Drastic field-induced resistivity upturns as signatures of unconventional magnetism in superconducting iron chalcogenides

Abstract

Electronic scattering is a powerful tool to identify underlying changes in electronic behavior and incipient electronic and magnetic orders. The nematic and magnetic phases are strongly intertwined under applied pressure in FeSe, however, the additional isoelectronic substitution of sulphur offers an elegant way to separate them. Here we report the detailed evolution of the electronic and superconducting behaviour of FeSe$_{0.96}$S$_{0.04}$ under applied pressure via longitudinal magnetoresistance studies up to 15T. At intermediate pressures, inside the nematic phase, the resistivity displays an upturn in zero magnetic field, which is significantly enhanced in the magnetic field, suggesting the stabilization of a spin-density wave phase, which competes with superconductivity. At higher pressures, beyond the nematic phase boundaries, the resistivity no longer displays any clear anomalies in the zero magnetic field, but an external magnetic field induces significant upturns in resistivity reflecting a field-induced order, where superconductivity and magnetic anomalies are enhanced in tandem. This study highlights the essential role of high magnetic fields in stabilizing different electronic phases and revealing a complex interplay between magnetism and superconductivity tuned by applied pressure in FeSe$_{1-x}$S$_{x}$.

Figures (3)

• Figure 1: The evolution of the transport behaviour under pressure in FeSe$_{0.96}$S$_{0.04}$.(a)-(b) Longitudinal resistivity $\rho_{xx}$ against temperature tuned under different applied pressure for samples S1 and S2. The down arrows mark the nematic transition temperature at $T_{\rm s}$, whereas the up arrows indicate the minimum in the first-order derivative at $T_{\rm{m}}$. The curves are shifted vertically for easier visualization. (c) The pressure dependence of the resistivity at different fixed temperatures. Shaded gray areas indicate boundaries between different electronic phases at $p_1$ and $p_2$. (d) The relative changes in the superconducting transition width, $\Delta T_{\rm c}/T_{\rm c} = (T_{\rm c,mid} - T_{\rm c, off})/T_{\rm c, mid}$, where $T_{\rm c,mid}$ is defined as the peak in first derivative (see Fig. S1 in the SM SM) for sample S1 (solid circles), S2 (solid diamonds), Fe$_{1-z}$Cu$_z$Se, $z=0.0025$ (after Ref. Zajicek2022) versus applied pressure. Shaded gray areas indicate phase boundaries between different electronic phases at $p_1$ and $p_2$.
• Figure 2: The magnetoresistance of FeSe$_{0.96}$S$_{0.04}$ for sample S2 tuned by applied pressure.(a) - (d). Temperature dependence of the longitudinal resistivity in magnetic fields of up to 15 T under pressures equal or greater than $p_1 \sim 10.6$ kbar. (e) - (h) The corresponding first derivatives of $\rho_{\rm xx}$ with respect to temperature related to raw data in panels (a) - (d) The development of the new field-induced phase are defined as the minimum in the derivative at $T_{\rm m}$ and the local minimum in resistivity data at $T_{\rm MI}$, whereas critical temperature is defined here as the maximum in the derivative at the midpoint transition, $T_{\rm c, mid}$ (see Figs. S1 and S2 in the SM SM). The magnetic field-temperature phase diagram indicating the different electronic phases, nematic (purple), magnetic M1 and M2 (green), superconducting SC1 and SC2 (red). The dashed lines close to the superconducting transition in zero magnetic field indicate the broadening of the superconducting transition widths close to $p_2$.
• Figure 3: Comparison of the $p-T$ phase diagrams and field-induced effects of FeSe$_{0.96}$S$_{0.04}$ under applied pressure.(a) Pressure-temperature phase diagram of FeSe$_{0.96}$S$_{0.04}$ for sample S1 (solid symbols) and sample S2 (open symbols) indicating the different competing electronic phases: nematic up to $p_1$ (purple area), magnetic (M1 green area) ($p_1<p<p_2$) and superconducting (SC1 and SC2). (b) The phase diagram of FeSe$_{0.96}$S$_{0.04}$ and Fe$_{0.9975}$Cu$_{0.0025}$Se in reduced temperature units in relation to their $T_{\rm s}$, $t=T/T_{\rm s}$. (c) Pressure-temperature phase diagram of FeSe and FeSe$_{0.96}$S$_{0.04}$ in magnetic fields. Symbols correspond to FeSe$_{0.96}$S$_{0.04}$ for samples S1 (solid green squares in 16 T) and S2 (solid triangles in 14 T) and FeSe (open circles in 16 T) after Ref. GuanYu2019. The green shaded region represents the magnetic phases in field (M1 and M2). (d) The pressure dependence of the effective energy, $\Delta_M$ (on the left $y$ axis) together with $k_{\rm B} T_{\rm m}$ in 15 T (on the right $y$ axis). $\Delta_m$ is defined from the slope from $\log \rho$ versus $1/T$ in (see Fig. S3 for S1 and Fig. S4 for S2 in the SM SM). (e) The field dependence of the relative changes in the magnetic transition, $\Delta T_{\rm m}/T_{\rm m} = [T_{\rm m}(\mu_0 H) - T_{\rm m}({\rm 15~T})]/T_{\rm}$(15 T), where $T_{\rm m}$ is taken as the minimum in the first derivative (see Fig. \ref{['Fig2_x4_TZ2_rhoxx_vs_T_fixB_fixp']}( e- h)). (f) The variation of the effective activation energy, $\Delta_m$, as a function of square root of magnetic field, $H^{0.5}$, for different pressures for sample S2 (see Fig. \ref{['Fig2_x4_TZ2_rhoxx_vs_T_fixB_fixp']}(a-d) and Fig. S5 in the SM SM). The solid line is a linear fit to the data and the curved lines are guides to the eye.