Ultrasonic investigation close to quantum critical point in YbTr₂Zn₂₀ (Tr: Co, Rh, and Ir)

We performed ultrasonic measurements on high quality single crystals of the Yb-based heavy fermion compounds YbTr₂Zn₂₀ (Tr: Co, Rh and Ir) over a temperature range from 200 K to 0.5 K, which seem to be close to a quantum critical point (QCP). A sharp contrast of the temperature dependence of elastic constants was found at low temperature among the three compounds, reflecting the 4f electronic state stemmed from Yb ion. The results indicate that a crystalline electric field (CEF) effect seems to be dominant in the systems YbRh₂Zn₂₀ and YbIr₂Zn₂₀ at low temperatures. On the other hand, the CEF effect is much less, but an additional effect would be dominant which is most probably ascribable to non Fermi liquid characteristics formed close to the QCP. We discuss briefly each 4f electronic state developed at the low temperatures and physical parameters relating to a renormalized band model in YbTr₂Zn₂₀ in the framework of a deformation potential approximation.