Topologically nontrivial $1/3$-magnetization plateau state in a spin-1/2 trimer chain

Abstract

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${}_{12}$ ($x=0,0.1\sim 1.5$). 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 $\hat{I}{¼}_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. $\hat{I}{¼}_0{H}_c=17$ 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 $\hat{I}{¼}_{0}H\ge 25.72$ T. These observations provide further insights into the Haldane physics.

6 pages, 4 figures