Ferromagnetic multilayers: Statics and dynamics

A theory of periodic multilayers consisting of two alternating ferromagnetic materials with different transition temperatures is presented. The theory is based on an inhomogeneous Ginzburg-Landau (GL) functional, where the GL coefficients are chosen to model the alternating layers and interface interactions. The transition temperature of the composite material is derived by use of the linear stability analysis of the inhomogeneous GL functional. The static magnetization profiles for different temperatures are calculated analytically. It is shown that the magnetization penetrating into the low-temperature ferromagnet falls off inversely with distance close to $T_1$ and exponentially far above $T_1$, where $T_1$ is the lower transition temperature. We also consider the average magnetization of this multilayer system and its characteristic temperature dependence. The spin dynamics are studied by use of a generalized Bloch equation. Different limiting cases as well as the general situation with both dipolar and exchange interactions are considered. The magnon dispersion relation is computed and by symmetry considerations, it is shown that the gaps vanish at certain values of the wave vector k. The inelastic neutron scattering cross section is calculated. With appropriate modifications the theory can be applied to other systems undergoing phase transitions, such as ferroelectrics.