Spin-dependent transport in a multiferroic tunnel junction: Theory for Co/PbTiO${}_3$/Co

Spin-dependent electronic transport through multiferroic Co/PbTiO${}_3$/Co tunnel junctions is studied theoretically. Conductances calculated within the Landauer-B"uttiker formalism yield both a large tunnel magnetoresistance (TMR) and a large tunnel electroresistance (TER). On top of this, we establish a four-conductance state. The conductances depend crucially on the details of the electronic structure at the interfaces. In particular, the spin polarization of the tunneling electronic states is affected by the hybridization of orbitals and the associated charge transfer at both interfaces. Digital doping of the PbTiO${}_3$ barrier with Zr impurities at the TiO${}_2$/Co${}_2$ interface significantly enhances the TMR@. In addition, it removes the metalization of the barrier.