Spin-$\frac{1}{2}$ chains with alternating antiferromagnetic (AF) and ferromagnetic (FM) couplings exhibit quantum entanglement as the integer-spin Haldane chains and might be similarly utilized for quantum computations. Such alternating AF-FM chains have been proposed to be realized in the distorted honeycomb lattice compound ${\mathrm{Na}}_2{\mathrm{Cu}}_2{\mathrm{TeO}}_6$, but to confirm this picture a comprehensive understanding of the exchange interactions including terms outside of the idealized model is required. Here, we employ neutron scattering to study the spin dynamics in ${\mathrm{Na}}_2{\mathrm{Cu}}_2{\mathrm{TeO}}_6$ and accurately determine the coupling strengths through the random phase approximation and density functional theory approaches. We find the AF and FM intrachain couplings are the dominant terms in the spin Hamiltonian, while the interchain couplings are AF but perturbative. This hierarchy in the coupling strengths and the alternating signs of the intrachain couplings can be understood through their different exchange paths. Our results establish ${\mathrm{Na}}_2{\mathrm{Cu}}_2{\mathrm{TeO}}_6$ as a weakly coupled alternating AF-FM chain compound and reveal the robustness of the gapped ground state in alternating chains under weak interchain couplings.

中文翻译：

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Na2Cu2TeO6变形蜂窝结构中的弱耦合交替S = 12链

自旋$\frac{\mathrm{1个}}{2}$具有交替反铁磁（AF）和铁磁（FM）耦合的碳链显示出与整数自旋Haldane链一样的量子纠缠，并且可以类似地用于量子计算。已经提出在扭曲的蜂窝状晶格复合物中实现这种交替的AF-FM链${娜}_2{铜}_2{\mathrm{特奥}}_6$，但要确认此图片，需要对交换交互（包括理想化模型之外的术语）有全面的了解。在这里，我们使用中子散射来研究中子的自旋动力学${娜}_2{铜}_2{\mathrm{特奥}}_6$通过随机相位近似和密度泛函理论方法准确确定耦合强度。我们发现，自旋哈密顿量中AF和FM链内耦合是主要术语，而链间耦合是AF但微扰。链内偶联的偶联强度和交替符号的这种等级可以通过它们的不同交换路径来理解。我们的结果证明${娜}_2{铜}_2{\mathrm{特奥}}_6$ 作为弱耦合的交替AF-FM链化合物，并揭示了弱链间耦合作用下交替链中空缺基态的稳健性。