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Three-dimensional extended Hückel theory-nonequilibrium Green’s function spin polarized transport model for Fe/MgO/Fe heterostructures
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Image of FIG. 1.
FIG. 1.

MgO EHT parameterization. For MgO, the k-resolved PDOS on atomic orbitals (not shown) is used to generate EHT parameters, which are benchmarked with the k-resolved PDOS on the Mg and O atomic orbitals calculated using the LDA-DFT. (a) A comparison of the k-sum PDOS between the EHT and the LDA-DFT is shown for Mg/O s and p orbitals. (b) MgO band structure calculations using the optimized parameters. The dispersions are shown along the various symmetry directions over the 3D Brillioun zone. The band structure with the experimental band gap is also shown, for which another set of parameters are optimized. Conduction and valence band offsets used in the transport calculations are shown with respect to the equilibrium chemical potential .

Image of FIG. 2.
FIG. 2.

Schematic device structure. Ball and stick model for an Fe/MgO/Fe MTJ device with four MgO layers and six Fe layers (atomic planes) on either side within the device region. Contacts consist of semi-infinite Fe regions. EHT is used for the device Hamiltonian and , where are the self-energies for the two contacts. Atomic visualization is done using Gaussview (Ref. 52).

Image of FIG. 3.
FIG. 3.

Equilibrium transmission at the chemical potential for 4, 8, and 12 layers of MgO in parallel (P)-majority, P-minority, and AP configurations over the transverse BZ. The transmission for P-majority is peaked around the point (the BZ center) which becomes more localized for thicker barriers. The P-minority transmission is peaked in a ring surrounding the point and the spread of this ring evolves around the point for thicker barriers. The transmission in the AP configuration shows a combination of the features observed in the P-majority and P-minority channels.

Image of FIG. 4.
FIG. 4.

Dependence of the zero-bias conductance and the TMR on the barrier thickness. (a) Zero-bias conductance with the LDA-DFT band gap at 300 K. An exponential dependence on the number of MgO layers is observed. The dotted line is shown to guide the eye. The slopes of the P and AP conductances are different indicating different exponential factors governing the decay of the conductances in these configurations as reported in Table III. The normalized TMR increases with the increasing MgO layers and ultimately saturates, whereas the optimistic TMR shows a monotonically increasing trend. (b) The experimental band gap results. As expected, the corresponding slopes of the P and AP conductances are higher due to the higher band gap and hence a higher barrier. The normalized and the optimistic TMRs are lower than the ones obtained by the LDA-DFT band gap.

Image of FIG. 5.
FIG. 5.

Transport properties for the LDA-DFT band gap. For four layers, a linear current dependence is observed in the P and AP configurations till about 0.8 V bias resulting in a fairly constant normalized and optimistic TMR with the applied bias. Beyond this voltage, an increase in the AP current density results in the TMR roll-off which ultimately becomes negative when the AP current becomes larger than the P current density. The bias dependence of the current density and the TMR for eight layers is similar to that of four layers but with a sharper TMR roll-off, which has also been observed elsewhere (Ref. 20). The optimistic TMR increases before the roll off similar to Ref. 44.

Image of FIG. 6.
FIG. 6.

Transport properties for the experimental band gap. The current values are an order of magnitude smaller than that with the LDA-DFT band gap due to a higher barrier. TMR is also smaller than that obtained for the LDA-DFT band gap. TMR roll-off for higher barrier thickness is sharper as in Ref. 20.


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Table I.

EHT parameter set for Mg and O atoms with the experimental band gap of 7.8 eV.

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Table II.

EHT parameter set for Mg and O atoms with the band gap of 5.2 eV.

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Table III.

Decay coefficient calculated using a least square fit to the zero-bias conductances in P and AP configurations (Fig. 4) for the LDA-DFT and the experimental band gap.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Three-dimensional extended Hückel theory-nonequilibrium Green’s function spin polarized transport model for Fe/MgO/Fe heterostructures