121,123Sb NQR as a microscopic probe in Te doped correlated semimetal FeSb2 : emergence of electronic Griffith phase, magnetism and metallic behavior %

$^{121,123}Sb$ nuclear quadrupole resonance (NQR) was applied to $Fe(Sb_{1-x}Te_x)_2$ in the low doping regime (\emph{x = 0, 0.01} and \emph{0.05}) as a microscopic zero field probe to study the evolution of \emph{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) $1/T_1(T)$ probes the fluctuations at the $Sb$ - site. The fluctuations originate either from conduction electrons or from magnetic moments. In contrast to the semi metal $FeSb_2$ with a clear signature of the charge and spin gap formation in $1/T_1(T)T ( \sim exp/ (\Delta k_BT) ) $, the 1\% $Te$ doped system exhibits almost metallic conductivity and a almost filled gap. A weak divergence of the SLRR coefficient $1/T_1(T)T \sim T^{-n} \sim T^{-0.2}$ points towards the presence of electronic correlations towards low temperatures wheras the \textit{5\%} $Te$ doped sample exhibits a much larger divergence in the SLRR coefficient showing $1/T_1(T)T \sim T^{-0.72} $. According to the specific heat divergence a power law with $n\ =\ 2\ m\ =\ 0.56$ is expected for the SLRR. Furthermore $Te$-doped $FeSb_2$ as a disordered paramagnetic metal might be a platform for the electronic Griffith phase scenario. NQR evidences a substantial asymmetric broadening of the $^{121,123}Sb$ NQR spectrum for the \emph{5\%} sample. This has purely 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.