  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, {\kappa}-(BEDT-TTF)2-Cu[N(CN)2]X ({\kappa}-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. 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 {\kappa}-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.
