Scaling of the magnetic Gr\"{u}neisen ratio near quantum critical point

The magnetic Gr\"{u}neisen ratio $\Gamma_{\mathrm{H}}=$(1/T)dT/dH is the most sensitive probe of quantum criticality. Its divergence signals the underlying instability. We have studied quantum criticality in the frustrated Kondo lattice system YbAgGe and the heavy fermion superconductor CeCoIn$_{\mathrm{5}}$ by high-precision magnetocaloric effect measurements. In the former, NFL behavior appears around a metamagnetic spin-flop transition between two symmetry broken phases. Previously, it was unclear how the two ordered phases are related to the NFL state. Here, we propose a novel quantum bicritical point (QBCP) scenario, which is distinct from either quantum critical end point or ordinary QCPs with single symmetry broken phase. The observed scaling behavior of $\Gamma_{\mathrm{H}}$ and its characteristic asymmetry across the critical field are consistent with a QBCP scenario. We also report a possible violation of Wiedemann-Franz law at the QBCP in YbAgGe. In CeCoIn$_{\mathrm{5}}$ indications of a quantum critical field hidden inside the superconducting (SC) phase have been extensively debated. We show $\Gamma_{\mathrm{H}}$ data and scaling analysis in the normal state, which surprisingly suggests a zero-field QCP. Anomalous behaviors of $\Gamma_{\mathrm{H}}$ and specific heat within the SC state further support this conclusion.\\[4pt] Work done in collaboration with Markus Garst, Institute for Theoretical Physics, University of Cologne; Jinkui Dong, I. Physical Institute, University of Goettingen; Sergey Bud'ko, Ames Laboratory; Eric Bauer; Los Alamos National Laboratory; Paul Canfield, Ames Laboratory; and Philipp Gegenwart, I. Physical Institute, University of Goettingen.