Field dependence of the magnetic eigenmode frequencies in layered nanowires with ferromagnetic and antiferromagnetic ground states: experimental and theoretical study

The magnetic field dependence of the magnetic eigenmode frequencies in 150 nm wide layered permalloy nanowires (NWs) has been studied by the Brillouin light scattering technique. The NWs have the following layering structure Py(30 nm)/Cu(10 nm)/Py(d)/Cu(10 nm)/Py(30 nm) with fixed thickness of the top and bottom stripe and differ by the thickness d of the middle Py stripe (with d = 15, 30, 60 nm). The magnetic field, applied along the length of the wires, has been swept from positive to negative saturation thus exploring both the ferromagnetic and the antiferromagnetic relative orientation of the magnetization in the middle stripe with respect to the outermost ones. In conjunction with the transition between the two different ground states, the mode frequencies undergo an abrupt variation. Moreover the mode frequencies in the antiferromagnetic state are relatively insensitive to the applied field strength. The experimental results (frequencies versus magnetic field strength) have been successfully interpreted by means of a microscopic (Hamiltonian-based) theory which incorporates both the exchange and dipole-dipole interactions as well as effects of single-ion anisotropy and an external magnetic field applied parallel to the NW axis. This model was extended to account for parallel and antiparallel magnetization orientations in the layered NWs, enabling us to also calculate the probability amplitude of each spin-wave eigenmode at any position in the trilayered NWs.