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 hcrit1/2 is approximately a linear function of the dc field, with the extrapolated intercept (zero threshold) at internal dc fields of −⅔Ha for [111], ½Ha for [110], and Ha for [100]. Here Ha=−2K1/M0 is the anisotropy field and it has been assumed that K1<0. For the [110] case the threshold is approximately hcrit1/2=(2γ/σQe)1/2(H−12Ha),where σ/γ=b22/C44M0 and Qe is the phonon Q. When magnetic loss is taken into account, hcrit1/2 still remains an approximately linear function of dc field, but the extrapolated intercept is moved to lower dc fieldstrengths.
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