Cadeia Cairo pentagonal geometricamente frustrado com acoplamentos Ising-Heisenberg

Abstract

Motivated by the recent discoveries of some compounds such as the Bi2Fe4O9 which crystallizes in an orthorhombic crystal structure with the Fe3+ ions forming a Cairo pentagonal tiling, and iron-based oxyfluoride Bi4Fe5O13F compounds with Cairo pentagonal structure, among some others. 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 an Ising exchange interaction will associate the other edges. We study the phase transition at zero temperature, illustrating five phases, one ferromagnetic phase (FM), one dimer antiferromagnetic (DAF), one plaquette antiferromagnetic (PAF), one typical antiferromagnetic (AFM) and a peculiar two coexisting frustrated phase (FRU). In the two-dimensional pentagonal lattice, the DAF phase will be transformed in a ferrimagnetic phase, due to the sharing spins between unit cell. However, AFM and PAF phase will be forbidden in the twodimensional lattice, because the sharing spins will not be compatible. To obtain the partition function of this model, we can use the direct decoration transformation, as well as transfer matrix approach and following the eight vertex model notation. Using this result we discuss the specific heat and the entropy as a dependence of temperature, and we observe an unexpected behavior in the low-temperature limit, besides residual entropy. Such as anomalous double peak due the existence of three phase transition occurring in a very close region to each other (FM, PAF e FRU). Consequently, the thermal excitation of low-lying energy generates this anomalous double peak, and we also discuss the internal energy in the low-temperature limit, where occurred this double peak curves.