arXiv subjects

S. L. Bud'ko

Publications and source records attributed to S. L. Bud'ko.

At least 37 records · Page 2Linked to original sources

arXiv2023

Strong enhancement of magnetic ordering temperature and structural/valence transitions in EuPd3S4 under high pressure

We present a comprehensive study of the mixed valent compound, EuPd3S4, by electrical transport, X-ray diffraction, time-domain 151Eu synchrotron Mössbauer spectroscopy, and X-ray absorption spectroscopy measurements under high pressure. The electrical transport measurements show that the antiferromagnetic ordering temperature, TN, increases rapidly from 2.8 K at ambient pressure to 23.5 K at ~19 GPa and plateaus between ~19 and ~29 GPa after which no anomaly associated with TN is detected. A pressure-induced first order structural transition from cubic to tetragonal is observed, with a rather broad coexistence region (~20 GPa to ~32 GPa) that corresponds to the TN plateau. Mössbauer spectroscopy measurements show a clear valence transition from approximately 50:50 Eu2+:Eu3+ to fully Eu3+ at ~28 GPa, consistent with the vanishing of the magnetic order at the same pressure. X-ray absorption data show a transition to a fully trivalent state at a similar pressure. Our results show that pressure first greatly enhances TN, most likely via enhanced hybridization between the Eu 4f states and the conduction band, and then, second, causes a structural phase transition that coincides with the conversion of the europium to a fully trivalent state.

cond-mat.str-el↗

arXiv2023

Magnetic ground state and perturbations of the distorted kagome Ising metal TmAgGe

We present the magnetic orders and excitations of the distorted kagome intermetallic magnet TmAgGe. Using neutron single crystal diffraction we identify the propagation vectors $\bf{k}$ = (1/2 0 0) and $\bf{k}$ = (0 0 0) and determine the magnetic structures of the zero-field and magnetic field-induced phases for $H$ along the $a$ and [-1 1 0] crystal directions. We determine the experimental magnetic field-temperature ($H$, $T$)-phase diagram and reproduce it by Monte-Carlo simulations of an effective spin exchange Hamiltonian for one distorted kagome layer. Our model includes a strong axial single-ion anisotropy and significantly smaller exchange couplings which span up to the third-nearest neighbours within the layer. Single crystal inelastic neutron scattering (INS) measurements reveal an almost flat, only weakly dispersive mode around 7 meV that we use alongside bulk magnetization data to deduce the crystal-electric field (CEF) scheme for the Tm$^{3+}$ ions. Random phase approximation (RPA) calculations based on the determined CEF wave functions of the two lowest quasi-doublets enable an estimation of the interlayer coupling that is compatible with the experimental INS spectra. No evidence for low-energy spin waves associated to the magnetic order was found, which is consistent with the strongly Ising nature of the ground state.

cond-mat.str-el↗

arXiv2023

Interrelationships between nematicity, antiferromagnetic spin fluctuations and superconductivity: Role of hotspots in FeSe$_{1-x}$S$_{x}$ revealed by high pressure $^{77}$Se NMR study

The sulfur-substituted FeSe, FeSe$_{1-x}$S$_{x} $, is one of the unique systems that provides an independent tunability of nematicity, antiferromagnetism and superconductivity under pressure ($p$). Recently Rana et al. [Phys. Rev. B 101, 180503(R) (2020)] reported, from $^{77}$Se nuclear magnetic resonance (NMR) measurements on FeSe$_{0.91}$S$_{0.09}$ under pressure, that there exists a clear role of nematicity on the relationship between antiferromagnetic (AFM) spin fluctuations and superconducting transition temperature ($T_{\rm c}$) where the AFM spin fluctuations are more effective in enhancing $T_{\rm c}$ in the absence of nematicity than with nematicity. Motivated by the work, we carried out $^{77}$Se NMR measurements on FeSe$_{1-x}$S$_{x}$ with $x$= 0.15 and 0.29 under pressure up to 2.10 GPa to investigate the relationship in a wide range of $x$ in the FeSe$_{1-x}$S$_x$ system. Based on the new results together with the previously reported data for $x$=0 [P. Wiecki et al., Phys. Rev. B 96, 180502(R) (2017)] and 0.09 [K. Rana et al. Phys. Rev. B 101, 180503(R) (2020)], we established a $p$ - $x$ - temperature ($T$) phase diagram exhibiting the evolution of AFM spin fluctuations. From the systematic analysis of the NMR data, we found that the superconducting (SC) state in nematic state arises from a non Fermi liquid state with strong stripe-type AFM spin fluctuations while the SC state without nematicity comes from a Fermi liquid state with mild stripe-type AFM spin fluctuations. Furthermore, we show that the previously reported impact of nematicity on the relationship between AFM fluctuations and superconductivity holds throughout the wide range of $x$ from $x$ = 0 to 0.29 in FeSe$_{1-x}$S$_{x}$ under pressure. We discuss the origin of the role of nematicity in terms of the different numbers of hotspots on Fermi surfaces with and without nematicity.

