CRITICAL SCATTERING OF SOUND IN RARE-EARTH METALS

We present ultrasonic attenuation measurements in the vicinity of the Néel temperature for terbium, dysprosium, and holmium. Longitudinal sound waves along the c axis exhibit a large critical attenuation, whereas shear waves show only a small but measurable effect in dysprosium. The spin-phonon coupling responsible for this critical attenuation is predominantly of volume-magnetostrictive character for longitudinal waves and of linear-magnetostrictive (single-ion-type) character for shear waves. Longitudinal wave attenuation in the paramagnetic region gives the following critical exponent η[αaω2(T-TN)-η]:terbiumA 1.24±0.1,A dysprosiumA 1.37±0.1,A holmiumA 1.0±0.1. Shear waves in dysprosium give η=0.8±0.15. These exponents, with the exception of the shear-wave case, can be fairly well accounted for by recent theories of ultrasonic attenation at magnetic phase transitions. The critical exponent η for shear waves in Dy, together with the magnitude of the effect, can tentatively be explained with present theories by considering higher-order terms in the spin-phonon coupling. For temperatures very close to TN the attenuation remains finite. We show this to be an impurity effect. © 1969 The American Physical Society.