Spin-wave dispersion and exchange interactions in ${\mathrm{Y}}_{0.90}$${\mathrm{Tb}}_{0.10}$ and ${\mathrm{Y}}_{0.90}$${\mathrm{Ho}}_{0.10}$ alloys

Neutron inelastic scattering experiments carried out on ${\mathrm{Y}}_{0.90}$ ${\mathrm{Tb}}_{0.10}$ and ${\mathrm{Y}}_{0.90}$ ${\mathrm{Ho}}_{0.10}$ at 4.7°K show that well-defined spin waves exist in dilute alloys of the heavy rare earths Tb and Ho in yttrium metal. The measured spin-wave dispersion relations are satisfactorily described by a mean-lattice model together with the assumption that the exchange interaction $\mathcal{J}\left(\overrightarrow{\mathrm{q}}\right)$ is related to the conduction-electron susceptibility $\chi \left(\overrightarrow{\mathrm{q}}\right)$ of yttrium and, hence, is common to both alloys. The $\mathcal{J}\left(\overrightarrow{\mathrm{q}}\right)$ function deduced from the data possesses a peak, at the wave vector of the helical magnetic structures of the alloys, that is much larger than those measured for the pure rare-earth metals. This result is consistent with theoretical calculations of $\chi \left(\overrightarrow{\mathrm{q}}\right)$ by Liu, Gupta, and Sinha from the electronic energy bands for yttrium and with measurements of the magnetic structures of yttrium-rare-earth alloys as a function of composition and applied magnetic field.