The spin-1/2 trimer system ${\mathrm{Na}}_2{\mathrm{Cu}}_3{\mathrm{Ge}}_4{\mathrm{O}}_{12}$ is proposed to host topologically nontrivial 1/3 magnetization $\left(M\right)$ plateau state. In this paper, we report a high-field nuclear magnetic resonance (NMR) study on the low-energy spin excitations of the $1/3\text{−}M$ plateau state in ${\mathrm{Na}}_2{\mathrm{Cu}}_3{\mathrm{Ge}}_4{\mathrm{O}}_{12}$ and Si-doped samples. First, the spin excitation gap supporting the high-field Haldane phase is indicated by the thermally activated behavior of spin-lattice relaxation rates in the $1/3\text{−}M$ plateau state. Second, by substituting ${\mathrm{Ge}}^{4+}$ with ${\mathrm{Si}}^{4+}$, the critical field for the 1/3-$M$ plateau significantly decreases, e.g., ${\mu }_0{H}_c=17$ T in the $x=1.0$ sample, which results from the suppressed intertrimer coupling $J_2$. The gapped spin excitation is observed above 17 T whose size shows the temperature-dependent behavior for ${\mu }_{0}H\ge 25.72$ T. These observations support the topological nontrivial characteristic of the $1/3\text{−}M$ plateau state.

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• Antiferromagnetism
• Exotic phases of matter
• High magnetic fields
• Spin dynamics
• Symmetry protected topological states
• 1-dimensional spin chains
• Nuclear magnetic resonance