Pulse echo study of the field-tuned nematic quantum phase transition in TmVO₄

Nematicity appears in a diverse array of strongly correlated systems – from high T_c to the fractional quantum Hall effect. In such materials, nematicity appears in conjunction with superconductivity, magnetism, and inevitably, disorder. The presence of metallic charge carriers makes understanding the impact of nematicity a non-trivial task, inspiring the search for a model system where nematicity occurs without conduction electrons. Ferroquadrupolar order of local moments provides one such realization. Here we explore a model system, TmVO₄, which undergoes a nematic ferroquadrupolar transition driven by the cooperative Jahn-Teller effect. Using pulse echo ultrasound, we measure the elastic constants as a function of temperature and applied magnetic field to determine the behavior of the quadrupole strain susceptibility (i.e. the nematic susceptibility) proximate to the field-tuned quantum phase transition. The softening of the c₆₆ elastic constant yields the strength of the short and long range quadrupolar interactions, while the ultrasonic attenuation characterizes the dynamics of the phase transition. Measurements on the doped system (Tm_1-xY_x)VO₄ for x= .05, x=.1, reveal the interplay between nematicity and disorder in the vicinity of the quantum critical point.