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The squeezed states of dressed magnons in ferromagnets have been investigated. No effective Debye cutoff frequency has been assumed unlike what has been done hitherto. Instead, the results have been expressed throughout in terms of the reduced temperature. The effect 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 significant role in determining the squeeze factor and the variation of the dressed magnon effective mass with temperature.

A theoretical study is given of thermal conductivity in antiferromagnetic materials. 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.

A theoretical study is given of magnon–phonon interactions in antiferromagnetic materials. The roles of magnons and phonons as heat carriers and as sources of thermal resistance have been taken into consideration. The exact collision operator which represents the magnon–phonon interactions involved in the transport Boltzmann equations has been replaced by a model operator which possesses the same important properties. The effect of other scattering processes that either phonons or magnons are involved has also been investigated. A new expression for the thermal conductivity has been derived. It includes terms which represent both Normal and Umklapp magnon–phonon processes. The results obtained by using the new expression agree quantitatively with the experimental measurements on Fe Cl2

A comparison is given between the variational and strong perturbation techniques. It has been shown that the variational method gives, in general, better results. Also, a new formulation is presented for the strong perturbation technique that depends on a simpler equivalent form of the perturbed part of the Hamiltonian. Moreover, common expressions which are valid for both treatments have been obtained. The results are applied to calculate the binding energy for a hydrogenic impurity placed in a finite confining potential spherical quantum dot in the states (1s), (2p) and (2s). The results obtained hitherto for a central impurity by using the strong perturbation technique are deduced in a much simpler way. As regards the off-central impurity some new expressions have been derived in both treatments. The numerical results for the two states (1s) and (2p) have also been investigated.