cond-mat.supr-con↗

arXiv2023

Unusual coercivity and zero field stabilization of fully saturated magnetization in single crystals of LaCrGe$_3$

LaCrGe$_3$ is an itinerant, metallic ferromagnet with a Curie temperature ($T_C$) of $\sim$ 86 K. Whereas LaCrGe$_3$ has been studied extensively as a function of pressure as an example of avoided ferromagnetic quantum criticality, questions about its ambient pressure ordered state remain; specifically, whether there is a change in the nature of the ferromagnetically ordered state below $T_C$ $\sim$ 86 K. We present anisotropic $M$($H$) isotherms, coupled with anisotropic AC susceptibility data, and demonstrate that LaCrGe$_3$ has a remarkable, low temperature coercivity associated with exceptionally sharp, complete magnetization reversals to and from fully polarized states. This coercivity is temperature dependent, it drops to zero in the 40 - 55 K region and reappears in the 70 - 85 K regions. At low temperatures LaCrGe$_3$ has magnetization loops and behavior that has previously associated with micromagnetic/nanocrystalline materials, not bulk, macroscopic samples.

cond-mat.str-el↗

arXiv2023

Superconductivity and magnetic and transport properties of single-crystalline CaK(Fe$_{1-x}$Cr$_{x}$)$_{4}$As$_{4}$

Members of the CaK(Fe$_{1-x}$Cr$_{x}$)$_{4}$As$_{4}$ series have been synthesized by high-temperature solution growth in single crystalline form and characterized by X-ray diffraction, elemental analysis, magnetic and transport measurements. The effects of Cr substitution on the superconducting and magnetic ground states of CaKFe$_4$As$_4$ ($T_c$ = 35 K) have been studied. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K as $x$ is increased from 0 to 0.038. The magnetic transition temperature increases in a roughly linear manner as Cr substitution increases. A temperature-composition (\textit{T}-\textit{x}) phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature, $T^*$, appearing near 22~K for $x$ $\sim$ 0.017 and rising slowly up to 60~K for $x$ $\sim$ 0.077. The $T$-$x$ phase diagrams for CaK(Fe$_{1-x}$$T$$_{x}$)$_4$As$_4$ for $T$ = Cr and Mn are essentially the same despite the nominally different band filling; this is in marked contrast to $T$ = Co and Ni series for which the $T$-$x$ diagrams scale by a factor of two, consistent with the different changes in band filling Co and Ni would produce when replacing Fe. Superconductivity of CaK(Fe$_{1-x}$Cr$_{x}$)$_{4}$As$_{4}$ is also studied as a function of magnetic field. A clear change in $H^\prime_{c2}$($T$)/$T_c$, where $H^\prime_{c2}$($T$) is d$H_{c2}$($T$)/d$T$, at $x$ $\sim$ 0.012 is observed and probably is related to change of the Fermi surface due to magnetic order. Coherence length and the London penetration depths are also calculated based on $H_{c1}$ and $H_{c2}$ data. Coherence lengths as the function of $x$ also shows changes near $x$ = 0.012, again consistent with Fermi surfaces changes associated with the magnetic ordering seen for higher $x$-values.

cond-mat.supr-con↗

arXiv2023

Antiferromagnetic order and its interplay with superconductivity in CaK(Fe$_{1-x}$Mn$_x$)$_4$As$_4$

