The magnetic anisotropy energy makes spin fluctuations extremely anisotropic near the Curie and N\'eel temperatures. Because of this anisotropy of the fluctuations and the symmetry of the shear-wave phonon-spin interaction, only shear waves with both propagation and polarization vectors in the easy directions of magnetization have critical attenuation at the phase transition temperatures and other shear waves do not have it. Experimental results on the heavy rare-earth metals are in agreement with these theoretical predictions.
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Tachiki et al. (1975) studied this question.
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