Broadband magnetoelastic coupling in magnonic-phononic crystals for high-frequency nanoscale spin-wave generation

Spin waves are promising candidates for information carriers in advanced technology. The interactions between spin waves and acoustic waves in magnetic nanostructures are of much interest because of their potential application for spin-wave generation, amplification, and transduction. We investigate numerically the dynamics of magnetoelastic excitations in a one-dimensional magnonic-phononic crystal consisting of alternating layers of permalloy and cobalt. We use the plane-wave method and the finite-element method for frequency- and time-domain simulations, respectively. The studied structure is optimized for hybridization of specific spin-wave and acoustic dispersion branches in the entire Brillouin zone in a broad frequency range. We show that this type of periodic structure can be used for efficient generation of high-frequency spin waves.

Figure 1

Geometry of the simulated system: (a) unit cell used in plane-wave method calculations; (b) NiFe/Co magnonic-phononic structure considered in finite-element method simulations, with a continuous acoustic wave excited by a point source $S$ and propagating along the $x_1$ axis. Both acoustic and spin waves are damped near the boundaries of the system.

Figure 2

(Right) Dispersion relation of the NiFe/Co magnonic-phononic crystal calculated by the PWM. In the color scale, blue and red correspond to acoustic and spin waves, respectively. Green indicates coupled magnetoelastic waves. (Left) Proportion of magnetic energy accumulated in the system in 1 ns of excitation by acoustic wave of a given frequency.

Figure 3

Magnified anticrossings C1, C2, C3, and C5 (indicated in the dispersion relation in Fig. 2) in the NiFe/Co magnonic-phononic crystal.

Figure 4

Acoustic- (left) and spin-wave (right) signals after 1 ns of excitation by an acoustic wave from a source point $S$ at 20, 50, and 90 GHz. Insets show enlarged plots of the 50 GHz acoustic and spin-wave signals beyond the magnonic-phononic crystal. Uniform gray and patterned areas represent the magnonic-phononic crystal and damping edges, respectively. The amplitude ratio of the acoustic and spin waves is preserved.