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Abstract The role played by magnon-phonon interactions in two important phenomena in magnetic materials has been investigated. The rst phenomenon is thermal conduction in antiferromagnetic materials. Thus the rst part of the thesis is concerned with performing a theoretical study of thermal conductivity in antiferromagnets. The study has the advantage that the three phonon interactions as well as the magnon phonon interactions have been represented by model operators that preserve the important properties of the exact collision operators. A new expression for thermal conductivity has been derived that involves the same terms obtained in our previous work in addition to two new terms. These two terms represent the conservation and quasi-conservation of wavevector that occur in the three-phonon Normal and Umklapp processes respectively. They gave appreciable contributions to the thermal conductivity and have led to an excellent quantitative agreement with the experimental measurements of the antiferromagnet FeCl2. The second phenomenon is magnon squeezing. Very important results concerning the time evolution operator and the time dependence of the operators involved that arise due to magnon-phonon interactions in antiferromagnets have been derived. However, the study of this phenomenon has been carried out mainly in the second part of the thesis in ferromagnetic materials. The squeezed states of dressed magnons in ferromagnets have been investigated. No eective Debye cuto frequency has been assumed unlike what has been done hitherto. Instead, the results have been expressed throughout in terms of the reduced temperature. The eect of dressed magnon-phonon interactions on the formulation of these states has been studied. It has been shown that the magnon-phonon interactions play a signicant role in determining the squeeze factor and the variation of the dressed magnon eective mass with temperature. The main results of Chapters 2 and 4 have been published in 1- I. F. I. Mikhail, I. M. M. Ismail, M. Ameen, Physica B 476 (2015) 29. 2- I. F. I. Mikhail, I. M. M. Ismail, M. Ameen, Physica B 530 (2017) 106. |