Spin-singlet state formation in the cluster Mott insulator ${\text{GaNb}}_4{\text{S}}_8$ studied by $\mu \text{SR}$ and NMR spectroscopy

Muon spin relaxation $\left(\mu \text{SR}\right)$ and nuclear magnetic resonance experiments revealed that the spin-singlet state with an excitation gap of $\sim 200\text{K}$ is realized from $S=1/2{\text{Nb}}_4$ tetrahedral clusters in a cluster Mott insulator ${\text{GaNb}}_4{\text{S}}_8$. The intercluster cooperative phenomenon to the singlet state at $T_{\text{S}}=32\text{k}$ is triggered by intracluster Jahn-Teller type structural instability developed from $\sim 3T_{\text{S}}$. Referring to the lattice symmetry, the formation of ${\text{Nb}}_8$ octamer (${\text{Nb}}_4{\text{-Nb}}_4$ bond) is suggested.

Figure 1

Proposed molecular orbital schemes of the ${\text{Nb}}_4$ unit above and below $T_{\text{S}}$.[5] To interpret isotropic and anisotropic hyperfine fields at the Nb site, schematic spin density distributions are shown for HOMO.

Figure 2

(Color online) The $T$ dependence of the ZF muon spin relaxation rate $\lambda$. The inset shows typical examples of $\text{ZF-}\mu \text{SR}$ spectra (at 4.5, 25, and 100 K). Solid curves indicate the fit by the damped KT function. Below $T_{\text{S}}$, the asymmetry is fit with the stretched exponential function.

Figure 3

(Color online) $T$ dependences of ${}^{93}\text{N}\text{b}$ and ${}^{71}\text{G}\text{a}$ hyperfine shifts, ${}^{93}K$ above $T_{\text{S}}$ (solid circles), ${{}^{71}K}_{\text{iso}}$ above $T_{\text{S}}$ (open circles) and ${{}^{71}K}_{\perp }$ below $T_{\text{S}}$ (open squares) (Ref. 10). The solid curve indicates the bulk susceptibility $\chi$. The broken curve represents $\text{exp}\left(-E_g/k_{B}T\right)$ with $E_g/k_B\simeq 220\text{K}$. The inset shows ${}^{93}\text{N}\text{b-NMR}$ lines (only the center line) above $T_{\text{S}}$, measured under an external field of 7.0071 T. The broken straight line indicates the zero shift position.

Figure 4

(Color online) ${}^{71}\text{G}\text{a}$ spectra measured above $T_{\text{S}}$ (a) and below $T_{\text{S}}$ (b), and magnified bottom structures above $T_{\text{S}}$ (c). The data were collected in a field of 7.0071 T and plotted with respect to peak positions. The spectrum of (b) was obtained by summing Fourier transforms of the spin-echo signal accumulated at different frequencies.

Figure 5

(Color online) (a) $T$ dependences of $1/T_1$ measured for ${}^{69}\text{G}\text{a}$ (open circles) and ${}^{71}\text{G}\text{a}$ (closed circles). Reliable ${}^{69}\left(1/T_1\right)$ was not obtained below $T_{\text{S}}$ due to overlap of ${}^{93}\text{N}\text{b}$ and ${}^{69}\text{G}\text{a}$ signals. (b) $T$ dependences of quadrupole (open squares) and magnetic (solid squares) components of ${}^{71}\left(1/T_1\right)$. (c) The Arrhenius plot of ${}^{71}\left(1/T_1\right)$ at low $T$. The solid line, corresponding to the solid curve in (a), gives $E_g/k_B\simeq 190\text{K}$.