Generation of Spin Waves in Nonuniform Magnetic Fields. III. Magnetoelastic Interaction

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Abstract
If a spin wave propagates through a region of nonuniform magnetic field in which the effective magnon wavenumber equals the phonon wavenumber, it is partially converted into an elastic wave. The conversion efficiency depends primarily on the field gradient (H′) at the crossover point. Theories have been developed both for the case of weak magnetoelastic coupling and strong magnetoelastic coupling. For weak coupling the magnon‐phonon conversion efficiency ηmp is ηmp=H′crit/|H′| (for |H′|>>H′crit), whereas for strong coupling ηmp = 1−π2exp(−H′crit/|H′|) (for |H′|<<H′crit). Here H′crit=πb22 ω/cMμ is a critical field gradient, b2 is one of the magnetoelastic constants, ω/2π the signal frequency, c the velocity of (transverse) sound, M the saturation magnetization, and μ the shear modulus. It has been assumed that the dc magnetic field is applied along a cube edge of a cubic crystal and that the material is elastically isotropic. For yttrium iron garnet (YIG) at room temperature and a signal frequency of 3×109 sec−1, H′crit≃5×104 Oe/cm. The field gradients encountered in practice are usually appreciably smaller. Thus the strong coupling theory applies and the magnon‐phonon conversion should be substantially complete. The magnetoelastic interaction also gives rise to a reflected wave which originates in the crossover region. The amplitude of the reflected wave is much smaller than the amplitude of the transmitted wave.