Evidence for structural and electronic instabilities at intermediate temperatures in $\kappa -(\mathrm{BEDT}-\mathrm{TTF}{)}_{2}X$ for $X={\mathrm{Cu}\left[\mathrm{N}\right(\mathrm{CN})\mathrm{}}_2]\mathrm{Cl},$ ${\mathrm{Cu}\left[\mathrm{N}\right(\mathrm{CN})\mathrm{}}_2]\mathrm{Br}$ and ${\mathrm{Cu}\left(\mathrm{NCS}\right)\mathrm{}}_2:$ Implications for the phase diagram of these quasi-two-dimensional organic superconductors

We present high-resolution measurements of the coefficient of thermal expansion $\alpha \mathrm{}\left(T\right)=\partial \ln l\left(T\right)/\partial T$ of the quasi-two-dimensional (quasi-2D) salts $\kappa -(\mathrm{BEDT}-\mathrm{TTF}{)}_{2}X$ with $X=\mathrm{Cu}(\mathrm{NCS}{)}_2,$ $\mathrm{Cu}\left[\mathrm{N}\right(\mathrm{CN}{)}_2]\mathrm{Br},$ and $\mathrm{Cu}\left[\mathrm{N}\right(\mathrm{CN}{)}_2]\mathrm{Cl}$ in the temperature range $T<~150\hspace{0.5em}\mathrm{K}.$ Three distinct kinds of anomalies corresponding to different temperature ranges have been identified. These are (A) phase-transition anomalies into the superconducting $(X=\mathrm{Cu}(\mathrm{NCS}{)}_2,$ $\mathrm{Cu}\left[\mathrm{N}\right(\mathrm{CN}{)}_2\left]\mathrm{Br}\right)$ and antiferromagnetic $(X=\mathrm{Cu}[\mathrm{N}\left(\mathrm{CN}{)}_2\right]\mathrm{Cl})$ ground state, (B) phase-transition-like anomalies at intermediate temperatures (30–50) K for the superconducting salts, and (C) kinetic, glasslike transitions at higher temperatures, i.e., (70–80) K for all compounds. By a thermodynamic analysis of the discontinuities at the second-order phase transitions that characterize the ground state of system (A), the uniaxial-pressure coefficients of the respective transition temperatures could be determined. We find that in contrast to what has been frequently assumed, the intraplane-pressure coefficients of $T_c$ for this family of quasi-2D superconductors do not reveal a simple form of systematics. This demonstrates that attempts to model these systems by solely considering in-plane electronic parameters are not appropriate. At intermediate temperatures (B), distinct anomalies reminiscent of second-order phase transitions have been found at $T^{*}=38\mathrm{}\hspace{0.5em}\mathrm{K}$ and 45 K for the superconducting $X=\mathrm{Cu}(\mathrm{NCS}{)}_2$ and $\mathrm{Cu}\left[\mathrm{N}\right(\mathrm{CN}{)}_2]\mathrm{Br}$ salts, respectively. Most interestingly, we find that the signs of the uniaxial pressure coefficients of $T^{*},$ $\partial T^{*}/\partial p_i$ $\mathrm{}(i=a,b,c),$ are strictly anticorrelated with those of $T_c.$ Based on comparative studies including the nonsuperconducting $X=\mathrm{Cu}\left[\mathrm{N}\right(\mathrm{CN}{)}_2]\mathrm{Cl}$ salt as well as isotopically labeled compounds, we propose that $T^{*}$ marks the transition to a density-wave state forming on minor, quasi-1D parts of the Fermi surface. Our results are compatible with two competing order parameters that form on disjunct portions of the Fermi surface. At elevated temperatures (C), all compounds show $\alpha \mathrm{}\left(T\right)\mathrm{}$ anomalies that can be identified with a kinetic, glasslike transition where, below a characteristic temperature $T_g,$ disorder in the orientational degrees of freedom of the terminal ethylene groups becomes frozen in. Our results provide a natural explanation for the unusual time- and cooling-rate dependences of the ground-state properties in the hydrogenated and deuterated $\mathrm{Cu}\left[\mathrm{N}\right(\mathrm{CN}{)}_2]\mathrm{Br}$ salts reported in the literature.