Low temperature magnetodielectric coupling in the spin-liquid candidate $\kappa $-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$

In the context of geometrical frustration of exchange coupling between spins on dimer orbitals, the possibility of a quantum spin-liquid state has been inferred for the quasi-2D organic Mott insulator $\kappa $-(BEDT-TTF)$_{2}$ Cu$_{2}$ (CN)$_{3}$. However, because the geometrical frustration effect is not strong, it has been proposed that the suppression of magnetic order could result from fluctuating quantum electric dipoles. Indeed, non-trivial charge degrees of freedom survive in this dimer Mott insulator as observed in dielectric measurements. Here, we report in-plane microwave dielectric measurements that reveal a coupling of the electric dipoles to the spins at low temperatures. Anomalies in the complex dielectric permittivity are observed at 6 K and around 3-4 K. The one at 6 K is in clear correlation with the thermal expansion measurements for which a second-order phase transition was inferred. The second dielectric anomaly is frequency dependent and cannot be associated to a phase transition; however, it is rapidly modified and ultimately suppressed by a magnetic field which effects are highly anisotropic. These results could be consistent with the scenario of a dipolar-spin liquid phase where spins couple to the dipoles through the interdimer charge fluctuation. Such a phase appears inhomogeneous since the dielectric anomalies are sensitive to thermal cycling and small pressures.