Theoretical Investigations Of Quantum Magnetism In Quantum Spin Systems And Magnetic Oxide Compounds

In recent years, with the rapid development in condensed matter physics, investigations for magnetic physics are also deepening continually. This is because that magnetic system is of many intriguing physical properties such as colossal magnetoresistance effect, magneto-optical effect and magnetostrictive effect etc. Especially, investigations show that the first generation Cu-oxygen high-temperature superconductor and the second generation Fe-base superconductor of magnetic properties can be theoretical analysis and forecasting by means of Heisenberg model. So investigated of magnetic materials has become the theorists and experimentalists technical application of the popular topics. In recent years, the investigations of development about these aspects are very rapid, and these achievements and findings will definitely stimulate the progress of physics other areas and related scientific. So from studying the origin of the magnetic properties,researching a new way to increase magnetism and finding a new application region for magnetic materials become the main investigated contents of the contemporary magnetism. Following this direction,we try to attack some corresponding theoretical problems.In this thesis, starting from the exchange interaction of microscopic model and coupled interaction of Hamiltonian model, double time Green's function is used to investigate the antiferromagnets and some magnetic oxide compounds of magnetic properties within the random phase decoupling approximation. The whole thesis consists of six chapters. The Chapter one aims at a brief overview of the history, basic concept and progress of magnetic system and some magnetic oxide compounds. In addition, the investigation technique (double time Green's function) of this thesis will also be described.In Chapter Two, the ordered and disordered phases of spin-1 Heisenberg and Ising antiferromagnets with easy-axis single-ion anisotropy on a three-dimensional lattice are investigated. By using of the double-time Green's function method within the Tyablikov decoupling for the exchange anisotropy and Callen's approximation for the single-ion anisotropy, the Néel temperature, magnetization and susceptibility are investigated. It shows that our results agree well with ones from spin wave theory at low temperature, and compare reasonably well with those obtained by the linked-cluster series expansion method, by the ratio method and using the high temperature series expansion approach at intermediate temperature and in the vicinity of the critical temperature at?= 1and D=0. For?= 1 and D=0.5, our results agree with the linked-cluster series expansion method ones and ratio method ones in the ranges1.2?T?2.75(sc) and1.5?T?4 (bcc), respectively. But for D=0 and D=0.5, our results deviate from those obtained by the linked-cluster series expansion method and the ratio method.In Chapter Three, the magnetic properties of two-dimensional quantum Heisenberg antiferromagnet on the square lattice with easy axis exchange anisotropy are investigated by means of Green's function approach within random phase and Callen's approximations. The Néel temperature TN , energy gap?0and staggered magnetization m of magnetic materials (CH 3 NH₃ )₂ MnCl₄, Rb₂ MnCl₄, Rb₂ MnF₄ , K 2 MnF₄ and K 2 NiF₄ are discussed in detailed. Comparing our results with other theoretical and experimental works, our investigations exhibit good results for the Néel temperature, energy gap and staggered magnetization. Meanwhile, our investigations show that result being in good agreement with experiment is obtained within RPA over the entire range of temperature, and it is stated that CA, although more complex, gives no further improvement to the RPA results. We conclude that the physical properties of the magnetic compounds are mainly determined by easy-axis anisotropy in the intralay exchange interaction and can be well modeled and described by the two-dimensional quantum Heisenberg antiferromagnet with this anisotropy.In Chapter Four, it applies the Heisenberg mixed-spin model to investigate the magnetic properties of the manganese oxide compound La_1-xSr_xMnO₃by using the technique of double-time Green's function. Within the RPA decoupling for higher order Green's functions, the analytic expressions of the magnetization, the transition temperature, the spin-wave dispersion relation and spin-wave stiffness are obtained. The phase diagram, magnetization, spin-wave dispersion and spin-wave stiffness of La_1-xSr_xMnO₃as a function of the temperature, magnetic field and doping concentration are discussed in detailed. Comparing our results with other theoretical and experimental works, our results are in agreement with other theoretical and experimental results. Meanwhile, it shows that our microscopic model and method can well describe the magnetic properties of the manganese oxide compound La_1-xSr_xMnO₃.In Chapter Five, the properties of two-dimensional square lattice mixed-spin anisotropic Heisenberg ferromagnet with a transverse magnetic field are studied by means of the double-time Green's function. The analytic expressions of the critical temperature, the high-temperature zero-field susceptibilities, the spin-wave velocity, spin-wave stiffness and spin-wave gap are obtained. For zero field, the relation[ g (0) ? g (T )]?T?is obtained for various mixed-spin. Our?value is close to the well-known Bloch exponent at low temperature. For h x?0, in the high temperature limit,?s?Js ( s + 1) /(3?BT) and?S?JS ( S + 1) /(3?BT)are in accordance with the Curie-Weiss law. For hx /J and D = 0, our results obey the Mermin-Wagner theorem. The phase diagrams in which the critical temperature, the reorientation temperature and the reorientation magnetic field are shown as a function of single-ion anisotropic parameter are discussed in detailed.In Chapter Six, based on our existing studies and further explore research in quantum magnetic system, the prospect of our future works is given in brief.