The magnetic order for several compositions of CaK(Fe$_{1-x}$Mn$_x$)$_4$As$_4$ has been studied by nuclear magnetic resonance (NMR), Mössbauer spectroscopy, and neutron diffraction. Our observations for the Mn-doped 1144 compound are consistent with the hedgehog spin vortex crystal (hSVC) order which has previously been found for Ni-doped $\text{Ca}\text{K}\text{Fe}_4\text{As}_4$. The hSVC state is characterized by the stripe-type propagation vectors $(π\,0)$ and $(0\,π)$ just as in the doped 122 compounds. The hSVC state preserves tetragonal symmetry at the Fe site, and only this SVC motif with simple AFM stacking along $\textbf{c}$ is consistent with all our observations using NMR, Mössbauer spectroscopy, and neutron diffraction. We find that the hSVC state in the Mn-doped 1144 compound coexists with superconductivity (SC), and by combining the neutron scattering and Mössbauer spectroscopy data we can infer a quantum phase transition, hidden under the superconducting dome, associated with the suppression of the AFM transition temperature ($T_\text{N}$) to zero for $x\approx0.01$. In addition, unlike several 122 compounds and Ni-doped 1144, the ordered magnetic moment is not observed to decrease at temperatures below the superconducting transition temperature ($T_\text{c}$).

cond-mat.str-el↗

arXiv2022

Canted Antiferromagnetic phases in the layered candidate Weyl material EuMnSb$_2$

EuMnSb$_2$ is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. We present a detailed analysis of the magnetic structure on three AFM phases based on single-crystal neutron diffraction, magnetization, and heat capacity data as well as polycrystalline $^{151}$Eu Mössbauer data. The Mn magnetic sublattice orders into a C-type AFM structure below $323(1)$~K with the ordered Mn magnetic moment $μ_{\text{Mn}}$ lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below $23(1)$~K with the ordered Eu magnetic moment $μ_{\text{Eu}}$ canted away from the layer normal and $μ_{\text{Mn}}$ retaining its higher-temperature order. $μ_{\text{Eu}}$ is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) $Pn^{\prime}m^{\prime}a^{\prime}$ with the chemical and magnetic unit cells having the same dimensions. Cooling below $=9(1)$~K reveals a third AFM phase where $μ_{\text{Mn}}$ remains unchanged but $μ_{\text{Eu}}$ develops an additional in-plane canting. This phase has MSG $P11\frac{2_1}{a^{\prime}}$. We additionally find evidence of short-range magnetic correlations associated with the Eu between $12~\text{K} \lesssim T \lesssim 30~\text{K}$. Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg-model. We then discuss implications of the various AFM states in EuMnSb$_2$ and its topological properties.

cond-mat.str-el↗

arXiv2022

Superconductivity and phase diagrams of CaK(Fe$_{1-x}$Mn$_{x}$)$_{4}$As$_{4}$ single crystals

Members of the CaK(Fe$_{1-x}$Mn$_{x}$)$_{4}$As$_{4}$ series have been synthesized in single crystalline form and characterized by elemental analysis, thermodynamic and transport measurements. These measurements show that the superconducting transition temperature decreases monotonically and is finally suppressed below 1.8 K. For $x$-values greater than 0.016, signatures of a magnetic transition can be detected in both thermodynamic and transport measurements in which kink-like features allow for the determination of the transition temperature, $T^*$, that increases as Mn substitution increases. A temperature-composition ($T$-$x$) phase diagram is constructed, revealing a half-dome of superconductivity with the magnetic transition temperature, $T^*$, appearing near 26 K for $x$ $\sim$ 0.017 and rising slowly up to 33 K for $x$ $\sim$ 0.036. Specific heat data are used to track the jump in specific heat at $T_c$; The CaK(Fe$_{1-x}$Mn$_x$)$_4$As$_4$ data does not follow the scaling of $Δ$$C_{p}$ with $T_{c}^3$ as many of the other Fe-based superconducting systems do. Elastoresistivity coefficients, $2m_{66}$ and $m_{11}-m_{12}$, as a function of temperature are also measured. $2m_{66}$ and $m_{11}-m_{12}$ are qualitatively similar to CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. This may indicate that the magnetic order in Mn substituted system may be still the same as CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. A clear change in $H^\prime_{c2}$($T$)/$T_c$, where $H^\prime_{c2}$($T$) is d$H_{c2}$($T$)/d$T$, at $x$ $\sim$ 0.015 is observed and probably is related to change of the Fermi surface due to magnetic order. Coherence lengths and the London penetration depths are also calculated based on $H_{c1}$ and $H_{c2}$ data. Coherence lengths as the function of $x$ also shows the changes near $x$ = 0.015.

