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
2Cu
3Ge
4−xSi
xO
12 (
x=0,0.1∼1.5). In the parent compound (
x=0), the spin-lattice relaxation rate (1/
T1) shows significantly different temperature dependence when the external magnetic field is increased above the critical field of
μ0Hc = 29 T. The spin excitation gap is evidenced from the thermally activated behavior of
1/T1(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.
μ0Hc=17 T in
x=1.0 samples, which results from the suppressed inter-trimer coupling
J2. The gapped spin excitation is confirmed again above 17 T, whose size shows temperature-dependent behavior for
μ0H≥25.72 T. These observations provide further insights into the Haldane physics.
The magnetization process and elementary excitation spectra of the spin-1/2 trimerized quantum Heisenberg chain are investigated by means of Green's function theory combined with Jordan-Wigner transformation. At zero temperature, a 1/3 magnetization plateau of the system is observed. Meanwhile, we obtain the ground state phase diagram, in which the Luttinger liquid phase, the magnetization plateau state, the gapless phase and the ferromagnetic state are revealed. At finite temperatures, the magnetization behaves differently, implying the system lies in different states under different magnetic fields. It is shown that the elementary excitation spectra can unpuzzle the magnetization process. It is also found that the energy gap in the spectra is responsible for the observed 1/3 magnetization plateau.