Unusual spin pseudogap behavior in the spin web lattice ${\mathrm{Cu}}_3\mathrm{Te}{\mathrm{O}}_6$ probed by ${}^{125}\mathrm{Te}$ nuclear magnetic resonance

We present a ${}^{125}\mathrm{Te}$ nuclear magnetic resonance (NMR) study in the three-dimensional spin web lattice ${\mathrm{Cu}}_3\mathrm{Te}{\mathrm{O}}_6$ which harbors topological magnons. The ${}^{125}\mathrm{Te}$ NMR spectra and the Knight-shift $\mathcal{K}$ as a function of temperature show a drastic change at $T_{\mathrm{S}}\sim 40\mathrm{K}$ much lower than the Néel ordering temperature $T_{\mathrm{N}}\sim 61\mathrm{K}$, providing evidence for the first-order structural phase transition within the magnetically ordered state. Most remarkably, the temperature dependence of the spin-lattice relaxation rate $T_1^{-1}$ unravels spin-gap-like magnetic excitations, which sharply sets in at $T^{*}\sim 75\mathrm{K}$, the temperature well above $T_{\mathrm{N}}$. The spin-gap behavior may be understood by weakly dispersive optical magnon branches of high-energy spin excitations originating from the unique corner-sharing Cu hexagon spin-1/2 network with low coordination number.

Figure 1

(a) ${\mathrm{Cu}}^{2+}$ magnetic lattice of ${\mathrm{Cu}}_3\mathrm{Te}{\mathrm{O}}_6$ taking into account only the nearest-neighbor exchange $J_1$ as viewed along the [111] direction (upper). There are eight Cu hexagons, each of which is formed by edge-sharing $\mathrm{Cu}{\mathrm{O}}_6$ irregular octahedra (lower left). As $H$ is applied along the [110] direction (lower right), there exist two groups of inequivalent ${}^{125}\mathrm{Te}$ sites. (b) Temperature dependence of ${}^{125}\mathrm{Te}$ NMR spectra measured at 8 T applied along the [110] direction of ${\mathrm{Cu}}_3\mathrm{Te}{\mathrm{O}}_6$. The left axis refers to the temperature at which each spectrum was obtained, whereas the amplitude of the spectra is plotted in arbitrary units. The Boltzmann correction was made by multiplying the temperature for each spectrum. The two NMR lines at ${\nu }_a$ and ${\nu }_b$ represent two inequivalent ${}^{125}\mathrm{Te}$ sites in this field direction. Below $T_{\mathrm{S}}\sim 40\mathrm{K}$, the line at ${\nu }_a$ is replaced by a new line at a lower frequency, whereas there appears a new line at 110.4 MHz with a slight decrease of the line at ${\nu }_b$. (c) Knight-shift $\mathcal{K}$ as a function of temperature. The local spin anisotropy is clearly detected. One could identify $T^{*}$ at the maximum and $T_{\text{S}}$ from the abrupt changes of the lines. Since $\mathcal{K}$ is barely affected by the AFM transition, $T_{\text{N}}$ was determined by the derivative of the bulk susceptibility $\chi \left(T\right)$.

Figure 2

(a) and (b) ${}^{125}\mathrm{Te}$ spin-lattice relaxation rate $T_1^{-1}$ and ${\left(T_{1}T\right)}^{-1}$ as a function of temperature, respectively, measured mainly at ${\nu }_a$ at 8 T. The sharp anomaly of ${\left(T_{1}T\right)}^{-1}$ is found at $T^{*}\sim 75\mathrm{K}$. Just below $T^{*}$, $T_1^{-1}$ decreases exponentially with a slight change at $T_{\mathrm{N}}\sim 61\mathrm{K}$. (c) $T_1^{-1}$ as a function of inverse temperature $1/T$. $T_1^{-1}$ decreases more than 4 decades in the 40-K temperature range, revealing the activation behavior with the gap $\mathrm{\Delta }\sim 235\mathrm{K}$ that is equivalent to $\sim 20\mathrm{meV}$. At low temperatures below 20 K, $T_1^{-1}$ deviates from the activation law, being described by the Raman relaxation rate $T_1^{-1}\propto T^7$.