Double tunneling in polarization switching

We present a theory of quantum switching of polarization in hydrogen-bonded order-disorder ferroelectrics, and examine the macroscopic quantum-tunneling rate of the polarization reversal for nano-samples induced by microscopic tunneling of protons between the two wells in potentials of hydrogen bonds. We compute the rate of the electric polarization tunneling through the barrier between two minima of the free energy density of a system. By using the instanton approach, we calculate a barrier factor and a prefactor multiplying the exponential of the action integral for the tunneling splitting at zero applied electric field. We compute the tunneling rate of domain walls. We obtain the double tunneling effect, i.e., the polarization tunneling related to the proton tunneling between the two minima in potentials of hydrogen bonds.