（Na，K）$_2$ Cu $_3$ O（SO $_4)_3$）矿物中磁性六聚体的层状相互作用
Magnetic hexamers interacting in layers in the (Na,K)$_2$Cu$_3$O(SO$_4)_3$ minerals
摘要：
本文报道了合成的$_2$-Cu-$_3$-O（SO $_4)_3$-fedotovite（A = K）和puninite（A = Na）矿物以及混合的Euchlorine型NaK-Cu-$_3$-O（SO $_4)_3$）的磁性和磁性模型。我们发现，所有这些化合物含有磁性铜$_6$六聚体单位，在温度低于约100 K作为单个自旋1实体。这些磁性分子之间的弱相互作用导致低于$T_N$ = 3.4 K（A = Na）、4.7 K（A = NaK）和约3.0 K（A = K）的长程有序。的磁性秩序的形成阐明从头计算，揭示了二维间六聚体的相互作用结晶$bc$平面内。该模型表明存在一个弱扭曲的正方形晶格的$S=1$磁性离子和挑战的早期描述的A $_2$铜$_3$ O（SO $_4)_3$矿物在Halfenes自旋链。
英文摘要：
Magnetic properties and underlying magnetic models of the synthetic A$_2$Cu$_3$O(SO$_4)_3$ fedotovite (A = K) and puninite (A = Na) minerals, as well as the mixed euchlorine-type NaKCu$_3$O(SO$_4)_3$ are reported. We show that all these compounds contain magnetic Cu$_6$ hexamer units, which at temperatures below about 100 K act as single spin-1 entities. Weak interactions between these magnetic molecules lead to long-range order below $T_N$ = 3.4 K (A = Na), 4.7 K (A = NaK), and about 3.0 K (A = K). The formation of the magnetic order is elucidated by ab initio calculations that reveal two-dimensional inter-hexamer interactions within crystallographic $bc$ planes. This model indicates the presence of a weakly distorted square lattice of $S=1$ magnetic ions and challenges the earlier description of the A$_2$Cu$_3$O(SO$_4)_3$ minerals in terms of Haldane spin chains.
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