Copper-based oxide materials have emerged as promising candidates for exploring low-dimensional magnetism due to their unique electronic and magnetic properties. Among these, Na${}_3$Cu${}_2$SbO${}_6$ stands out as a particularly intriguing compound for both experimental and theoretical investigations, owing to its distorted honeycomb lattice structure and the presence of spin-gap behavior. In this study, we conducted comprehensive magnetization, heat capacity, and muon spin relaxation ($\mu$SR) measurements on the layered honeycomb oxide Na${}_3$Cu${}_2$SbO${}_6$ to elucidate its magnetic ground state and probe the complex spin dynamics in detail. Na${}_3$Cu${}_2$SbO${}_6$ crystallizes in a $C$-centered monoclinic structure with the space group $C2/m$ (No. 12). Magnetization and specific heat measurements reveal the absence of long-range magnetic ordering down to 2 K. Furthermore, specific heat data exhibit a Schottky-like anomaly at low temperatures, indicative of short-range magnetic correlations, while no evidence of long-range ordering is observed. The temperature dependence of the muon spin relaxation rate $\lambda$ suggests the presence of spin fluctuations or a quantum-disordered ground state in Na${}_3$Cu${}_2$SbO${}_6$. The absence of oscillations in the zero-field (ZF) $\mu$SR spectra further confirms the lack of long-range magnetic order in the material. Longitudinal field (LF) $\mu$SR experiments provide additional insights, revealing that the spin fluctuations persisting at low temperatures are dynamic in nature. Our findings indicate that the disordered and fluctuating magnetic ground state in Na${}_3$Cu${}_2$SbO${}_6$ can be attributed to magnetic frustration arising from competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions along the $b$ axis within the $ab$ plane. These results highlight the rich magnetic behavior of Na${}_3$Cu${}_2$SbO${}_6$ and its potential as a model system for studying low-dimensional magnetism and quantum spin phenomena.

中文翻译：

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探究蜂窝氧化物 Na3Cu2SbO6 中的无序磁基态和自旋动力学

铜基氧化物材料由于其独特的电子和磁性，已成为探索低维磁性的有前途的候选材料。其中，NaCuSbO 因其扭曲的蜂窝晶格结构和自旋间隙行为的存在，在实验和理论研究中都是一种特别有趣的化合物。在本研究中，我们对层状蜂窝氧化物 NaCuSbO 进行了全面的磁化强度、热容和 μ 子自旋弛豫 （ $\mu$ SR） 测量，以阐明其磁性基态并详细探测复杂的自旋动力学。NaCuSbO 结晶为 $C$ 具有空间群 $C2/m$ （12 号）的中心单斜晶结构。磁化强度和比热测量显示不存在低至 2 K 的长程磁有序。此外，比热数据在低温下表现出类似肖特基的异常，表明短程磁相关性，而没有观察到长程有序的证据。μ 子自旋弛豫速率 $\lambda$ 的温度依赖性表明 NaCuSbO 中存在自旋波动或量子无序基态。零场 （ZF） $\mu$ SR 光谱中没有振荡，进一步证实了材料中缺乏长程磁序。纵场 （LF） $\mu$ SR 实验提供了额外的见解，揭示了在低温下持续的自旋波动本质上是动态的。 我们的研究结果表明，NaCuSbO 中的无序和波动磁基态可归因于沿 $ab$ 平面 $b$ 内轴的竞争性铁磁最近邻和反铁磁次近邻相互作用引起的磁挫败。这些结果突出了 NaCuSbO 丰富的磁性行为及其作为研究低维磁性和量子自旋现象的模型系统的潜力。