What is the origin of anomalous dielectric response in 2D organic dimer Mott insulators κ-(BEDT-TTF)2Cu[N(CN)2]Cl and κ-(BEDT-TTF)2Cu2(CN)3

Novel forms of the low-temperature phases in the two-dimensional molecular solids with competing interactions between charges, spins and lattice, in particular those featuring anomalous dielectric relaxation, have been the focus of intense activity in recent years. Open issues concern the nature of collective charge excitations as well as their coupling to applied ac and dc electric fields. The charge response is reasonably well understood by now in the charge-ordered phase with the formation of ferroelectric-like domains below the metal-to-insulator phase transition. Conversely, the dielectric response observed in dimer Mott insulator phases with no complete evidence for charge ordering is rather intriguing. We overview our recent results of anisotropic complex conductivity (dc – MHz) in the magnetic phase of κ-(BEDT-TTF)2Cu[N(CN)2]Clκ-(BEDT-TTF)2Cu[N(CN)2]Cl and in the spin-liquid phase of κ-(BEDT-TTF)2Cu2(CN)3κ-(BEDT-TTF)2Cu2(CN)3. We discuss possible explanations for the observed dynamics within current theoretical models and compare them with the well-known fingerprints of the spin density wave response to ac electric fields.