Bulk band structure of Fe and MgO. Subfigure (a) provides the Fe (100) crystal bulk band structure with the Fermi energy situated at 0 eV. Subfigure (b) provides the strained MgO bulk band structure with the Fermi energy positioned to match that of MgO sandwiched between two Fe(100) slabs. The LSDA calculated band structure is shown as a dashed blue line. The LSDA SEP fit is shown in as a solid green line. The modified LSDA SEP result fitted to the bulk MgO band gap of 7.7 eV (Ref. 33) is shown as a dotted black line.
Spherical SEPs for each of the elements. Subfigures (a) and (b) show the LSDA Mg and O SEPs for MgO in solid green and the MgO band gap fit correction to the LSDA SEPs in dotted black. The MgO band gap fit corrections should be read off the left axis and the LSDA SEPs should be read off the right axis. Subfigure (c) shows the LSDA Fe up spin SEP in solid green (read off the right axis) and difference between the Fe down spin and Fe up spin LSDA SEPs as a double-dot-dashed black line (read off the left axis). The vacuum level is set at 0 eV.
Fe/MgO/Fe five layer device geometry. The atomic color index is as follows: iron atoms are colored gold, the magnesium atoms are colored green, and oxygen atoms are colored red. The system is mirror symmetric along the -axis about layer 11 (the middle of the barrier).
The total NEGF-LSDA spin down potential is shown as a dotted black line, with its axis given on the right hand side of the figure (the vacuum level is set at 0 eV). The bulk LSDA SEP interface error is shown in green and the interface spherical SEP correction to the error is shown in red (both potentials are read off the left axis). Subfigure (a) displays the system potential as a linear cut in the -direction through the Mg atom at the Fe/MgO interface. Subfigure (b) displays the system potential as a linear cut in the -direction through the FeO bond at the Fe/MgO interface. An atomistic cartoon is shown to scale above each potential plot, where a dip in the total potential corresponds to an atomic nuclear position––Fe atoms are gold, O atoms are red, and Mg atoms are green. Up spin results are nearly identical. The SEP MgO band gap corrections (see Figs. 1 and 2) are not included in this comparison.
Fe/MgO/Fe SEP parallel orientation PDOS before approaching the interface (layer 6), at the interface (layers 8 and 9), and in the middle of the barrier (layer 11)––see Fig. 3 for details on the layer numbering. The Fermi energy is located at 0 eV, the imaginary Green’s function broadening is set at 25 meV, and the -point sampling set at in the transverse Brillouin zone. The up spin PDOS is shown on the positive axis and the down spin PDOS is shown on the negative axis. The reference two probe NEGF-LSDA PDOS is shown as a dashed dark blue line in each figure. The bulk SEP fit (displayed in solid green) applied to the two probe geometry is shown in the first column. When ghost SEPs (displayed in solid red) are introduced at the interface to correct the bulk Fe and MgO SEP transferability errors, an accurate fit is obtained, as shown in the second column.
Subfigures (a)–(c) display the parallel and antiparallel zero bias total transmission with respect to energy through the five layer Fe/MgO/Fe MTJ geometry shown in Fig. 3. The self-consistent LSDA total transmission is shown in dashed dark blue, the bulk SEP result is shown in solid green, the ghost SEP result is shown in solid red, and the band gap corrected ghost SEP result is shown in dotted black. The biased device parallel (upward pointing triangles) and antiparallel (downward pointing triangles) currents for the ghost SEP (red solid line) and bulk SEP (green solid line) approximations are shown in (d) in units of nanoamperes per unit cell (2.87 by 2.87 Å). The voltage profile is assumed to drop linearly across the MgO barrier for the calculated IV points. The ghost SEP (red solid line) and bulk SEP (green solid line) TMR ratios under bias are shown in (e). The Fermi energy is set at 0 eV, the imaginary Green’s function broadening is set at 25 meV, and the -point sampling set at in the transverse Brillouin zone. We define , where is the parallel current and is the antiparallel current.
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