Study On Spin Waves In Ferromagnetic Bilayers With BCC Structure

On the basis of the Heisenberg exchange model, the spin-wave eigen-problem in the ferromagnetic bilayers with simple cubic structure is solved exactly at the low temperature. With this theory, we focus on the effect of the magnetic field on the system band structure and spin waves in the paper. The results show that the magnetic field effected energy bands in three aspects as follows:(1) With the increasing of the magnetic field, band A and B are both moving up, and B moves faster than A. This phenomenon means that the energy of all the modes increases, and the energy of band B increases faster. (2) Bulk modes change with transverse spin waves periodically, and with the increase of the magnetic field, bulk modes move up too. When the magnetic field takes a certain critical value, band A and B are separation, moreover the bulk modes disappear. (3) As the magnetic field changes, the conversion takes between the interface modes and bulk modes, and with the magnetic field, the interface modes move away from band A. The effect of magnetic field on spin waves exists in the following three aspects:(1) The magnetic field influence on the waveform, which is exhibited in the type of the spin waves can be changed when the magnetic being changed. (2) The magnetic field have effect on the phenomenon of the spin wave modulation. When the magnetic field reaches a certain critical value, the modulation phenomenon disappears. (3) The magnetic field also have an impact on the spin-wave oscillations. We find that the oscillation of the waveform can be changed by the magnetic field excitation.