The Study Of Collective Excitations And Invar Effect Dynamics In Heisenberg System Based On Magnon-phonon Interaction

It is discovered that there exist broadening in the magnon line-width and magnon softening on the zone-boundary in the perovskite structure manganese oxide inelastic-neutron scattering experiment at low-temperature. It is also discovered that below the magnetic phase transition temperature there exists softening of transverse acoustic phonon in crystal state Invar alloys such as Fe₆₅Ni₃₅, Fe_(?)Pt₂₈ and Fe₃₀Mn₃₀ by the inelastic-neutron scattering experiment. But there has been no softening of longitudinal acoustic phonon discoved. The above phenomena are all related to the collective excitations of magnetic ordered material. Therefore, in this thesis Matsubara Green function theory has been used to explore magnon excitations and phonon excitations of two-dimensional Heisenberg ferromagnetic system under magnon-phonon coupling. New views have been obtained which accord with experimental phenomena. The results may be summarized as the following.First, under the consideration that any unitary transformation of a system does not change its physical property, the Hamiltonian in the form of two-body couplingH|(?)_k = A₁a_k⁺a_k + A₂b_k⁺b_k + (Ba_k⁺b_k⁺ + B^*a_kb_k) + (Ca_k⁺b_k + C^*b_k⁺a_k) is diagonalized. The resultis universal for finding the solution of simple harmonic magnon energy of various magnetic ordered material and suitable for programming. Furthermore this kind of diagonalization method by unitary transformation has distinct physics thought.Secondly, in order to confirm the broadening in the magnon spectrum line-width and softening when magnon mixed with optical-phonon at low temperature as the inelastic-neutron scattering experiment on perovskite ferromagnetic materials revealed, the action of magnon-phonon coupling on the magnetic excitations has been studied systematically in the cases of the simple triangular insulating ferromagnetic lattice in which the nearest-neighbour force constant is considered only, the simple square insulating ferromagnetic lattice in which the second-nearest-neighbouring force constant...