Effects of anisotropic exchange and magnetoelastic coupling on magnetic phase transitions in holmium and erbium

The effects of both anisotropic exchange and magnetoelastic coupling on phase transitions involving flat, conical and tilted spiral phases are investigated. Also the conditions under which the magnon modes in conical and flat spiral phases may soften are examined when anisotropic exchange is taken into account. It is found that both anisotropic exchange and magnetoelastic coupling can inhibit the instability of the magnon mode with q=Q in the flat spiral phase, but that the nature of the transition which occurs is quite different in each case. These results are discussed with reference to the phase transitions which occur in holmium and erbium near 20K.