A high frequency (111.2–420 GHz) electron spin resonance study of the interlayer spin diffusion is presented in the conducting phases of the layered organic compounds, $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]$X$ ($\kappa$-ET${}_2$-$X$), $X=\text{Cl}$ or Br. The interlayer spin cross relaxation time $T_x$ and the intrinsic spin relaxation time $T_2$ of single layers are measured as a function of temperature and pressure. Spin diffusion is two dimensional in the high temperature bad-metal phase (i.e., electrons are confined to a single molecular layer for longer than $T_2$). The interlayer electron hopping frequency ${\nu }_{\perp }=1/\left(2T_x\right)$ decreases along the bad-metal to Mott insulator crossover and increases along the bad-metal to normal metal (or superconductor) crossover. The density of states (DOS) is determined from a comparison of $T_x$ and the interlayer resistivity. In the bad-metal phase it is four to five times larger than the DOS calculated from the electronic structure neglecting electron correlations. In $\kappa$-ET${}_2$-$X$ the DOS increases with pressure along the bad-metal to normal metal crossover. Results are compared with predictions of the dynamical mean field theory.

• Received 27 February 2011

DOI:https://doi.org/10.1103/PhysRevB.84.075124