cond-mat.supr-con↗

arXiv2022

Effects of magnetic and non-magnetic doping on the vortex lattice in MgB$_2$

Using small-angle neutron scattering we have studied the vortex lattice in superconducting MgB$_2$ with the magnetic field applied along the $c$-axis, doped with either manganese or carbon to achieve a similar suppression of the critical temperature. For Mn-doping, the vortex lattice phase diagram remains qualitatively similar to that of pure MgB$_2$, undergoing a field-and temperature-driven $30^{\circ}$ rotation transition, indicating only a modest effect on the vortex-vortex interaction. In contrast, the vortex lattice rotation transition is completely suppressed in the C-doped case, likely due to a change in the electronic structure which affects the two-band/two-gap nature of superconductivity in MgB2. The vortex lattice longitudinal correlation length shows the opposite behavior, remaining roughly unchanged between pure and C-doped MgB$_2$ while it is significantly reduced in the Mn-doped case. However, the extensive vortex lattice metastability and related activated behavior, observed in conjunction with the vortex lattice transition in pure MgB$_2$, is also seen in the Mn doped sample. This shows that the vortex lattice disordering is not associated with a substantially increased vortex pinning.

cond-mat.supr-con↗

arXiv2022

On the analysis of the tin-inside-H3S Mössbauer experiment

A simple analysis is presented of the particular experiment used to prove the bulk nature of very-high-Tc superconductivity in H3S compound under ultra-high pressure. In the experiment, an internal magnetic field was sensed by the synchrotron Mössbauer spectroscopy in tin placed inside the H2S sample. The experiment showed peculiar anisotropy with respect to the direction of the applied field at first sight. By considering actual experimental geometries and parameters of the experiment, we show that this particular observation is consistent with the expectations for a regular type-II superconductor with Meissner expulsion and pinning.

cond-mat.supr-con↗

arXiv2022

Effects of external pressure on the narrow gap semiconductor Ce$_{3}$Cd$_{2}$As$_{6}$

Here we report the magnetic and electronic properties of recently discovered Ce$_{3}$Cd$_{2}$As$_{6}$. At ambient pressure, Ce$_{3}$Cd$_{2}$As$_{6}$ presents a semiconducting behavior with an activation gap of 74(1)~meV. At 136~K, a sudden increase of the electrical resistivity and a peak in specific heat are consistent with a charge density wave transition. At low temperatures, antiferromagnetic order of the Ce$^{3+}$ ions occurs below $T_{\rm N} = 4.0$~K with a magnetic hard axis along the $c$-axis and a $Γ_{6} = |\pm1/2\rangle$ doublet ground state. The application of external pressure strongly suppresses the charge density wave order, which is completely suppressed above 0.8(1)~GPa, and induces a metallic ground state. No evidence for superconductivity is detected above 2~K. Conversely, the antiferromagnetic state is favored by pressure, reaching a transition temperature of 5.3~K at 3.8(1)~GPa. Notably, the resistivity anomaly characterizing the antiferromagnetic order changes with increasing pressure, indicating that two different magnetic phases might be present in Ce$_{3}$Cd$_{2}$As$_{6}$ under pressure. This change in ordering appears to be associated to the crossing of the $T_{\rm CDW}$ and $T_{\rm N}$ lines.

cond-mat.str-el↗

arXiv2021

Temperature dependent striction effect in a single crystalline Nd2Fe14B revealed using a novel high temperature resistivity measurement technique

We studied the temperature dependence of resistivity in a single crystalline Nd2Fe14B using a newly developed high temperature probe. This novel probe uses mechanical pin connectors instead of conducting glue/paste. From warming and cooling curves, the Curie temperature was consistently measured around Tc = 580 K. In addition, anomalous discrete jumps were found only in cooling curves between 400 and 500 K, but not shown in warming curves. More interestingly, when the jumps occurred during cooling, the resistivity was increased. This phenomenon can be understood in terms of temperature dependent striction effect induced by the re-orientation of magnetic domains well below the Curie temperature.

