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

Spin-dependent electronic transport through multiferroic $\mathrm{Co}/{\mathrm{PbTiO}}_3/\mathrm{Co}$ tunnel junctions is studied theoretically in view of the recent observation of an inverse TMR in $\mathrm{Co}/{\mathrm{PbTiO}}_3/{\mathrm{LaSrMnO}}_3$ heterostructures. Conductances calculated within the Landauer-Büttiker formalism yield a four-conductance state characterized by sizable positive tunnel magnetoresistances (TMR) and tunnel electroresistances (TER). 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 ${\mathrm{PbTiO}}_3$ barrier with Zr impurities at the ${\mathrm{TiO}}_2/{\mathrm{Co}}_2$ interface removes the excessive metalization of the barrier and significantly enhances the TMR but is not sufficient to switch the TMR's sign. Our results indicate that the origin of the TMR inversion might be attributed to the magnetoelectrically active ${\mathrm{LaSrMnO}}_3/{\mathrm{PbZr}}_{0.2}{\mathrm{Ti}}_{0.8}{\mathrm{O}}_3$ interface.

Figure 1

Structural models for Co/PTO/Co (a) and Co/PTO-ZO/Co (b) multiferroic tunnel junctions for the two ferroelectric polarizations $P_{\leftarrow }$ and $P_{\to }$ of the barriers. The chemical compositions of the interfaces are marked below each structure. The effective thickness $d_{\mathrm{eff}}$ of the barrier, i.e., the distance between the Co electrodes, is indicated in (a). In (c), both an original (left, used in the geometry optimization) and a doubled supercell (right, used in the transport calculations) are sketched.

Figure 2

Magnetoelectric coupling in a Co/PTO-ZO/Co tunnel junction. (Top) Difference of the layer-resolved magnetic moments $M_i$ upon reversal of the ferroelectric polarization in the barrier ($P_{\leftarrow }$ and $P_{\to }$): $\mathrm{\Delta }{M}_i\equiv M_i\left(P_{\to }\right)-M_i\left(P_{\leftarrow }\right), i$ layer index. (Bottom) Spin-resolved charge densities for the two ferroelectric polarizations (majority: red; minority: blue).

Figure 3

Effect of the ferroelectric polarization $P$ in a Co/PTO-ZO/Co tunnel junction on the electronic structure at the interfaces for $P_{\to }$ (top) and $P_{\leftarrow }$ (bottom) configurations. Spin-resolved densities of states are depicted for Co atoms in line with Pb [Co (Pb)] and in line with O [Co (O)], as well as for O and Pb cations at the ${\mathrm{Co}}_2$/PbO interface.

Figure 4

Electronic structure of Co/PTO/Co [upper two panels, (a) and (b)] and Co/PTO-ZO/Co [lower two panels, (c) and (d)] tunnel junctions for parallel alignment of the lead magnetizations (black vertical arrows, $\uparrow \uparrow$) and for the two polarizations $P_{\leftarrow }$ [(a) and (c)] and $P_{\to }$ [(b) and (d)] in the ferroelectric barrier (as indicated in each panel by horizontal arrows). Spin-resolved densities of states are shown for the series of unit cells across the barriers; majority spin red, minority spin blue.

Figure 5

Spin-dependent transport in Co/PTO/Co (top row) and Co/PTO-ZO/Co (bottom row) tunnel junctions. In each panel, transmission maps $T(k_x,k_y)$ are shown as a color scale for the parallel ($\uparrow \uparrow$) and the antiparallel ($\downarrow \uparrow$) configuration of magnetic Co electrodes as well as for the two ferroelectric polarizations of the barriers (indicated by horizontal arrows). Color scales in units of ${10}^{-5}{e}^2/h$.