A high frequency (111.2-420 GHz) electron spin resonance study of the inter-layer (perpendicular) spin diffusion as a function of pressure and temperature is presented in the conducting phases of the layered organic compounds, κ-(BEDT-TTF)2-Cu[N(CN)2]X (κ-ET2-X), X=Cl or Br. The resolved ESR lines of adjacent layers at high temperatures and high frequencies allows for the determination of the inter-layer cross spin relaxation time, Tx and the intrinsic spin relaxation time, T2 of single layers.

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... In the bad metal phase spin diffusion is two-dimensional, i.e. spins are not hopping to adjacent layers within T2. Tx is proportional to the perpendicular resistivity at least approximately, as predicted in models where spin and charge excitations are tied together. In κ-ET2-Cl, at zero pressure Tx increases as the bad metal-insulator transition is approached. On the other hand, Tx decreases as the normal metal and superconducting phases are approached with increasing pressure and/or decreasing temperature.