cond-mat.mtrl-sci↗

arXiv2021

Visualizing band selective enhancement of quasiparticle lifetime in a metallic ferromagnet

Electrons navigate more easily in a background of ordered magnetic moments than around randomly oriented ones. This fundamental quantum mechanical principle is due to their Bloch wave nature and also underlies ballistic electronic motion in a perfect crystal. As a result, a paramagnetic metal that develops ferromagnetic order often experiences a sharp drop in the resistivity. Despite the universality of this phenomenon, a direct observation of the impact of ferromagnetic order on the electronic quasiparticles in a magnetic metal is still lacking. Here we demonstrate that quasiparticles experience a significant enhancement of their lifetime in the ferromagnetic state of the low-density magnetic semimetal EuCd2As2, but this occurs only in selected bands and specific energy ranges. This is a direct consequence of the magnetically induced band splitting and the multi-orbital nature of the material. Our detailed study allows to disentangle different electronic scattering mechanisms due to non-magnetic disorder and magnon exchange. Such high momentum and energy dependence quasiparticle lifetime enhancement can lead to spin selective transport and potential spintronic applications.

cond-mat.str-el↗

arXiv2021

Magnetic field-induced softening of spin waves and hard-axis order in Kondo-lattice ferromagnet CeAgSb$_{2}$

A significant number of Kondo-lattice ferromagnets order perpendicular to the easy magnetization axis dictated by the crystalline electric field. The nature of this phenomenon has attracted considerable attention, but remains poorly understood. In the present paper we use inelastic neutron scattering supported by magnetization and specific heat measurements to study the spin dynamics in the hard-axis ferromagnet CeAgSb2. In the zero field state we observed two sharp magnon modes, which are associated with Ce ordering and extended up to $\approx 3 meV with a considerable spin gap of 0.6 meV. Application of a magnetic field perpendicular to the moment direction reduces the spectral intensity and suppresses the gap and significantly enhances the low-temperature specific heat at a critical field of Bc ~ 2.8 T via a mean-field-like transition. Above the transition, in the field polarized state, the gap eventually reopens due to the Zeeman effect. We modeled the observed dispersion using linear spin-wave theory (LSWT) taking into account the ground state Gamma 6 doublet and exchange anisotropy. Our model correctly captures the essential features of the spin dynamics including magnetic dispersion, distribution of the spectral intensity as well as the field-induced behavior, although several minor features remain obscure. The observed spectra do not show significant broadening due to the finite lifetime of the quasiparticles. Along with a moderate electronic specific heat coefficient gamma = 46 mJ/mol K2 this indicates that the Kondo coupling is relatively weak and the Ce moments are well localized. Altogether, our results provide profound insight into the spin dynamics of the hard-axis ferromagnet CeAgSb2 and can be used as solid ground for studying magnetic interactions in isostructural compounds including CeAuSb2, which exhibits nematicity and unusual mesoscale magnetic textures.

cond-mat.str-el↗

arXiv2021

Magnetic properties of the itinerant ferromagnet LaCrGe3 under pressure studied by 139La NMR

$^{139}$La nuclear magnetic resonance (NMR) measurements under pressure ($p = 0-2.64$ GPa) have been carried out to investigate the static and dynamic magnetic properties of the itinerant ferromagnet LaCrGe$_3$. $^{139}$La-NMR spectra for all measured pressures in the ferromagnetically ordered state show a large shift due to the internal field induction $|$$B_{\rm int}$$|$ $\sim$ 4 T at the La site produced by Cr ordered moments. The change in $B_{\rm int}$ by less than 5\% with $p$ up to 2.64~GPa indicates that the Cr 3$d$ moments are robust under pressure. The temperature dependence of NMR shift and $B_{\rm int}$ suggest that the ferromagnetic order develops below $\sim$ 50~K under higher pressures in a magnetic field of $\sim$ 7.2 T. Based on the analysis of NMR data using the self-consistent-renormalization (SCR) theory, the spin fluctuations in the paramagnetic state well above $T_{\rm C}$ are revealed to be three dimensional ferromagnetic throughout the measured $p$ region.

