First Principles Modeling of Tunnel Magnetoresistance of $\mathrm{Fe}/\mathrm{MgO}/\mathrm{Fe}$ Trilayers

We report ab initio calculations of nonequilibrium quantum transport properties of $\mathrm{Fe}/\mathrm{MgO}/\mathrm{Fe}$ trilayer structures. The zero bias tunnel magnetoresistance is found to be several thousand percent, and it is reduced to about 1000% when the $\mathrm{Fe}/\mathrm{MgO}$ interface is oxidized. The tunnel magnetoresistance for devices without oxidization reduces monotonically to zero with a voltage scale of about 0.5–1 V, consistent with experimental observations. We present an understanding of the nonequilibrium transport by investigating microscopic details of the scattering states and the Bloch bands of the Fe leads.

Figure 1

(a) Schematic plot of a two probe $\mathrm{Fe}(100)/\mathrm{MgO}(100)/\mathrm{Fe}(100)$ device. The system has infinite extent in the $(x,y)$ direction with a lattice constant of 2.82 Å and extends to $\pm \infty$ in the $z$ direction. (b) Band structure of a periodic $\cdots \mathrm{Fe}/\mathrm{MgO}/\mathrm{Fe}/\mathrm{MgO}\cdots$ lattice obtained using optimized LCAO pseudopotentials and basis sets compared to that from the full potential LAPW method. A good agreement is found to be necessary in order to carry out the NEGF-DFT analysis for the two probe $\mathrm{Fe}/\mathrm{MgO}/\mathrm{Fe}$ devices.

Figure 2

(a),(b) $I\mathrm{\text{−}}V$ curves for the 5-layer PC and APC, respectively. Solid line (diamonds): total current; dashed line (squares): $I_{\uparrow }$; dotted line (circles): $I_{\downarrow }$. Upper inset: $I\mathrm{\text{−}}V$ curves for a 3-layer device. Lower inset: majority current $I_{\uparrow }$ vs $V_b$ for small ranges of $V_b$. (c) TMR vs bias $V_b$ for a 5-layer device (diamonds). The solid squares are data for 50% oxidization of the two $\mathrm{Fe}/\mathrm{MgO}$ interfaces. Inset: TMR for a 3-layer device. (d) Histogram of TMR for several 5-layer devices with a variation in the position of the surface atoms. Inset: Histogram for varying all of the Mg and O atoms in the device. (e) Transmission coefficient $T_{\sigma }$ versus energy $E$ for $V_b=0$. $E=0$ is the Fermi energy of leads. Solid line: $T_{\uparrow }$ for PC setup; dashed line: $T_{\downarrow }$ for the PC; dotted line: $T_{\uparrow }=T_{\downarrow }$ for the APC. Inset: The same transmission coefficients at energies between $-3$ and 1 eV. (f) The magnitude of the output signal modulation $V_{\mathrm{out}}$ as a function of bias. Inset: Semilog plot of zero bias total transmission coefficients $T$ versus the number of MgO layers for PC setup, indicating an exponential decrease of $T$.

Figure 3

(a),(b) Fe bands at $|k_x|=|k_y|=0.12\pi$ versus $k_z$ for majority and minority electrons, respectively. (c),(d) Total BZ resolved transmission coefficient at $E_f$ versus $k_x$, $k_y$, for 5-layer MgO (c) for $V_b=0$ and (d) for $V_b=0.05\mathrm{V}$. The dominant peaks are near $|k_x|=|k_y|=0.12$.