Coupled-mode theory for the interaction between acoustic waves and spin waves in magnonic-phononic crystals: Propagating magnetoelastic waves

Abstract

We have investigated co-directional and contra-directional couplings between spin wave and acoustic wave in one-dimensional periodic structure (magphonic crystal). The system consists of two ferromagnetic layers alternating in space. We have taken into consideration materials commonly used in magnonics: yttrium iron garnet, CoFeB, permalloy, and cobalt. The coupled mode theory (CMT) formalism have been successfully implemented to describe magnetoelastic interaction as a periodic perturbation in the magphonic crystal. The results of CMT calculations have been verified by more rigorous simulations by frequency-domain plane wave method and time-domain finite element method. The presented resonant coupling in the magphonic crystal is an active inspace mechanism which spatially transfers energy between propagating spin and acoustic modes, thus creating propagating magnetoelastic wave. We have shown, that CMT analysis of the magnetoelastic coupling is an useful tool to optimize and design a spin wave -acoustic wave transducer based on a magphonic crystals. The effect of spin wave damping has been included to the model to discuss the efficiency of such a device. Our model shows that it is possible to obtain forward conversion of the acoustic wave to the spin wave in case of co-directional coupling and backward conversion in case of contra-directional coupling. *

Co- and contra-directional vertical coupling between ferromagnetic layers with grating for short-wavelength spin wave generation

“…The possibility of miniaturization of spin-wave-based logic devices is dependent on the wavelength, thus the attention is focused on searching the ways of generation of short SWs. Several approaches has been recently reported: shortening the wavelength in a tapered waveguide [9], microwave-to-SW transducers based either on magnetic wires [10], nanostructure edges [11], diffraction gratings [12][13][14], coplanar waveguides [15] or anisotropy-modulated multiferroic heterostructures [16], transduction of acoustic waves into short SWs due to magneto-elastic coupling [17,18], and emitters based on current-driven oscillating pinned domain walls [19].…”

Magnetic domain walls as broadband spin wave and elastic magnetisation wave emitters

“…In an analytical approach, the dispersion relation is compared to the expected linear dependence for an elastic shear wave. For this the velocity of sound c was calculated using where G CoFeB = 70 GPa is the shear modulus of CoFeB 33 . With the volumetric mass density 33 ρ CoFeB = 7050 kg/m 3 , a shear wave propagation velocity of c = 3.151 km/s is calculated.…”

“…Due to the numerical gradient evaluation, the force input was reduced by one cell along the z -direction compared to the micromagnetically simulated magnetisation distribution. For the calculation the following isotropic material parameters were used a Young’s modulus of E CoFeB = 182 GPa, a Poisson’s ratio of ν CoFeB = 0.3, and a density of ρ CoFeB = 7050 kg/m 3 33 , and respectively E glass = 82 GPa, ν glass = 0.206, and ρ glass = 2510 kg/m 3 40 .…”

Confined magnetoelastic waves in thin waveguides

“…Most of these studies have focused on the interaction between surface acoustic waves propagating at the interface between a (piezoelectric) substrate and a thin magnetostrictive film with macroscopic dimensions [5,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35]. In addition, also numerical and theoretical studies on magnetoelastic plane waves in bulk media have been reported [36][37][38][39][40].…”