NMR evidence for static local nematicity and its cooperative interplay with low-energy magnetic fluctuations in FeSe under pressure

We present ${}^{77}\mathrm{Se}$-NMR measurements on single-crystalline FeSe under pressures up to 2 GPa. Based on the observation of the splitting and broadening of the NMR spectrum due to structural twin domains, we discovered that static, local nematic ordering exists well above the bulk nematic ordering temperature, $T_{\mathrm{s}}$. The static, local nematic order and the low-energy stripe-type antiferromagnetic spin fluctuations, as revealed by NMR spin-lattice relaxation rate measurements, are both insensitive to pressure application. These NMR results provide clear evidence for the microscopic cooperation between magnetism and local nematicity in FeSe.

Figure 1

Representative NMR spectra at indicated $T$ for all measured pressures. The two peaks arise from inequivalent nematic domains with $H\parallel a$ and $H\parallel b$. The solid red line is the bulk $T_{\mathrm{s}}$, as determined by a kink in the NMR shift (see Fig. 2). The dashed blue line is $T_{\mathrm{N}}$ and the dot-dashed dark-yellow line is $T_{\mathrm{c}}$. $T_{\mathrm{N}}$ and $T_{\mathrm{c}}$ were determined from data shown in [20]. The colors of the spectra correspond to different phases: black for the paramagnetic state, dark yellow for below $T_{\mathrm{c}}$, blue for below $T_{\mathrm{N}}$, and red for the bulk nematic ordered state.

Figure 2

Upper panels: NMR shift $K$ as a function of $T$ as obtained from a two-Lorentzian fit for indicated pressures. The orange triangles and teal circles represent $K_a$ and $K_b$, while the black squares are the average of the two, $K_{\mathrm{avg}}$. The black vertical lines indicate the corresponding bulk $T_{\mathrm{s}}$ for each pressure. $T_{\mathrm{c}}$ and $T_{\mathrm{N}}$ for different pressures are also shown by the vertical broken lines. Lower panels: FWHM of NMR spectral peaks for two $ab$ plane orientations: $\theta =0^{\circ }$ (filled symbols) and $\theta \sim {25}^{\circ }$ (open symbols). Below $T_s$, the FWHM of each of the two peaks is shown separately. The low-frequency peak (teal) has consistently greater FWHM than the high-frequency peak (orange). Above $T_s$ the FWHM of a single-peak model is shown (black). Arrows denote $T_{\mathrm{FWHM}}^{*}$.

Figure 3

$T$ dependence of $\mathrm{\Delta }K$ for the indicated pressures. $\mathrm{\Delta }K$ is a measure of the local nematic order parameter. The dashed vertical lines indicate the bulk $T_{\mathrm{s}}$.

Figure 4

$\sqrt{1/T_{1}T}$ versus $K\left(T\right)$ plot with $T$ as an implicit parameter for indicated pressures. $T_{\mathrm{spin}}^{*}$, the onset of low-energy spin fluctuations, is determined by the deviation of the data from high-$T$-linear behavior shown by solid lines (see text). Bulk $T_{\mathrm{s}}$ is indicated for comparison.

Figure 5

Phase diagram of pressurized FeSe incorporating microscopic details of the paramagnetic phase as revealed by NMR.