Suppression of orbital ordering by chemical pressure in ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$

We report a high-resolution angle-resolved photoemission spectroscopy study of the evolution of the electronic structure of ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ single crystals. Isovalent S substitution onto the Se site constitutes a chemical pressure which subtly modifies the electronic structure of FeSe at high temperatures and induces a suppression of the tetragonal-symmetry-breaking structural transition temperature from 87 to 58 K for $x=0.15$. With increasing S substitution, we find smaller splitting between bands with $d_{yz}$ and $d_{xz}$ orbital character and weaker anisotropic distortions of the low-temperature Fermi surfaces. These effects evolve systematically as a function of both S substitution and temperature, providing strong evidence that an orbital ordering is the underlying order parameter of the structural transition in ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$. Finally, we detect the small inner hole pocket for $x=0.12$, which is pushed below the Fermi level in the orbitally ordered low-temperature Fermi surface of FeSe.

Figure 1

High-temperature electronic structure of ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$. ARPES data for (a) $x=0$ and (b) $x=0.15$ for the holelike bands at the $Z$ point (measured using a photon energy of 23 eV). (c) Band dispersions from a DFT calculation at the $Z$ point, compared to (d) the extracted peak positions (from fits to MDCs) for $x=0$ and $x=0.15$. (e)–(h) ARPES data, DFT calculation, and extracted band positions for the electron pockets at the $M$ point (at 37 eV). The predicted outer electron band $\delta$ with $d_{xy}$ orbital character is not observed. Bands are labeled $\alpha -\epsilon$, as in previous studies [10, 18].

Figure 2

Suppression of orbital ordering with S substitution on the electron pockets. (a)–(h) ARPES data for a cut through the $M$ point ($\mathrm{\Gamma }-M-\mathrm{\Gamma }$ direction) at low and high temperatures for ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$ with $x=0–0.15$ showing the prominent splitting of intensity below $T_s$. (i) High- and (j) low-temperature Fermi surface maps for $x=0.15$. Cartoon insets show schematic Fermi surface above $T_s$ (top), which is distorted below $T_s$ (middle), and the experimental case of twinned crystals where the $d_{xy}$ electron band is not observed (bottom). (k) Comparison of low-temperature EDCs at the $M$ point showing the reduction of the splitting parameter, ${\mathrm{\Delta }}_M$, with S substitution. (l) Temperature dependencies of the Fermi $k_F$ vector of the $d_{yz}$ portion of the Fermi surface, indicating a distortion $\mathrm{\Delta }{k}_F$ which onsets at $T_s$. The temperature dependence of the extracted order parameters of the orbital ordering, (m) ${\mathrm{\Delta }}_M$ and (n) $\mathrm{\Delta }{k}_F$, as a function of S substitution, as discussed in the main text. Solid lines are guides to the eye.

Figure 3

Emergence of the small inner hole band at low temperatures for $x=0.12$. (a)–(c) ARPES data for a high-symmetry cut through the center of the Brillouin zone at 23 eV (near the $Z$ point) at $T\approx 11$ K for $x=0–0.12$. Solid black lines are the MDCs at the Fermi level, indicating the splitting of the outer hole band $\alpha$ and the emergence of the inner $\beta$ band for $x=0.12$. (d)–(f) As above, but for a cut at the $\mathrm{\Gamma }$ point (37 eV). (g) Photon energy dependence of the Fermi level MDC at $x=0.12$, indicating that the inner hole band forms a 3D pocket around the $Z$ point, as also shown by the Fermi surface maps at (h) the $Z$ (23 eV) and (i) $\mathrm{\Gamma }$ point (37 eV). Cartoon insets show how the apparent splitting of bands arises from Fermi surface distortion and sample twinning.

Figure 4

Proposed phase diagram of ${\mathrm{FeSe}}_{1-x}{\mathrm{S}}_x$. (a) $T_s$ and $T_c$ values extracted from our resistivity measurements [26], compared to literature values of $T_c$ reported in Ref. [23] (resistivity midpoint) and Ref. [30] (heat capacity). OO and SC refer to orbital order and the superconducting phase, respectively. (b) and (c) Evolution of the band splitting, ${\mathrm{\Delta }}_M$, and Fermi surface deformation, $\mathrm{\Delta }{k}_F/k_{F0}$, with S substitution at low temperature, demonstrating that the magnitude of the orbital ordering is directly correlated with the suppression of $T_s$.