Mott criticality and multiferroicity in organic $\kappa$ -(BEDT-TTF)$_{2}$X salts

Layered organic charge-transfer (CT) salts of the $\kappa$-(BEDT-TTF)$_{\mathrm{2}}$X family show a wealth of electronic phases resulting from the interplay of strong electron-electron correlations, reduced dimensions and magnetic frustration. Of particular interest has been the bandwidth-controlled Mott transition, separating an antiferromagnetic (afm) insulating state from a correlated metallic and superconducting state. Whereas the hydrogenated X $=$ Cu[N(CN)$_{\mathrm{2}}$]Br salt is located on the metallic side, the deuterated variant, denoted $\kappa $-D8, is situated in splitting distance to the Mott transition, enabling the s-shaped transition line $T_{\mathrm{MI}}$ to be crossed via temperature sweeps. The talk will address the following aspects: 1) Thermal expansion measurements on single crystalline $\kappa $-D8 reveal discontinuous changes of the lattice parameters on crossing the Mott transition line and a huge anomaly close to the second-order critical end point of $T_{\mathrm{MI}}$ [1]. By elaborating on a scaling theory [2], we found that (i) the latter effect is a consequence of an almost divergence of the Gr\"{u}neisen parameter $\Gamma $ at the finite-$T$ critical end point, and (ii) that the expansivity data of [1] are in excellent agreement with the Mott criticality lying within the 2D Ising universality class [2], at variance with results from conductivity measurements [3]. Thermal expansion measurements under Helium-gas pressure are underway for providing thermodynamic information at variable pressure. 2) Surprisingly, for the isostructural X $=$ Cu[N(CN)$_{\mathrm{2}}$]Cl salt, located close to the Mott transition on the insulating side, we found that besides the well-established afm order at $T_{\mathrm{N}}$ $\sim$ 27 K, the system also reveals a ferroelectric transition at $T_{\mathrm{FE}}$, making this material the first multiferroic CT salt [4]. Most remarkably, the measurements reveal $T_{\mathrm{FE}} \approx T_{\mathrm{N}}$, suggesting a close interrelation between both types of ferroic order.\\[4pt] The work was performed in collaboration with M. de Souza, L. Bartosch, P. Lunkenheimer, J. M\"{u}ller, S. Krohns, A. Loidl, B. Hartmann, J. A. Schlueter \\[4pt] [1] M. De Souza \textit{et al.}, Phys. Rev. Lett. \textbf{99}, 037003 (2007) \\[0pt] [2] L. Bartosch, M. de Souza, M. Lang, Phys. Rev. Lett. \textbf{104}, 245701 (2010) \\[0pt] [3] F. Kagawa, K. Miyagawa, K. Kanoda, Nature \textbf{436}, 543 (2005) \\[0pt] [4] P. Lunkenheimer \textit{et al.}, Nature Mater. \textbf{11}, 755 (2012)