High-field NMR study on the topologically nontrivial 1/3 magnetization plateau state in dopedNa2⁢Cu3⁢Ge4−𝑥⁢Si𝑥⁢O12

The spin-1/2 trimer system Na2⁢Cu3⁢Ge4⁢O12 is proposed to host topologically nontrivial 1/3 magnetization (𝑀) 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−𝑀 plateau state in Na2⁢Cu3⁢Ge4⁢O12 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−𝑀 plateau state. Second, by substituting Ge4+ with Si4+, the critical field for the 1/3-𝑀 plateau significantly decreases, e.g., 𝜇0⁢𝐻𝑐=17 T in the 𝑥=1.0 sample, which results from the suppressed intertrimer coupling 𝐽2. The gapped spin excitation is observed above 17 T whose size shows the temperature-dependent behavior for 𝜇0⁢𝐻≥25.72 T. These observations support the topological nontrivial characteristic of the 1/3−𝑀 plateau state.