Magnetoelectric Effect And Thermodynamic Properties Of Low Dimensional Quantum Systems

In recent years, low-dimensional quantum magnetic systems have attracted much attention due to their various fascinating magnetic properties and thermodynamic behaviors. Based on the synthesis of low-dimensional quantum materials experimentally, we propose theoretical models to investigate two kinds of one-dimensional quantum magnetic systems, such as one-dimensional (1D) multiferroics and1D tetrameric bond alternating chain. By means of Green’s function theory, the magnetic order, ferroelectric property and thermodynamics are calculated and discussed, which will provide theoretical guide for the design of molecular devices, and promote the development of organic spintronics. In addition, correlation is of importance for condensed matter physics. Both entanglement entropy and concurrence are good indicators of quantum phase transitions (QPTs), which can be used to characterize quantum correlation. To characterize the phase transition further, we also calculate the entanglement entropy and concurrence to study the QPTs in systems. Research achievements are summarized as following:(1) Based on the synthesis of organic charge transfer compounds experimentally, we propose a theoretical model for anisotropic multiferroics to study the effect of anisotropy on ferroelectric property, magnetic behavior, phase transition and thermodynamics. It is found that the anisotropy not only plays an important role on the ferroelectric phase transition, but also enhances the ferroelectric polarization. Under different anisotropy, the phase diagram and temperature dependence of the magnetic susceptibility and dielectric constant are also presented. It reveals that the transition temperature and the transition magnetic field increase as anisotropy ascends, which is attributed to the energy gap. Moreover, the potential magnetoelectric coupling is taken into account. The magnetic field reduces the polarization, while the electric field makes the magnetization plateau wider hindering the collapse of singlet state.(2) Unlike the symmetric-exchange-driven ferroelectrics, the Dzyaloshinskii-Moriya (DM) interaction can also affect the ferroelectric properties. On the basis of theoretical model for1D multiferroics, we have studied the effect of DM interaction on ferroelectric and magnetic properties. It is shown that the uniform DM interaction will reduce the polarization, and make the magnetization plateau narrows down, which are related to the energy bands. In order to clarify the transition temperature and transition magnetic field under different uniform DM interaction, we construct the phase diagram. Moreover, both the entanglement entropy and concurrence are calculated, which show that the transition temperature decreases with the DM interaction increasing. In addition, the staggered DM interaction, related to intersite distance, is also discussed. We can see a critical point, above or below which the staggered DM interaction plays different roles on polarization, transition temperature and magnetic behavior.(3) Based on the synthesis of a fourfold magnetic periodic system experimentally, we have studied two kinds of1D tetrameric bond alternating chain, which are AF1-AF2-AF3-AF2and AF1-AF2-AF3-AF4.The results show that there are five magnetic phases under different fields, which are two gapless phases and three magnetic plateaus (M=0,1/2and saturated magnetization). Investigations of both entanglement entropy and concurrence show that they are good indicators of QPTs. We also investigate the susceptibility and specific heat in different magnetic phases, which can be explained by the competition between hole and fermion excitations. In addition, the magnetization of every site in the unit cell behaves different for the two kinds of chain, which can be explained by the concurrence.