS₀.₁₂ 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 crucial 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 reconstructed, and the reconstruction of the Fermi surfaces 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 ⁷⁷ Se-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 JP18H01181 and a grant from Mitsubishi Foundation. We thank H. Kontani and P. Toulemonde for discussion.

 

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