The Effect of Anisotropy Field on the Dispersion Relation and Thermodynamic Properties of Antiferromagnetic Materials : Employing the Quantum Field theory
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Date
2024-08
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Addis Ababa University
Abstract
In this thesis, we look at the complex dynamics of spin waves in a two-sublattice antiferromagnetic (AFM) system, with an emphasis on spin interactions and the magnon dispersion relation. The main purpose of this study was to examine spin wave interaction and how anisotropy field influence on dispersion relation and characteristics of (AMF) systems. The theoretical framework is based on the Heisenberg Hamiltonian model, which was specifically built to manage a uniaxial
anisotropy field within an antiferromagnetic system. To overcome the problem, we employ quantum field theory, namely the double-time temperature-dependent Green function technique to achieve magnon dispersion. A random phase approximation is used to decouple and diagonalize higher order components. The discovery of a relationship between the anisotropy field and the dispersion relation for the wave vector k at low temperatures is particularly interesting. The findings indicate that as the anisotropic field becomes stronger, the magnon dispersion progressively shifts from a curved trajectory to linearity, finally adopting a sinusoidal form with further expansion into the first Brillouin zone. Furthermore, we investigate the thermodynamic parameters
of magnetization and heat capacity within the uniaxial symmetric AFM crystal lattice, concentrating on excitation temperature at low temperatures
and utilizing the long-wavelength approximation. The results show that AFM magnetization and heat capacities are sensitive to anisotropic fields, with magnetization trending upward and the greatest peak of heat capacity dropping as anisotropy increased. The findings provide understanding of the complicated relationship between anisotropy and exchange fields in antiferromagnetic systems, indicating their significant impact on magnetization, heat capacity, and other thermodynamic parameters. Furthermore, this model gives information on the variations in susceptibility and heat capacity between transition metal antiferromagnetic fluorides. Further investigation may be necessary in this situation.
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Effect of Anisotropy, Dispersion Relation, Thermodynamic Properties, Antiferromagnetic Materials, Employing the Quantum Field theory