Probing the d x2 - Y2 -wave Pomeranchuk instability by ultrasound

Selection rules of ultrasound attenuation and sound-velocity renormalization are analyzed in view of their potential application to identify Pomeranchuk instabilities (electronic nematic phase). It is shown that the transverse sound attenuation along [110] direction is enhanced by the Fermi-surface fluctuations near a d x2 - y2 -wave Pomeranchuk instability, while the attenuation along [100] direction remains unaffected. Moreover the fluctuation regime above the instability is analyzed by means of a self-consistent renormalization scheme. The results could be applied directly to Sr3 Ru2 O7 which is a potential candidate for a Pomeranchuk instability at its metamagnetic transition in strong magnetic fields.