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arXiv:2407.03581

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

Yuyan Han, Yu, B. C., Zhijun Du, Langsheng Ling, Zhang, L., Wei Tong, Chuanying Xi, J. L. Zhang, Shang, T., Li Pi, Long Ma

Published Jul 4, 2024• 0 citations
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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$_{12}$ ($x=0, 0.1\sim1.5$). 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 $μ_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. $μ_0H_{c}=17$ 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 $μ_0H\geq25.72$ T. These observations provide further insights into the Haldane physics.

DOI
10.48550/arxiv.2407.03581

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Theoretical and experimental studies of melting of the 1/3 magnetization plateau in a frustrated S=1/2S=1/2S=1/2 antiferromagnetic trimerized quantum Heisenberg spin chain compound Na2Cu3Ge4O12\hbox {Na}_2\hbox {Cu}_3\hbox {Ge}_4\hbox {O}_{12}Na2​Cu3​Ge4​O12​
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Low-dimensional quantum magnets provide an ideal platform to explore spin-lattice coupling-mediated quantum correlations, which give rise to emergent quasiparticle excitations. The antiferromagnetically coupled spin-1/2 trimer chain of copper ions in Na2_22​Cu3_33​Ge4_44​O12_{12}12​ (NCGO) hosts high-energy spin excitations of different species, whose energy scales overlap with those of lattice vibrations. Here, we report a comprehensive temperature-dependent Raman spectroscopic study performed between 80 and 400 K. The dynamic spin susceptibility, as obtained from the analysis of the broad spectral background, reveals the emergence of quasiparticle excitations below 170 K. We further identify an unusual crossover of phonon dynamics when the material transits from a normal paramagnetic state to a correlated quantum magnetic state. A power law dependence of the integrated Raman susceptibility of the phonon modes, Iχ′′i∼∣T−Tc∣βI_{χ^{\prime\prime}}^{i}\sim|T-T_{c}|^βIχ′′i​∼∣T−Tc​∣β, is observed with the critical temperature TcT_cTc​=167$\pm$1 K, and critical exponent β=0.24±0.02β= 0.24\pm 0.02β=0.24±0.02. The combined results obtained from the broad spectral background and sharp phonon peaks further indicate that the phonon renormalization observed across the crossover is driven by dynamic spin states. Additionally, statistical correlations among phonon energy eigenvalues, quantified through matrix-norm and power-test analyses of 200 spectra recorded at 80 K, reveal an unexpected linear correlation among phonon modes, also indicating that the collective lattice response is governed by spin correlations. These findings establish NCGO as a model system for investigating cooperative spin-lattice coupling and critical scaling behavior of phonon dynamics in low-dimensional magnetic materials.