Resistivity and magnetoresistance of FeSe single crystals under helium-gas pressure

We present temperature-dependent in-plane resistivity measurements on FeSe single crystals under He-gas pressure up to 800 MPa and magnetic fields $B\le 10$ T. A sharp phase transition anomaly is revealed at the tetragonal-to-orthorhombic transition at $T_s$ slightly below 90 K. $T_s$ becomes reduced with increasing pressure in a linear fashion at a rate $d{T}_s/dP\simeq -31$ K/GPa. This is accompanied by a $P$-linear increase of the superconducting transition temperature at $T_c\sim 8.6$ K with $d{T}_c/dP\simeq +5.8$ K/GPa. Pressure studies of the normal-state resistivity highlight two distinctly different regimes: for $T>T_s$, i.e., in the tetragonal phase, the in-plane resistivity changes strongly with pressure. This contrasts with the state deep in the orthorhombic phase at $T\ll T_s$, preceding the superconducting transition. Here, a $T$-linear resistivity is observed the slope of which does not change with pressure, pointing against a spin-fluctuation origin of this term. Resistivity studies in varying magnetic fields both at ambient and finite pressure reveal clear changes of the magnetoresistance, $\Delta \rho \propto B^2$, upon cooling through $T_s$. Our data are consistent with a reconstruction of the Fermi surface accompanying the structural transition.

Figure 1

Normalized in-plane resistance of three FeSe single crystals (1 and 3 studied in this work and a crystal investigated by Kasahara et al. [33]) from the same source (Karlsruhe Institute of Technology, KIT). The inset shows the data around the superconducting transition on enlarged scales.

Figure 2

Electrical resistivity of single crystalline FeSe (sample 1) at varying pressures up to $P=780$ MPa applied at 100 K. The inset shows the evolution of the pressure, initially set to $P=590$ MPa, upon cooling. An abrupt pressure loss of about 30% occurs due to the solidification of the helium at 46 K for this pressure value.

Figure 3

In-plane resistivity data for single crystalline FeSe slightly above and around the superconducting transition temperature under varying hydrostatic pressure values up to 780 MPa. The onset of superconductivity, $T_c^{\mathrm{onset}}$, is defined as the point where the data deviate from the in-$T$ linear low-temperature behavior, and $T_c^{\mathrm{mid}}$ where the drop amounts to 50% of the extrapolated linear behavior.

Figure 4

Temperature variation of the slopes $A_i$, determined as described in the text, for $P=0$, 110, 230, and 350 MPa. The inset shows the in-plane resistivity data for sample 1 at $P=0$ and 110 MPa for $T\le 70$ K. $T_0$ (up arrow) marks the temperature above which $A_i\left(T\right)$ departs from the average slope (represented by the black solid line) by one standard deviation. $T_{\mathrm{He}}^{\mathrm{solid}}$ (down arrow) indicates the solidification temperature of ${}^4\mathrm{He}$. The data for $P=110$ MPa were shifted vertically for clarity.

Figure 5

Compilation of the transition temperatures $T_s\left(P\right)$ and $T_c\left(P\right)$ in a temperature-pressure phase diagram for FeSe derived from this work (filled symbols). $T_{\mathrm{He}}^{\mathrm{solid}}$ (orange solid line) marks the solidification line of helium used as a pressure-transmitting medium. For those pressures where $T_c\left(P\right)$ lies below $T_{\mathrm{He}}^{\mathrm{solid}}\left(P\right)$, the corresponding pressure values have been corrected for the 30% pressure loss accompanying the solidification of helium, cf. the inset of figure 2. Also shown are the pressure data reported by Miyoshi et al. [35] taken on single crystalline FeSe employing oil as a pressure-transmitting medium: $T_s\left(P\right)$ (blue open circles) and $T_c^{\mathrm{zero}}$ (red open circles) were obtained via transport measurements, $T_c^{\mathrm{diamag}}$ (black open symbols and black solid line) corresponds to the onset of diamagnetism in susceptibility measurements.

Figure 6

In-plane resistivity of single crystalline FeSe (sample 1) at ambient pressure for magnetic fields $B\le 9$ T aligned parallel to the $ab$ plane (a) and parallel to the $c$ axis (b). The insets show the data in the vicinity of the superconducting transition on expanded scales.

Figure 7

Normalized in-plane magnetoresistance $\Delta {\rho }_{ab}$ = ${\rho }_{ab}\left(B\right)-{\rho }_{ab}\left(0\right)$ measured at temperatures slightly below (red solid line for $T_1=81$ K) and above (black solid line for $T_2=89$ K) the structural transition at $T_s=86.5$ K of sample 2 plotted vs $B^2$. Thin straight lines are guides to the eyes. The inset shows the slopes $d(\Delta {\rho }_{ab}/{\rho }_{ab})/d{B}^2$ vs temperature for sample 1 (filled triangles) and sample 2 (filled circles) derived from isothermal field sweeps as shown in the main panel. The arrows at $T_s$ mark the structural transition temperatures as determined from the kinks in the resistivity.

Figure 8

Temperature dependence of the in-plane resistivity for single crystalline FeSe sample 1 under hydrostatic pressure of (a) 690 and (b) 780 MPa measured in $B=0$ (black lines) and 10 T (red lines) applied parallel to the $c$ axis. The insets show the data around the structural transition $T_s$ marked by an up arrow. The down arrows indicate the solidification temperature at the given pressure value.