Local tunneling magnetoresistance control with surface-state confinement and external electric field

On the basis of density functional calculations, the possibility of using spin-polarized confinement and band structure manipulation by means of external electric fields to tune the local spin polarization of electrons and the local magnetoresistance ratio of a tunneling junction is discussed. To illustrate the concept, a model system of a bilayer Co island supported on a Cu(111) surface is used.

Figure 1

Spectral density maps of majority (top panels) and minority (bottom panels) states along the $\mathrm{K}-\overline{\Gamma }-\mathrm{M}$ path in the vicinity of the $\overline{\Gamma }$ point plotted for electric fields of (a) $0.0\mathrm{V}/\AA$ and (b) $+0.6\mathrm{V}/\AA$. The boundaries of the projected band gap of Cu(111) are lined by dashed contours. The bands are traced by red (majority) and blue (minority) lines. (c) The sketch of the band structure and the field induced shifts. The dashed lines show the zero external field case. The solid lines stand for the band structure in the field of $0.6\mathrm{V}/\AA$. Majority and minority bands are plotted with red blue curves, respectively. Gray shaded area shows the bulk states continuum. (d) The binding energies ($E_0$) and effective masses ($m^{*}$) of majority (red circles) and minority (blue squares) surface bands are plotted.

Figure 2

Electron density of states for $E_F$ ($\Delta E=0$) (a) and $E_F+0.1\mathrm{eV}$ ($\Delta E=0.1\mathrm{eV}$), (c) in zero external electric field ($EF=0.0\mathrm{V}/\AA$), and for $E_F$ in an external field of $EF=0.6\mathrm{V}/\AA$ (e) are plotted for majority and minority (insets) electrons. The colormap is given on the right of the figure. The numbers next to electron density of states distributions denote (top to bottom) the current strength of the external electric field, the electron energy for which the map is plotted and the maximum values of the majority (red) and minority (blue) electron densities. The minimal values are always $01/\mathrm{eV}$ (white). Subfigures (b), (d), and (f) show the TMR distribution maps for the above cases, calculated with Eqs. (8) and (5). The polarization of the tip has been assumed to be $0.2$. The numbers next to the maps denote the boundaries of the colorscale. White always corresponds to zero TMR.