Abstract
A normal-mode theory for the dipole-exchange spin-wave spectrum in the finite-width ferromagnetic waveguide is presented. The theory takes into account a nonuniform character of the demagnetizing field in the waveguide cross section and, therefore, can be applied to any infinitely long, rectangular rod, even with square cross section. The inhomogeneity of static and dynamic dipole fields is taken into account using the same tensorial Green’s function, obtained from Maxwell equations, this fact allows to simplify the spectrum calculation procedure. According to the elaborated theory the spin-wave spectrum in the finite-width ferromagnetic waveguide can be calculated with simultaneous account of the dipole-dipole and exchange interaction, surface anisotropy, arbitrary direction of the external bias magnetic field and for any possible width-thickness aspect ratio of the magnonic waveguide. It is shown that the previously used analytical methods of the accounting of the finite width of the magnetic waveguides give unsuitable results for nanometer-size waveguides.
Highlights
A demand of miniaturization in nanoelectronics leads to a size reduction of the ferromagnetic elements used in microwave devices
It is well known that the conditions of the wave propagation in confined waveguiding structures differ drastically from the infinite-film ones
A finite width of the waveguiding structure is taken into account simultaneously with the arbitrary type of surface anisotropy on the edges of the waveguide
Summary
A demand of miniaturization in nanoelectronics leads to a size reduction of the ferromagnetic elements used in microwave devices. In the magnetic finite-width waveguides a lot of new effects appear due to the strong confinement of propagating spin waves [1,2,3,4]. From these perspectives, commonly used approximate theoretical methods cannot meet the demands of the theoretical analysis of the obtained experimental data. To illustrate the presented theoretical approach, the numerical calculations of the spin-wave spectrum were done for the most common case of tangentially magnetized waveguiding structure. It is demonstrated that the approximate analytical methods, which are widely used for the accounting of finite-size effects in ferromagnetic waveguides, give a large discrepancy for micron- and nanometer-size samples
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