Classification of materials with divergent magnetic Gr\"uneisen parameter

At any quantum critical point (QCP) with a critical magnetic field $H_c$, the magnetic Gr\"uneisen parameter $\Gamma_{\rm H}$, which equals the adiabatic magnetocaloric effect, is predicted to show characteristic signatures such as a divergence, sign change and $T/(H-H_c)^\epsilon$ scaling. We categorize thirteen materials, ranging from heavy fermion metals to frustrated magnets, where such experimental signatures have been found. Remarkably, seven stoichiometric materials at ambient pressure show $H_c=0$. However, additional thermodynamic and magnetic experiments suggest that most of them do not show a zero-field QCP. While the existence of a pressure insensitive "strange metal" state is one possibility, for some of the materials $\Gamma_{\rm H}$ seems influenced by impurities or a fraction of moments which are not participating in a frozen state. To unambiguously prove zero-field and pressure sensitive quantum criticality, a $\Gamma_{\rm H}$ divergence is insufficient and also the Gr\"uneisen ratio of thermal expansion to specific heat must diverge.