We present a comprehensive experimental and theoretical study of the structural, electronic, magnetic, and thermodynamic properties of a ${\mathrm{Pb}}_6{\mathrm{Co}}_9{\left({\mathrm{TeO}}_6\right)}_5$ single crystal. The ${\mathrm{Pb}}_6{\mathrm{Co}}_9{\left({\mathrm{TeO}}_6\right)}_5$ crystal has shown a unique type of magnetic spin-lattice coupling, in which the lattice structure consists of four different Co ions sites with distorted octahedral coordinations. The x-ray photoelectron spectroscopy (XPS) results confirmed the oxidation states of Pb, Co, Te, and O elements in the sample. Moreover, XPS spectra revealed the adsorbed oxygen in the defect/vacancy sites of the lattice structure. The dc magnetization measurements exhibited a complex magnetic behavior with ferrimagnetic (FIM) transition with Curie temperature $T_C$ at $\sim 21$ K. At lower magnetic fields $H$, the zero-field-cooled and field-cooled curves showed a broad hump at $\sim 10.8$ K and a shoulder peak at $\sim 6.2$ K, which are suppressed at higher magnetic fields. The ac susceptibility data indicated spin-glass-like features. The heat capacity $C_P$ measurements confirmed the FIM transition at $T_C$ at $\sim 21$ K, but without any trace of additional peaks at lower temperatures. The estimated Curie-Weiss constant ${\theta }_{\mathrm{CW}}$ showed a peculiar field-dependent behavior along the $H\parallel c$ direction of the single crystal, where ${\theta }_{\mathrm{CW}}$ is less field dependent for the $H\perp c$ direction. A large coercivity (13 kOe) is observed at 2 K for $H\parallel c$, whereas the magnetization curve of the single crystal is dominated by an antiferromagnetic feature for $H\perp c$. The behaviors indicate the anisotropy nature of the exchange interactions in the compound. The local spin density approximation $+ U$ total energy calculations were performed for various collinear spin configurations of a classical Heisenberg model in order to obtain the magnetic exchange interactions $J_i$ at different distances for different neighbors.

中文翻译：

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蜂窝结构Pb6Co9(TeO6)5化合物中的磁自旋序

我们对结构、电子、磁性和热力学特性进行了全面的实验和理论研究。 ${铅}_6{\mathrm{公司}}_9{\left({\mathrm{氧化钛}}_6\right)}_5$单晶。这${铅}_6{\mathrm{公司}}_9{\left({\mathrm{氧化钛}}_6\right)}_5$晶体显示出一种独特的磁性自旋晶格耦合，其中晶格结构由四个不同的 Co 离子位点组成，具有扭曲的八面体配位。X 射线光电子能谱 (XPS) 结果证实了样品中 Pb、Co、Te 和 O 元素的氧化态。此外，XPS 光谱揭示了在晶格结构的缺陷/空位位置吸附的氧。直流磁化测量表现出复杂的磁性行为，具有居里温度的亚铁磁 (FIM) 转变${吨}_C$ 在 $～21$ K. 在较低磁场下 $H$，零场冷和场冷曲线在 $～10.8$ K 和肩峰位于 $～6.2$ K，在更高的磁场中被抑制。交流磁化率数据表明具有类似旋转玻璃的特征。热容量$C_{磷}$ 测量证实了 FIM 转变在 ${吨}_C$ 在 $～21$ K，但在较低温度下没有任何额外峰值的痕迹。估计的居里-魏斯常数${\theta }_{\mathrm{连续波}}$ 表现出一种特殊的场依赖行为 $H\parallel C$ 单晶方向，其中 ${\theta }_{\mathrm{连续波}}$ 对场的依赖性较小 $H\perp C$方向。在 2 K 时观察到较大的矫顽力 (13 kOe)$H\parallel C$，而单晶的磁化曲线由反铁磁特征支配 $H\perp C$. 这些行为表明化合物中交换相互作用的各向异性性质。局部自旋密度近似$+ 你$ 对经典海森堡模型的各种共线自旋配置进行了总能量计算，以获得磁交换相互作用 $J_{\mathrm{一世}}$ 不同的邻居在不同的距离。