The minerals $A_2{\mathrm{Cu}}_3\mathrm{O}{\left({\mathrm{SO}}_4\right)}_3(A_2={\mathrm{Na}}_2,\mathrm{NaK},{\mathrm{K}}_2)$ constitute quantum spin systems with copper hexamers as basic structural units. Strong intrahexamer spin couplings give rise to an effective triplet ground state. Weak interhexamer spin couplings are responsible for two-dimensional long-range magnetic order in the ($b,c$) plane below $3.0<T_c<4.7\mathrm{K}$. We investigated the magnetic excitations at $T=1.5$ K by inelastic neutron scattering (INS). The INS technique was based on the observation of wave vector dependent slices in reciprocal space in order to selectively probe the magnetic signals in different Brillouin zones with different weight. Due to the imbalance of the spin couplings, the data analysis relies on a model in which the interhexamer spin couplings are treated perturbatively on top of the exact $S=1$ ground state. The interhexamer spin couplings turn out to be ferromagnetic.

中文翻译：

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铜六聚体化合物A2Cu3O(SO4)3(A2=Na2,NaK,K2)中的不平衡自旋耦合

矿物质 ${\mathrm{一种}}_2{铜}_3\mathrm{哦}{\left({\mathrm{所以}}_4\right)}_3({\mathrm{一种}}_2={钠}_2,\mathrm{钠钾},{\mathrm{钾}}_2)$以铜六聚体为基本结构单元构成量子自旋系统。强内六聚体自旋耦合产生有效的三重基态。弱六聚体自旋耦合负责 ($乙,C$) 平面下方 $3.0<{吨}_C<4.7\mathrm{钾}$. 我们研究了在$吨=1.5$K 通过非弹性中子散射 (INS)。INS 技术基于对倒易空间中波矢量相关切片的观察，以便选择性地探测不同权重的不同布里渊区中的磁信号。由于自旋耦合的不平衡，数据分析依赖于一个模型，其中六聚体自旋耦合在精确的基础上进行微扰处理$秒=1$基态。六聚体自旋耦合被证明是铁磁性的。