Spin-Wave Resonances Affected by Skin-Effect in Conducting Magnetic Nanowire Arrays at Terahertz Frequencies

Abstract

The properties of localized standing spin wave (SW) resonances are investigated numerically for a regular 2-D array of 10 nm diameter, 300 nm long metallic (iron) nanowires, magnetized at different orientations of the bias magnetic field 0 with respect to the wire axis. At 30 THz the penetration depth of the electromagnetic (EM) waves can be close to the diameter of the nanowires, leading to interesting resonance effects as a result of the inhomogeneous magnetization distribution across the nanowire diameter. The mathematical model considers the metallic character of the wires and the exchange interactions between the wires, when solving Maxwell equations simultaneously with the Landau-Lifshitz equation for the magnetization. The transmission coefficients T 21 of TEM waves through arrays with different wire radius were determined. There are well-defined extrema of T 21 at certain values of the bias magnetic field 0 , corresponding to ferromagnetic resonance (FMR) and antiresonance (FMAR) modes. The position of these maxima and minima does not depend on the orientation of H 0 , although T 21 is sensitive to the direction of 0 . The distribution of the magnetization component across the nanowire is calculated for the second and low order exchange SW modes.Index Terms-Electromagnetic propagation in magnetic media, magnetic materials, magnetic resonance, nanotechnology.

Spin waves and electromagnetic waves in magnetic nanowires

“…Measurements of this angular dependence is a convenient tool to extract the interaction field in nanostructures (Pardavi-Horvath et al, 2011). The internal field contains the demagnetizing field, determined by the shape of the specimen.…”

“…The rf magnetization profiles of the exchange SW modes modes are numerically simulated taking into account the skin depth of the EMW in a ferromagnetic metal (Fe) at THz frequencies (Pardavi-Horvath et al, 2011). The EMW having a wave vector k ¼ kz 0 and fields E ¼ Ex 0 , H ¼ Hy 0 is incident on a 2-D array of ferromagnetic metallic nanowires, biased by a magnetic field H 0 ?…”

Towards high-frequency negative permeability using magnonic crystals in metamaterial design

“…One can see from Eqs. (16) and 17that only the modes that have a nonzero net dynamic magnetic moment contribute to the absorption and hence can be efficiently excited by the external uniform ac field. In other words, the efficiency of coupling is determined by the overlap integral of the mode and the field profiles.…”

“…Maxwell equations simultaneously with the Landau-Lifshitz (LL) equation for the magnetization have been solved to obtain the transmission coefficients for the array of nanowires. 16 Extrema in the transmission function have been found due to spin-wave resonance and antiresonance modes.…”

“…25,26 At frequencies larger than the resonance frequency, the magnetic permeability goes from negative to positive values through zero, the latter point called antiresonance condition. 16 Because the antiresonance occurs at frequencies shifted away from the resonances, the absorption decreases.…”