Hall effect in charged conducting ferroelectric domain walls

Enhanced conductivity at specific domain walls in ferroelectrics is now an established phenomenon. Surprisingly, however, little is known about the most fundamental aspects of conduction. Carrier types, densities and mobilities have not been determined and transport mechanisms are still a matter of guesswork. Here we demonstrate that intermittent-contact atomic force microscopy (AFM) can detect the Hall effect in conducting domain walls. Studying YbMnO₃ single crystals, we have confirmed that p-type conduction occurs in tail-to-tail charged domain walls. By calibration of the AFM signal, an upper estimate of ∼1 × 10¹⁶ cm^-3 is calculated for the mobile carrier density in the wall, around four orders of magnitude below that required for complete screening of the polar discontinuity. A carrier mobility of∼50 cm²V^-1s^-1 is calculated, about an order of magnitude below equivalent carrier mobilities in p-type silicon, but sufficiently high to preclude carrier-lattice coupling associated with small polarons.