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We present a $^{125}$Te nuclear magnetic resonance (NMR) study in thethree-dimensional spin web lattice Cu$_3$TeO$_6$, which harbors topologicalmagnons. The $^{125}$Te NMR spectra and the Knight shift $\mathcal{K}$ as afunction of temperature show a drastic change at $T_\text{S}\sim 40$ K muchlower than the N\'eel ordering temperature $T_\text{N}\sim 61$ K, providingevidence for the first-order structural phase transition within themagnetically ordered state. Most remarkably, the temperature dependence of thespin-lattice relaxation rate $T_1^{-1}$ unravels spin-gap-like magneticexcitations, which sharply sets in at $T^*\sim 75$ K, the temperature wellabove $T_\text{N}$. The spin gap behavior may be understood by weaklydispersive optical magnon branches of high-energy spin excitations originatingfrom the unique corner-sharing Cu hexagon spin-1/2 network with lowcoordination number.

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