Phonon-magnon resonant processes with relevance to acoustic spin pumping

The recently described phenomenon of resonant acoustic spin pumping is due to resonant coupling between an incident elastic wave and spin waves in a ferromagnetic medium. A classical one-dimensional discrete model of a ferromagnet with two forms of magnetoelastic coupling is treated to shed light on the conditions for resonance between phonons and magnons. Nonlinear phonon-magnon interactions in the case of a coupling restricted to diagonal terms in the components of the spin degrees of freedom are analyzed within the framework of the multiple timescale perturbation theory. In that case, one-phonon-two-magnon resonances are the dominant mechanism for pumping. The effect of coupling on the dispersion relations depends on the square of the amplitude of the phonon and magnon excitations. A straightforward analysis of a linear phonon-magnon interaction in the case of a magnetoelastic coupling restricted to off-diagonal terms in the components of the spins shows a one-phonon to one-magnon resonance as the pumping mechanism. The resonant dispersion relations are independent of the amplitude of the waves. In both cases, when an elastic wave with a fixed frequency is used to stimulate magnons, application of an external magnetic field can be used to approach resonant conditions. Both resonance conditions exhibit the same type of dependency on the strength of an applied magnetic field.

Figure 1

Schematic illustration of the one-dimensional discrete atomic model supporting coupled spin waves and elastic waves. The $x$ axis is defined along the chain of atoms.

Figure 2

(a) Denominator of functions $P$ and $Q$ versus reduced wave number $ka$ for different values of the parameter ρ. The inset represents the magnon (dotted line) and the phonon (solid line) dispersion curves at $\rho =1$. The condition for resonance ${\omega }_0^{\prime }\left(2k\right)=({\omega }_0\left(k\right)+{\omega }_0^{\prime }\left(k\right))$ is highlighted with vertical lines. (b) $P$ and (c) $Q$ as functions of $ka$ and ρ.