Magnetoresistance in terbium and holmium single crystals

The longitudinal magnetoresistance of single crystals of terbium and holmium metals in their low-temperature ferromagnetic phase has been investigated in magnetic fields up to 80 kOe. Typical magnetoresistance isotherms exhibit a minimum which increases in depth and moves to higher fields as the temperature increases. The magnetoresistance around 1 K, where inelastic scattering is negligible, has been interpreted as the sum of a negative contribution due to changes in the domain structure and a positive contribution due to normal magnetoresistance. At higher temperatures, a phenomenological approach has been developed to extract the inelastic phonon and spin-wave components from the total measured magnetoresistance. In the temperature range 4-20 K (approximately), the phonon resistivity varies as $T^{3.7}$ for all samples. Approximate upper and lower bounds have been placed on the spin-wave resistivity which is also found to be described by a simple power law in this temperature range. The implications of this result for theoretical treatments of spin-wave resistivity due to $s-f$ exchange interactions are considered. It is concluded that the role played by the magnon energy gap is far less transparent than previously suggested.