Sign change of the Grüneisen parameter and magnetocaloric effect near quantum critical points

Abstract

We consider the Gr\"uneisen parameter and the magnetocaloric effect near a pressure and magnetic field controlled quantum critical point, respectively. Generically, the Gr\"uneisen parameter (and the thermal expansion) displays a characteristic sign change close to the quantum-critical point signaling an accumulation of entropy. If the quantum critical point is the endpoint of a line of finite temperature phase transitions, ${T}_{c}\ensuremath{\propto}{({p}_{c}\ensuremath{-}p)}^{\ensuremath{\Psi}}$, then we obtain for $p<{p}_{c}$, (1) a characteristic increase $\ensuremath{\Gamma}\ensuremath{\sim}{T}^{\ensuremath{-}1∕(\ensuremath{\nu}z)}$ of the Gr\"uneisen parameter $\ensuremath{\Gamma}$ for $T>{T}_{c}$, (2) a sign change in the Ginzburg regime of the classical transition, (3) possibly a peak at ${T}_{c}$, (4) a second increase $\ensuremath{\Gamma}\ensuremath{\sim}\ensuremath{-}{T}^{\ensuremath{-}1∕(\ensuremath{\nu}z)}$ below ${T}_{c}$ for systems above the upper critical dimension, and (5) a saturation of $\ensuremath{\Gamma}\ensuremath{\propto}1∕({p}_{c}\ensuremath{-}p)$. We argue that due to the characteristic divergencies and sign changes the thermal expansion, the Gr\"uneisen parameter and magnetocaloric effect are excellent tools to detect and identify putative quantum critical points.