具有Ising和Heisenberg交换作用的几何受挫Cairo五边形晶格条纹
Geometrically frustrated Cairo pentagonal lattice stripe with Ising and Heisenberg exchange interactions
摘要：
受最近发现的一些化合物的启发，例如在一些其它化合物中，以正交晶体结构与$\mathrm{Fe}^{3+}$离子结晶的$\mathrm{Bi}_{2}\mathrm{Fe}_{4}\mathrm{O}_{9}$和遵循Cairo五边形结构模式的铁基氟氧化物${\rm Bi}_{4}{\rm Fe}_{5}{\rm O}_{13}{\rm F}$化合物。我们提出了一个模型的开罗五边形伊辛-海森堡晶格的一个条纹，一个五边形的边缘是不同的，这个边缘将与海森堡交换相互作用，而伊辛交换相互作用将关联的其他边缘。我们研究了零温下的相变，描述了五个相：铁磁相（FM）、二聚体反铁磁相（DFM）、元胞反铁磁相（PAF）、典型反铁磁相（AFM）和两种具有相同能量的阻挫态共存的特殊阻挫相（FRU）.为了得到该模型的配分函数，我们使用了传递矩阵方法，并遵循八顶点模型符号。利用这一结果，我们讨论了比热、内能和熵随温度的变化，并在低温极限下观察到了一些意想不到的行为，如由于在一个相互靠近的区域内存在着三个相变（FRU，PAF（AFM）和FM）而导致的反常的比热双峰。因此，低能热激发产生了这种双反常峰，我们还讨论了出现这种双峰曲线的低温极限处的内能。我们的结果的一些性质与二维开罗五边形晶格，以及正交二聚体元格Ising-Heisenberg链进行了比较。
英文摘要：
Motivated by the recent discoveries of some compounds such as the $\mathrm{Bi}_{2}\mathrm{Fe}_{4}\mathrm{O}_{9}$ which crystallizes in an orthorhombic crystal structure with the $\mathrm{Fe}^{3+}$ ions, and iron-based oxyfluoride ${\rm Bi}_{4}{\rm Fe}_{5}{\rm O}_{13}{\rm F}$ compounds following the pattern of Cairo pentagonal structure, among some other compounds. We propose a model for one stripe of the Cairo pentagonal Ising-Heisenberg lattice, one of the edges of a pentagon is different, and this edge will be associated with a Heisenberg exchange interaction, while the Ising exchange interactions will associate the other edges. We study the phase transition at zero temperature, illustrating five phases: a ferromagnetic phase (FM), a dimer antiferromagnetic (DAF), a plaquette antiferromagnetic (PAF), a typical antiferromagnetic (AFM) and a peculiar frustrated phase (FRU) where two types of frustrated states with the same energy coexist. To obtain the partition function of this model, we use the transfer matrix approach and following the eight vertex model notation. Using this result we discuss the specific heat, internal energy and entropy as a function of the temperature, and we can observe some unexpected behavior in the low-temperature limit, such as anomalous double peak in specific heat due to the existence of three phase (FRU, PAF(AFM) and FM) transitions occurring in a close region to each other. Consequently, the low-lying energy thermal excitation generates this double anomalous peak, and we also discuss the internal energy at the low temperature limit, where this double peak curve occurs. Some properties of our result were compared with two dimensional Cairo pentagonal lattices, as well as orthogonal dimer plaquette Ising-Heisenberg chain.
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