Effect of the applied magnetic field and the layer thickness on the magnon properties in bilayers Co/Pt and symmetrical trilayer Pt/Co/Pt

We have studied the elementary magnetic excitations and their dynamics in multilayer Co(t Co)/Pt(t Pt) and Pt(t Pt)/Co(t Co)/Pt(t Pt) under an applied magnetic field. The Heisenberg hamiltonian used takes into account the magneto-crystalline and surface anisotropies, the exchange and dipolar interactions. The calculated excitation spectrum εN(k) presents a structure with two sub-bands corresponding to the magnons of surface and volume respectively. The existence of a gap of creating these magnons is also highlighted. The lifetimes deduced from these gaps are in good agreement with the results of previous studies. The thermal evolution of the magnetization mz indicates that the system undergoes a dimensional crossover 3D-2D when the temperature increases. The calculated and measured magnetizations are compared and they are in good agreement. The exchange integral and critical temperature values deduced from these adjustments are in very good agreement with the results of previous works.