Spin dynamics and spin freezing behavior in the two-dimensional antiferromagnet Ni Ga 2 S 4 revealed by Ga-NMR, NQR and μ SR measurements

We have performed $^{69,71}\mathrm{Ga}$ nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), and muon spin rotation and resonance on the quasi-two-dimensional antiferromagnet $\mathrm{Ni}{\mathrm{Ga}}_{2}{\mathrm{S}}_{4}$, in order to investigate its spin dynamics and magnetic state at low temperatures. Although there exists only one crystallographic site for Ga in $\mathrm{Ni}{\mathrm{Ga}}_{2}{\mathrm{S}}_{4}$, we found two distinct Ga signals by NMR and NQR. The origin of the two Ga signals is not fully understood, but possibly due to stacking faults along the $c$ axis which induce additional broad Ga NMR and NQR signals with different local symmetries. We found the spin freezing occurring at ${T}_{\mathrm{f}}$, at which the specific heat shows a maximum, from a clear divergent behavior of the nuclear spin-lattice relaxation rate $1∕{T}_{1}$ and nuclear spin-spin relaxation rate $1∕{T}_{2}$ measured by Ga-NQR as well as the muon spin relaxation rate $\ensuremath{\lambda}$. The main sharp NQR peaks exhibit a stronger tendency of divergence, compared with the weak broader spectral peaks, indicating that the spin freezing is intrinsic in $\mathrm{Ni}{\mathrm{Ga}}_{2}{\mathrm{S}}_{4}$. The behavior of these relaxation rates strongly suggests that the Ni spin fluctuations slow down towards ${T}_{\mathrm{f}}$, and the temperature range of the divergence is anomalously wider than that in a conventional magnetic ordering. A broad structureless spectrum and multicomponent ${T}_{1}$ were observed below $2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, indicating that a static magnetic state with incommensurate magnetic correlations or inhomogeneously distributed moments is realized at low temperatures. However, the wide temperature region between $2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and ${T}_{\mathrm{f}}$, where the NQR signal was not observed, suggests that the Ni spins do not freeze immediately below ${T}_{\mathrm{f}}$, but keep fluctuating down to $2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with the MHz frequency range. Below $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, all components of $1∕{T}_{1}$ follow a ${T}^{3}$ behavior. We also found that $1∕{T}_{1}$ and $1∕{T}_{2}$ show the same temperature dependence above ${T}_{\mathrm{f}}$ but different temperature dependence below $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. These results suggest that the spin dynamics is isotropic above ${T}_{\mathrm{f}}$, which is characteristic of the Heisenberg spin system, and becomes anisotropic below $0.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$.