Room temperature local nematicity in FeSe superconductor

We report pair distribution function measurements of the iron-based superconductor FeSe above and below the structural transition temperature. Structural analysis reveals a local orthorhombic distortion with a correlation length of about 4 nm at temperatures where an average tetragonal symmetry is observed. The analysis further demonstrates that the local distortion is larger than the global distortion at temperatures where the average observed symmetry is orthorhombic. Our results suggest that the low-temperature macroscopic nematic state in FeSe forms from an imperfect ordering of orbital-degeneracy-lifted nematic fluctuations which persist up to at least 300 K.

Figure 1

Perspective view of the FeSe structure with tetragonal symmetry. Iron is shown in brown, and selenium in green. Pair distances constrained by tetragonal symmetry to be identical are highlighted by dashed lines of the same color. Tetragonal symmetry allows only a single Fe-Fe pair distance (brown dashed lines), and the orthorhomic distortion allows these distances to differentiate. The three unique Se-Se pair distances shown by red, green, and blue dashed lines become five distinct Se-Se pairs within the orthorhombic symmetry.

Figure 2

The signature of local nematicity. PDF of best-fit model (red solid line) to observed data (open circles) from FeSe at 300 K, fitted up to $r=50\AA$ using the tetragonal model (overall $R_w=0.08$). The fit is presented over the abbreviated range $1.5<r<15\AA$ for clarity. The difference curve is shown displaced below (green solid line), and shaded to highlight the signature of local nematicity. $R_w$ values over selected abbreviated $r$ ranges are presented to highlight low-$r$ misfit. Different coloring of the $x$ axes of two panels signals that the scales are distinct to highlight the signal at low $r$. The $y$-axis scales are preserved between the two panels. Importantly, there is also a subtle misfit of the Fe-Fe peak at 2.7 Å (see text for details).

Figure 3

PDF of best-fit model (red solid line) and observed data (open circles) from FeSe at 300 K, fitted up to $r=5\AA$ using orthorhombic (nematic) symmetry constraints ($R_w=0.04$). The difference curve is shown displaced below (green solid line). $R_w$ values over selected $r$ ranges are presented to highlight the discrepancy between the optimal local structure and the observed average structure. Different coloring of the $x$ axes of two panels signals that the scales are distinct to highlight the signal at low $r$. The $y$-axis scales are preserved between the two panels. The orthorhombic model provides an observably better account of the Fe-Fe NN PDF peak as compared to the tetragonal model (Fig. 2).

Figure 4

The measured orthorhombic distortion obtained by using an orthorhombic model over a narrow $r$ range, $\eta$, is plotted vs the PDF fit window center, $r_m$, for data measured at 300 (orange line) and 84 K (blue line). The value of $\eta$ at 84 K as extracted from the average structure is represented by the dashed horizontal line. Inset is a top view of the FeSe crystal structure, schematically showing the projected orientations of the Fe $3d_{yz}$ and $3d_{xz}$ orbitals implicated in this work and elsewhere. Atom and dashed line colors are consistent with Fig. 1 and the axes labels are consistent with the orthorhombic setting. Full PDF fits associated with the distortion magnitudes in this plot are shown in Fig. S2 in Ref. [16].