Dependence of the Phonon-Instability Threshold for Parallel Pumping on Crystal Orientation and Magnetic Fieldstrength

Abstract

The theory of phonon instability under parallel pumping is extended by taking account of magnetocrystalline and magnetoelastic anisotropy. Previous results apply to real materials only when the magnetic field is along a [100] direction. Results are obtained for the instability threshold when the magnetic fields are along a [110] or a [111] direction. When magnetic loss is neglected the calculated threshold (minimum with respect to all directions of propagation) for all three principal crystal directions varies with dc field‐strength in such a way that h_crit^1/2 is approximately a linear function of the dc field, with the extrapolated intercept (zero threshold) at internal dc fields of −⅔H_a for [111], ½H_a for [110], and H_a for [100]. Here H_a=−2K₁/M₀ is the anisotropy field and it has been assumed that K₁<0. For the [110] case the threshold is approximately $$h_{\mathrm{crit}}^{\text{1/2}}{\text{=(2γ/σQ}}_e{)}^{\text{1/2}}\mathrm{(H-}\frac{1}{2}{H}_{\mathrm{a}}\mathrm{),}$$ where σ/γ=b₂²/C₄₄M₀ and Q_e is the phonon Q. When magnetic loss is taken into account, h_crit^1/2 still remains an approximately linear function of dc field, but the extrapolated intercept is moved to lower dc fieldstrengths.