Ultrasound in a Metamagnet and the Single Energy Scale Model

Ultrasound velocity measurements in the heavy electron compound UPt$_{\mathrm{3}}$ for magnetic fields up to 33 T are reported. We show that the single energy scale model (B.S.Shivaram et al., Phys. Rev., B89, 24110799(R), 2014) captures the observed key features of the field dependence in the sound velocity shift, $\delta $v$_{\mathrm{s}}$. The shift $\delta $v$_{\mathrm{s}}$ at H$_{\mathrm{c}}$ is inversely dependent on temperature above a certain ``Dingle Temperature'' and assumes a fixed value at very low T. This ``saturation'' in $\delta $v$_{\mathrm{s}}$ is accounted for by level broadening in the single energy scale model..