Observation of Fowler–Nordheim hole tunneling across an electron tunnel junction due to total symmetry filtering

Using a ${\mathrm{SrTiO}}_3\left(001\right)$ barrier and ${\mathrm{La}}_{0.7}{\mathrm{Sr}}_{0.3}{\mathrm{MnO}}_3\left(001\right)$ electrodes, we study the case of coherent spin-polarized tunneling of electrons that exhibit a symmetry mismatch with respect to the lower electron barrier height. Due to this mismatch, electrons with energy above this barrier height continue to tunnel thanks to total symmetry filtering. This allows us to observe symmetry-matched hole tunneling across this electron tunnel junction, and in particular spin-polarized oscillations in the Fowler-Nordheim hole regime above the hole barrier height, thereby enriching the present theoretical picture of coherent spin-polarized tunneling at finite bias.

Figure 1

(Color online) Complex band structures of (a) $\mathrm{MgO}$ and (b) ${\mathrm{SrTiO}}_3$ along [001]. Numbers indicate the $\Delta$ symmetries (e.g., $1={\Delta }_1$). The CNL is the charge neutrality level.

Figure 2

Schematic of the electronic symmetry resolved DOS of STO(001) and the LSMO/STO(001) interfaces for (a) $eV=0$ and (b) $eV={\Phi }_h$. Here ${\Delta }_{2^{\prime },5}$ is $t_{2g}$ and ${\Delta }_1$ is ($e_g$, $\mathrm{O}2p$). In part from Refs. 20, 21, 25, 26, 27.

Figure 3

(Color online) Bias dependencies of (a) TMR and diff. TMR, (b) differential conductance, and (c) Î$(10\mathrm{K},70\mathrm{K})=\left[I\right(70\mathrm{K})-I(10\mathrm{K}\left)\right]∕I\left(10\mathrm{K}\right)$ in the parallel (P) and antiparallel (AP) states. Panel (d) and its inset, and the inset to panel (a), provide closeups of diff. TMR and TMR, respectively.