Wide-band electromagnetic wave propagation and resonance in long cobalt nanoprisms

Abstract

Electromagnetic wave interaction with confined metallic magnetic structures is complex due to the excitation of non-uniform electromagnetic fields and magnetic precession and spinwave modes over length scales that are dependent on the geometric, electromagnetic and micromagnetic properties of the magnetic structures. In this article we solve the coupled system of Maxwell's equations and the Landau-Lifshitz-Gilbert equation using a stable algorithm based on the finite-difference time-domain method to study the transient, wide-band electromagnetic propagation and resonance in infinitely long cobalt nano-prisms with square cross-section of side lengths 50 - 1000 nm. In particular we identify the resonance mechanisms through studying the local transient and spectral distributions of the magnetization in the prisms. The nano-prisms were excited by an axially polarized plane wave at normal incidence with a 70 GHz Gaussian pulse profile. For this incident wave condition, the simulations confirmed that resonance in the cobalt prisms is excited mainly by the currentinduced magnetic fields, and indicated a magnetization curling resonance mode for prism side lengths less than 100 nm. The eigen frequencies for the curling mode were confirmed theoretically using a model for an equivalent long circular cylinder with radial spin-wave modes. For prisms side lengths larger than 100 nm (but less than the non-magnetic skin depth), the magnetic response was confined to thin regions along the prism edges due to resonance induced skin effects. The simulations indicated predominately uniform magnetization precession in the confined edge regions with increased pinning in the corners. The uniform resonance mode in the central part of the edge regions increases in intensity with prism size, with frequency described using Kittel's ferromagnetic resonance frequency of a thin planar structure. A higher frequency, size-independent uniform resonance mode was observed in the corner regions with frequency determined by the local demagnetizing factors. Local and integrated power absorption spectra were calculated using the simulated transient magnetization and fields, and confirmed the resonance modes and frequencies in the cobalt prisms and their size dependence. The profile of the local power absorption spectra was also used to estimate the thickness of the confined edge regions or magnetic skin depth in the cobalt prisms at the fundamental resonance mode and was found to be approximately 50 nm. The outcomes of this work would benefit the design and engineering of light-weight and compact materials and devices incorporating metallic magnetic nano-structures. This work also provides foundation for further modelling and understanding of electromagnetic transmission and propagation in more complex metallic ferromagnetic structures and composites excited by different electromagnetic wave conditions.