Origin of the Tetragonal-to-Orthorhombic Phase Transition in FeSe: A Combined Thermodynamic and NMR Study of Nematicity

The nature of the tetragonal-to-orthorhombic structural transition at $T_s\approx 90\mathrm{K}$ in single crystalline FeSe is studied using shear-modulus, heat-capacity, magnetization, and nuclear magnetic resonance measurements. The transition is shown to be accompanied by a large shear-modulus softening, which is practically identical to that of underdoped $\mathrm{Ba}(\mathrm{Fe},\mathrm{Co}{)}_2{\mathrm{As}}_2$, suggesting a very similar strength of the electron-lattice coupling. On the other hand, a spin-fluctuation contribution to the spin-lattice relaxation rate is only observed below $T_s$. This indicates that the structural, or “nematic,” phase transition in FeSe is not driven by magnetic fluctuations.

Figure 1

(a) Specific heat $C_p$ divided by $T$ vs $T$ of an FeSe single crystal. Insets show data around $T_c$ and $T_s$ on an enlarged scale revealing relatively sharp, mean-field-like transitions. Data for 2% Co-substituted ${\mathrm{BaFe}}_2{\mathrm{As}}_2$ are shown for comparison. (b) Young’s modulus $Y$ (left scale) and orthorhombic distortion $\delta$ (right scale) of FeSe single crystals vs $T$, compared with slightly underdoped $\mathrm{Ba}(\mathrm{Fe},\mathrm{Co}{)}_2{\mathrm{As}}_2$. The inset shows data around $T_c$ of FeSe and 4.3% Co-substituted ${\mathrm{BaFe}}_2{\mathrm{As}}_2$. Note the different vertical scales in the inset.

Figure 2

(a),(b) NMR spectra of a collection of $\sim 10$ FeSe single crystals with field $H||ab$ and $H||c$, respectively, at $H=9\mathrm{T}$. (c) $K^{\alpha }$ (left scale) and uniform magnetic susceptibility (right scale) for the indicated field directions. (d) $1/T_{1}T$ and its anisotropy with respect to the applied field $R_{ac}=[{(1/T_1)}_{H||“a”}+{(1/T_1)}_{H||“b”}]/2/{(1/T_1)}_{H||c}$ and $R_{ab}={(1/T_1)}_{H||“a”}/{(1/T_1)}_{H||“b”}$ (inset). (e) Square root of $1/T_{1}T$ vs $K$ with temperature as implicit parameter, indicated in units of K. Bold straight lines show a linear fit to the data for $T>T_s$, Eq. (3), deviations from which demonstrate the emergence of spin fluctuations. Thin lines are a guide to the eye. $K^{\alpha }(T_s)$ is indicated by vertical arrows.

Figure 3

(a) Normalized nematic susceptibility ${\lambda }^2{\chi }_{\phi }/C_{66,0}=1-C_{66}/C_{66,0}$ of FeSe and $\mathrm{Ba}(\mathrm{Fe},\mathrm{Co}{)}_2{\mathrm{As}}_2$ (from Ref. [21]). Data on FeSe are found to be practically identical to $\mathrm{Ba}(\mathrm{Fe},\mathrm{Co}{)}_2{\mathrm{As}}_2$ with the same $T_s$. (b) $1/T_{1}T$ of FeSe and $\mathrm{Ba}(\mathrm{Fe},\mathrm{Co}{)}_2{\mathrm{As}}_2$ (from Refs. [35, 36]) for in-plane field, demonstrating very distinct behavior in the two systems. Arrows mark $T_s$ of ${\mathrm{BaFe}}_2{\mathrm{As}}_2$, $\mathrm{Ba}({\mathrm{Fe}}_{0.98}{\mathrm{Co}}_{0.02}{)}_2{\mathrm{As}}_2$, and FeSe.