${}^{121,123}\mathrm{Sb}$ nuclear quadrupole resonance as a microscopic probe in the Te-doped correlated semimetal ${\mathrm{FeSb}}_2$: Emergence of electronic Griffith phase, magnetism, and metallic behavior

${}^{121,123}\mathrm{Sb}$ nuclear quadrupole resonance (NQR) was applied to $\text{Fe}{\left({\text{Sb}}_{1-x}{\text{Te}}_x\right)}_2$ in the low doping regime $(x=0$, 0.01, and 0.05) as a microscopic zero field probe to study the evolution of $3d$ magnetism and the emergence of metallic behavior. Whereas the NQR spectra itself reflects the degree of local disorder via the width of the individual NQR lines, the spin lattice relaxation rate (SLRR) $1/T_1\left(T\right)$ probes the fluctuations at the Sb site. The fluctuations originate either from conduction electrons or from magnetic moments. In contrast to the semimetal ${\mathrm{FeSb}}_2$ with a clear signature of the charge and spin gap formation in $1/T_1\left(T\right)T[\sim exp/\left(\mathrm{\Delta }{k}_{B}T\right)]$, the 1% Te-doped system exhibits almost metallic conductivity and the SLRR nicely confirms that the gap is almost filled. A weak divergence of the SLRR coefficient $1/T_1\left(T\right)T\sim T^{-n}\sim T^{-0.2}$ points towards the presence of electronic correlations towards low temperatures. This is supported by the electronic specific heat coefficient $\gamma =(C_{\text{el}}/T)$ showing a power-law divergence $\gamma \left(T\right)\sim T^{-m}\sim {(1/T_{1}T)}^{1/2}\sim T^{-n/2}\sim C_{\text{el}}/T$ which is expected in the renormalized Landau Fermi liquid theory for correlated electrons. In contrast to that the 5% Te-doped sample exhibits a much larger divergence in the SLRR coefficient showing $1/T_1\left(T\right)T\sim T^{-0.72}$. According to the specific heat divergence a power law with $n=2m=0.56$ is expected for the SLRR. This dissimilarity originates from admixed critical magnetic fluctuations in the vicinity of antiferromagnetic long range order with $1/T_1\left(T\right)T\sim T^{-3/4}$ behavior. Furthermore Te-doped ${\mathrm{FeSb}}_2$ as a disordered paramagnetic metal might be a platform for the electronic Griffith phase scenario. NQR evidences a substantial asymmetric broadening of the ${}^{121,123}\mathrm{Sb}$ NQR spectrum for the 5% sample. This has a predominant electronic origin in agreement with the electronic Griffith phase and stems probably from an enhanced Sb-Te bond polarization and electronic density shift towards the Te atom inside Sb-Te dumbbell.

Figure 1

${}^{121,123}\mathrm{Sb}$ spectra measured at 4.2 K in $\mathrm{Fe}({\mathrm{Sb}}_{1-x}{\mathrm{Te}}_x$)${}_2$ compounds with $x=0.01$ (lower panel) and 0.05 (upper panel). For comparison, the same Sb NQR lines for the undoped ${\mathrm{FeSb}}_2$ measured at 10 K and retrieved from [19] are presented (lower panel). The intensities of all transitions except ${\nu }_2$ line (55.9 MHz; $|\pm 3/2\rangle \leftrightarrow |\pm 5/2\rangle$ transition) for the $\mathrm{Fe}({\mathrm{Sb}}_{0.95}{\mathrm{Te}}_{0.05}$)${}_2$ sample are normalized on their maximum intensity values. Inset: ${}^{123}\mathrm{Sb} {\nu }_3$ line (88.0 MHz; $|\pm 5/2\rangle \leftrightarrow |\pm 7/2\rangle$ transition) and ${}^{122}\mathrm{Sb} {\nu }_2$ line (95.1 MHz; $|\pm 5/2\rangle \leftrightarrow |\pm 7/2\rangle$ transition) without normalization for the $\mathrm{Fe}({\mathrm{Sb}}_{0.95}{\mathrm{Te}}_{0.05}$)${}_2$ sample. Solid lines are guides for eye.

Figure 2

${}^{123}\mathrm{Sb}$ magnetization recovery curves for the ${\nu }_2$ NQR line (quadrupole transition $|\pm 3/2\rangle \leftrightarrow |\pm 5/2\rangle$) in the $\text{Fe}{\left({\text{Sb}}_{1-x}{\text{Te}}_x\right)}_2 (x=0.01$, 0.05) samples at 4.2 K and ${\text{FeSb}}_2$ at 10 K. The latter curve was adopted from Ref. [19]. Solid lines are the best fits to Eq. (2) with $n=1$, 0.73(1), 0.64(2) for $x=0$, 0.01, 0.05, respectively.

Figure 3

$1/T_{1}T$ as a function of temperature for the ${}^{123}\mathrm{Sb} {\nu }_2$ NQR line $\left(\right|\pm 3/2\rangle \leftrightarrow |\pm 5/2\rangle$) in $\text{Fe}{\left({\text{Sb}}_{1-x}{\text{Te}}_x\right)}_2$ compounds $(x=0$, 0.01, and 0.05). Solid straight lines are the best linear fits according to formula $1/T_{1}T=a*T^{-2(1+\lambda )}$ (see text).

Figure 4

Upper panel: $C/T$ vs $T$ plot in $\text{Fe}{\left({\text{Sb}}_{1-x}{\text{Te}}_x\right)}_2$ compounds $(x=0.01$ and $x=0.05$). Solid lines are the best fits to Eq. (2) (see text). Lower panel: Low temperature part of the $C/T$ vs $T$ plot for the $\text{Fe}{\left({\text{Sb}}_{0.95}{\text{Te}}_{0.05}\right)}_2$ sample. Dashed and solid lines are the best fits to Eqs. (2) and (5), respectively.

Figure 5

Schematic illustration of the first two coordination spheres of Sb-Sb dumbbell in the ${\text{FeSb}}_2$ crystal structure. Sb atoms are indicated as green spheres, Fe are dark blue spheres. ${\mathrm{Fe}}_6$ octahedron surrounding the center of the Sb-Sb dumbbell (black point in the center of an octahedron) is indicated by green-blue.