ESR study of the (super)conducting charge-transfer salts $\beta ^{\prime\prime}$-(ET)$_4$\-[(H$_3$\-O)M\-(C$_2$\-O$_4$)$_3$]{\it S}

We present a spin resonance investigation of the family of quasi- two-dimensional organic (super)conductors {$\beta^{\prime\prime} $-(ET)$_4$\-[(H$_3$\-O)M\-(C$_2$\-O$_4$)$_3$]{\it S}} (M = Cr$^ {3+}$, Fe$^{3+}$;~{\it S}~is a guest molecule). The spin systems are probed by means of both resonant cavity perturbation and field modulation techniques in the frequency range 50-313 GHz. The role of the different solvent molecules in determining the degree of spin-orbit coupling and the local symmetry at the metal ion site is established. Intensities, positions and widths of the resonant lines reveal significant modifications of the spin-orbit coupling, and of the inter- and intra-ionic spin-spin interactions below $T=10$K. Despite the onset of a weak antiferromagnetic internal field at low temperature, the ultimate narrowing of the lines suggests spin-lattice interactions are still the dominant relaxation process. Additional lineshifts observed below $B~=~2.5$~{\rm T} and $T~=~4 $~{\rm K}, attributed to the presence of diamagnetic currents in the mixed state of the superconducting samples, provide a threshold for full field penetration within the ``insulating" anion layers.