Pressure evolution of the low-temperature crystal structure and bonding of the superconductor FeSe $\left(T_c=37\text{K}\right)$

$\alpha \text{-FeSe}$ with the PbO structure is a key member of the family of high-$T_c$ iron pnictide and chalcogenide superconductors, as while it possesses the basic layered structural motif of edge-sharing distorted ${\text{FeSe}}_4$ tetrahedra, it lacks interleaved ion spacers or charge-reservoir layers. We find that the application of hydrostatic pressure first rapidly increases $T_c$ which attains a broad maximum of 37 K at $\sim 7\text{GPa}$ before decreasing to 6 K upon further compression to $\sim 14\text{GPa}$. Complementary synchrotron x-ray diffraction at 16 K was used to measure the low-temperature isothermal compressibility of $\alpha \text{-FeSe}$, revealing an extremely soft solid with a bulk modulus, $K_0=30.7\left(1.1\right)\text{GPa}$ and strong bonding anisotropy between interlayer and intralayer directions that transforms to the more densely packed $\beta$ polymorph above $\sim 9\text{GPa}$. The nonmonotonic $T_c\left(P\right)$ behavior of FeSe coincides with drastic anomalies in the pressure evolution of the interlayer spacing, pointing to the key role of this structural feature in modulating the electronic properties.

Figure 1

(Color online) Resistance against temperature for FeSe at several applied pressures for (a) run 1 and (b) run 2.

Figure 2

(Color online) Final observed (red circles) and calculated (blue solid line) synchrotron x-ray $\left(\lambda =0.41118\text{Å}\right)$ powder-diffraction profiles at 16 K for the FeSe sample at (a) 0.25 GPa, (b) 4.0 GPa, (c) 9.0 GPa, and (d) 12.1 GPa. The lower green solid lines show the difference profiles and the tick marks show the reflection positions of the $\alpha$-(upper) and $\beta$-(lower) phases, respectively. The diffraction profile collected at 12.1 GPa clearly shows the $\alpha \to \beta$ phase transformation. The $\beta$ phase undergoes a phase transition from hexagonal to orthorhombic at 6.0 GPa.

Figure 3

(Color online) Pressure dependence of: (a) the orthorhombic lattice constants $a$ (circles), $b$ (diamonds), and $c$ (squares), (b) the unit-cell volume, $V$, (c) the $\left[2c/\left(a+b\right)\right]$ ratio, and (d) the superconducting transition temperature, $T_c$ (runs 1–3) of $\alpha \text{-FeSe}$. The inset in (b) shows the pressure dependence of the $\alpha \text{-FeSe}$ phase fraction at 16 K. The solid lines through the data points to 7.5 GPa in (a) and (b) are least-squares fits to the Birch-Murnaghan equation of state while the dotted lines are guides to the eye.

Figure 4

(Color online) [(a)–(c)] Pressure dependence of: (a) the Fe-Se bond distances, (b) the three distinct Se-Fe-Se bond angles, and (c) the interlayer Se-Se contacts and the height of the Se atoms above the Fe plane for the orthorhombic crystal structure of $\alpha \text{-FeSe}$ at 16 K. (d) Schematic diagram of the crystal structure of $\alpha \text{-FeSe}$ with selected distances at 16 K and 0.25 GPa. (e) Geometry of the ${\text{FeSe}}_4$ units and definition of the three Se-Fe-Se bond angles together with their values at 16 K and 0.25 GPa. (f) Pressure dependence of the $\left[\left(a+b\right)/2c\right]$ ratio at 16 K and the superconducting $T_c$ of $\alpha \text{-FeSe}$. The lines through the points are guides to the eye.