Theoretical Study On The Magnetism And Ferroelectricity In The Low-Dimensional Frustrated Spin Systems

Low-dimensional frustrated spin systems have been studied intensively because of their abundant physical mechanisms and interesting thermodynamic behaviors at finite temperature. Molecule-based magnetic materials and multiferroic materials as members of the new function material family, own many compounds involving close relation with spin frustration, therefore the investigations on this class of materials will be helpful in understanding frustrated phenomenon and have profound guiding significance for material design and magnetoelectric devices development.In this dissertation, we explore the magnetism and ferroelectricity in several typical low-dimensional frustrated spin compounds by using transfer-matrix method and Monte Carlo simulation. The main works and conclusions are as follows:1. For the molecule magnetic materials with spin-ladder sturcture, a two-leg mixed spin Ising ladder with next-nearest neighbor interaction and single-ion anisotropy has been constructed. We focus on the frustrated situation by assuming that all the magnetic bonds are antiferromagnetic, and study the ground state properties, low-temperature magnetization behavior and thermodynamics of the system. The results reveal that frustration can enhance the low-temperature inverse magnetic entropy and thereby promote the refrigerating capacity of the magnetic materials. Furthermore, we also find that when the easy-plane and ease axis anisotropies coexist, the temperature dependence of zero-field magnetic susceptibility and specific heat exhibit double peaks, indicating the sensitivity of the low-dimensional system to the thermal fluctuation eventhough in the presence of spin frustration.2. Spin-1/2 and mixed spin-(1/2,1) Ising-Heisenberg frustrated diamond chains are considered respectively. These two models are exactly solved by using transfer-matrix method. It is demonstrated that the existence of the antiferromagnetic interactions between next-nearest neighbor Ising spins will increase frustration effects and lead to a rich ground-state phase diagram. When the value of Heisenberg spin varies from 1/2 to 1, the system exhibits more quantum ground states containing entangled spin states. The nature of the zero-temperature phase transitions at different critical fields are vividly demonstrated by the low-temperature magnetization curves. Furthermore, in the mixed-spin diamond chain system, the magnetic specific heat curves present diverse double-peak structure with the variation of next-nearest neighbor interaction. More interestingly, when only the interactions between Heisenberg dimmers are considered, the double-peak structure can still be oberseved, indicating the furious competition arsing from biquadratic interaction and single-ion anisotropy.3. Based on the magnetic structure and characters of Ca3CoMnO6, one-dimensional elastic Ising model with nearest and next-nearest neighbour interactions as well as the magnetic-phonon coupling has been constructed. Transfer-matrix method has been employed to obtain exact solution. The analysis on the ground states shows that regardless of the ferromagnetic or antiferromagnetic interactions between nearest-neighbor spins, the up-up-down-down or up-down-down-up spin configuration can be presented at ground state if the next-nearest neighbour antiferromagnetic couplings are close to or stronger than thoes nearest ones. However these two spin configurations are degenerated under zero electric field, therefore the system does not exhibit macroscopic electric polarization at finite temperature. A non-zero electric field can elimate the degeneration at ground state. In addition, when the nearest-neighbor is antiferromagnetic coupling, the system demonstrates a rich ground-state phase diagram under the modulation of magnetic field. And a particular up-donw-up spin configuration appears which corresponds to 1/3 magnetization plateau.4. According to the magnetic structure of LiCu2O2 compound and the assumption of 45°-tilt ellipsoidal spiral order at ground state, a quasi-one-dimensional Heisenberg spin model by taking into account the interchain coupling and exchange anisotropy has been constructed. Monte Carlo simulation has been employed to qualitatively fit the exotic magnetoelectric properties in LiCu2O2. The simulation results show that the DM interaction or spin-current model still works in this compound. And the interchain interaction inside the zigzag ladder has great modulation effects on the spiral order at ground state. When it is in a strong antiferromagntic coupling, a perfect spiral order forms at low temperature. And the corresponding thermal dependence of magnetization, electric polarization, magnetic susceptibility and elecric susceptibility qualitatively exhibit the main characters of LiCu2C>2 compound. In addition, we also find that the easy-plane exchange anisotropy plays a crucial role both on the high-temperature phase transition and low-temperature spiral order.