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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)
2- I. F. I. Mikhail, I. M. M. Ismail, M. Ameen, Physica B 530 (2017)