Spin wave relaxation and magnetic properties in [M/Cu] super-lattices; M=Fe, Co and Ni

In this work, we study the elementary excitations and magnetic properties of the [M/Cu] super-lattices with: M=Fe, Co and Ni, represented by a Heisenberg ferromagnetic system with N atomic planes. The nearest neighbour (NN), next nearest neighbour (NNN) exchange, dipolar interactions and surface anisotropy effects are taken into account and the Hamiltonian is studied in the framework of the linear spin wave theory. In the presence of the exchange alone, the excitation spectrum E(k) and the magnetization 〈Sz〉/S analytical expressions are obtained using the Green's function formalism. The obtained relaxation time of the magnon populations is nearly the same in the Fe and Co-based super-lattices, while these magnetic excitations would last much longer in the Ni-based super lattice. A numerical study of the surface anisotropy and long-ranged dipolar interaction combined effects are also reported. The exchange integral values deduced from a comparison with experience for the three super-lattices are coherent.