| Studying the various thermodynamic properties of magnetic crystals and their dependence on temperature and anisotropy allow us to better understand the application of magnetic materials,they provide data support for related research in the experimental and industrial fields.The application is very extensive,especially for spintronic devices.The modified spin wave method is suitable for low-temperature and low-dimensional fields,and this paper will be used to study the S=1/2 anisotropic ferromagnetic chain with the nearest neighbor and the next nearest neighbor interaction,as well as the single-ion anisotropy S=1double sublattice antiferromagnetic chain,both models are based on the one-dimensional Heisenberg model.We found that the relevant thermodynamic properties are significantly correlated with temperature changes and exhibit significant anisotropy dependence;the corresponding results are significantly correlated with the data obtained by other methods;compared with traditional spin wave and Green's function methods,our method shows the superiority.The full text is divided into four chapters,the distribution is as follows:In the first chapter,the foreword shows the background and problems,the basic framework of the paper,and the methods used in the research.For the Heisenberg model of ferromagnetic and antiferromagnetic,this part introduces the research object,the research method,the current progress,the significance of the research and the main contents of this paper.In addition,we have discussed in detail the symmetry theory and the modified spin wave method.In the second chapter,we establish a ferromagnetic Heisenberg model with the nearest neighbor and the next nearest anisotropic interaction,and use the modified spin wave method to explore the low temperature thermodynamic properties under one-dimensional conditions.By controlling the total magnetization of the z-axis to zero and introducing an effective Hamiltonian,the diagonalization is achieved,then the dispersion relation and the self-consistent equation are obtained.In this chapter,the ground state energy,specific heat peak and corresponding position,specific heat coefficient peak and corresponding position,magnetic susceptibility coefficient peak and position satisfy the power law,exponential law,and linear law;for specific heat and its coefficient,we find the double peak behavior;whetherit is anisotropic or isotropic,its critical condition is ?=-0.25,and at critical conditions,the specific heat and magnetic susceptibility behave as T^1/4 and T^-4/3,respectively.In the third chapter,we establish a single-ion anisotropic double sublattice antiferromagnetic Heisenberg model,and use the modified spin wave method to explore the low temperature thermodynamic properties under one-dimensional conditions.By introducing the free energy of the constraint condition,the free energy is zero to the total number of spin wave quantum and Lagrangian factor,and the dispersion relation and the self-consistent equation are obtained.In this chapter,the critical temperature and its function,critical excitation energy and its function are discussed;Haldane's conjecture on the integer spin gap is verified;for internal energy and free energy,we will renewal the results obtained by the modified spin wave method.The results of traditional spin waves are collated into images for comparative analysis.It is found that the modified spin wave method can overcome the thermodynamic divergence problem of the traditional spin wave method.When the temperature is lower than 0.4,the excitation energy and specific heat show the exponential change of temperature law.In the fourth chapter,the phenomena of the second chapter and the third chapter is compared,analyzed and summarized,and we point out the limitations and prospects. |
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