cond-mat.str-el↗

arXiv2021

Magnetic crystalline-symmetry-protected axion electrodynamics and field-tunable unpinned Dirac cones in EuIn2As2

Knowledge of magnetic symmetry is vital for exploiting nontrivial surface states of magnetic topological materials. EuIn$_{2}$As$_{2}$ is an excellent example, as it is predicted to have collinear antiferromagnetic order where the magnetic moment direction determines either a topological-crystalline-insulator phase supporting axion electrodynamics or a higher-order-topological-insulator phase with chiral hinge states. Here, we use neutron diffraction, symmetry analysis, and density functional theory results to demonstrate that EuIn$_{2}$As$_{2}$ actually exhibits low-symmetry helical antiferromagnetic order which makes it a stoichiometric magnetic topological-crystalline axion insulator protected by the combination of a 180$^{\circ}$ rotation and time-reversal symmetries: $C_{2}\times\mathcal{T}=2^{\prime}$. Surfaces protected by $2^{\prime}$ are expected to have an exotic gapless Dirac cone which is unpinned to specific crystal momenta. All other surfaces have gapped Dirac cones and exhibit half-integer quantum anomalous Hall conductivity. We predict that the direction of a modest applied magnetic field of $H\approx1$ to $2$ T can tune between gapless and gapped surface states.

cond-mat.str-el↗

arXiv2020

Magnetic detwinning and biquadratic magnetic interaction in EuFe2As2 revealed by 153Eu NMR

In the nematic state of iron-based superconductors, twin formation often obscures the intrinsic, anisotropic, in-plane physical properties.Relatively high in-plane external magnetic fields $H_{\rm ext}$ greater than the typical lab-scale magnetic fields 10--15 T are usually required to completely detwin a sample. However, recently a very small in-plane $H_{\rm ext} \sim$ 0.1 T was found to be sufficient for detwinning the nematic domains in EuFe$_2$As$_2$. To explain this behavior, a microscopic theory based on biquadratic magnetic interactions between the Eu and Fe spins has been proposed. Here, using $^{153}$Eu nuclear magnetic resonance (NMR) measurements below the Eu$^{2+}$ ordering temperature, we show experimental evidence of the detwinning under small in-plane $H_{\rm ext}$. Our NMR study also reveals the evolution of the angles between the Eu and Fe spins during the detwinning process, which provides the first experimental evidence for the existence of biquadratic coupling in the system.

cond-mat.str-el↗

arXiv2020

Impact of Nematicity on the Relationship between Antiferromagnetic Fluctuations and Superconductivity in FeSe0.91S0.09 Under Pressure

The sulfur substituted FeSe system, FeSe$_{1-x}$S$_{x}$, provides a versatile platform for studying the relationship between nematicity, antiferromagnetism, and superconductivity. Here, by nuclear magnetic resonance (NMR) and resistivity measurements up to 4.73 GPa on FeSe$_{0.91}$S$_{0.09}$, we established the pressure($p$)-temperature($T$) phase diagram in which the nematic state is suppressed with pressure showing a nematic quantum phase transition (QPT) around $p$ = 0.5 GPa, two SC regions, separated by the QPT, appear and antiferromagnetic (AFM) phase emerges above $\sim$3.3 GPa. From the NMR results up to 2.1 GPa, AFM fluctuations are revealed to be characterized by the stripe-type wavevector which remains the same for the two SC regions. Furthermore, the electronic state is found to change in character from non-Fermi liquid to Fermi liquid around the nematic QPT and persists up to $\sim$ 2.1 GPa. In addition, although the AFM fluctuations correlate with $T_{\rm c}$ in both SC states, demonstrating the importance of the AFM fluctuations for the appearance of SC in the system, we found that, when nematic order is absent, $T_{\rm c}$ is strongly correlated with the AFM fluctuations, whereas $T_{\rm c}$ weakly depends on the AFM fluctuations when nematic order is present. Our findings on FeSe$_{0.91}$S$_{0.09}$ were shown to be applied to the whole FeSe$_{1-x}$S$_{x}$ system and also provide a new insight into the relationship between AFM fluctuations and SC in Fe-based superconductors.

cond-mat.str-el↗