  Topologically nontrivial Haldane phase is theoretically proposed to be
realized in the 1/3-magnetization ($M$) plateau of spin-1/2 trimer systems.
However, the spin excitation gap, typical characteristic of Haldane phase, is
not yet experimentally verified. Here, we report the nuclear magnetic resonance
investigations into the low-energy spin dynamics in the $S=1/2$ spin-trimer
antiferromagnetic chain compound Na$_2$Cu$_3$Ge$_{4-x}$Si$_{x}$O$_{12}$ ($x=0,
0.1\sim1.5$). In the parent compound ($x=0$), the spin-lattice relaxation rate
(1/$T_1$) shows significantly different temperature dependence when the
external magnetic field is increased above the critical field of $\mu_0$$H_{c}$
= 29 T. The spin excitation gap is evidenced from the thermally activated
behavior of $1/T_1(T)$ in the 1/3-$M$ plateau state. By substituting Ge$^{4+}$
with Si$^{4+}$, the critical field for the 1/3-$M$ plateau significantly
decreases, e.g. $\mu_0H_{c}=17$ T in $x=1.0$ samples, which results from the
suppressed inter-trimer coupling $J_2$. The gapped spin excitation is confirmed
again above 17 T, whose size shows temperature-dependent behavior for
$\mu_0H\geq25.72$ T. These observations provide further insights into the
Haldane physics.
