The Study Of The Spin Dynamics Of Exchange Coupling In A Ferromagnetic Bilayer Film

Currently, the ferromagnetic film systems play important roles in modern information technology ranging from magnetic data storage to sensors or magnetic random access memory. For a functioning device, when a field is sensed or data are written, the magnetic system is excited. Moreover, an important role for the speed of magnetization reversal is played by confined spin waves. Therefore, studying spin excitations in magnetic multilayers will improve understanding their magnetic properties. Under the aperiodic boundary condition, eigenmodes and resonance of spin waves in a ferromagnetic bilayer system are explored by using the interface rescaling approach in this paper.Firstly, we have deduced the uniform micro-spin-wave theory of magnetic multilayer systems and applied it to the symmetrical magnetic bilayer systems. The eigenproblems are examined in this system and the criteria of conditions for the existence of eigenmodes are given. The results show that if the interface coupling is ferromagnetic, all modes non-affected by the interface coupling are symmetrical modes, while all those affected are antisymmetrical modes. For antiferromagnetic interface coupling, the reverse holds. We compare the results with those H. Puszkarski had discussed and found that they are consistent. Furthermore, we have discussed the spin-wave resonance. It is shown that only the single-line intensity is non-zero when k=0 and this is the case of ordinary ferromagnetic resonance when the spectrum presents but one resonance line. Multi-peak bilayer spin-wave resonance therefore requires antiferromagnetic interface coupling.Secondly, we applied this theory to the unsymmetrical magnetic bilayer systems, we turn to analyze numerically in detail the energy-band configuration of the longitudinal spin waves with the transverse wave vectorΓ// varying along the high-symmetry paths of two dimensional (2D) Brillouin zone. There are two types of the energy-band structure. Whenβ< 2/3, an energy gap between the two subbands exists (see FIG.1), otherwise the energy gap will disappear forβ> 2/3. In the regions of the bulk modes, the phenomenon of hybridization between subbands can be observed due to the distinction of JASA and JBSB. When the magnitude ofβincreases, the hybridization regions become larger, and vice versa. We also detailed the evolutive conditions of different spin waves and the evolution of spin-wave resonance. It is shown that the sharp intensity may exists critical point where different eigenmodes transform each other.Thirdly, we discussed the effects of the bulk anisotropy for the eigenmodes in the bilayer system. The results show that the higher subband moves up globally with increasing DA or drops globally with the declining DA. However, the lower subband is fixed; the hybridized (or seem overlap) branches reduces with the increasing DA or the hybridized (or seem overlap) branches enhances with the decreasing DA Moreover, we deduced conditions for the existence of energy-band gap in the whole first Brillouin zone. Because there are the complicated energy band fine structure, double Sharp intensity maybe exist.At last, the effects of the surface anisotropy for the eigenmodes in the symmetrical bilayer system are investigated. It is shown that when the anisotropy is easy-axis type the eigenmodes are pinned. While the two energetically lowest eigenmodes evolve into surface modes. when the anisotropy is easy-plane type. Moreover, whether the exchange coupling of interface is ferromagnetic or antiferromagnetic, multi-peak bilayer spin-wave resonance will appear.