Spin-transfer torque in spin filter tunnel junctions

Spin-transfer torque in a class of magnetic tunnel junctions with noncollinear magnetizations, referred to as spin filter tunnel junctions, is studied within the tight-binding model using the nonequilibrium Green's function technique within Keldysh formalism. These junctions consist of one ferromagnet (FM) adjacent to a magnetic insulator (MI) or two FM separated by a MI. We find that the presence of the magnetic insulator dramatically enhances the magnitude of the spin-torque components compared to conventional magnetic tunnel junctions. The fieldlike torque is driven by the spin-dependent reflection at the MI/FM interface, which results in a small reduction of its amplitude when an insulating spacer (S) is inserted to decouple MI and FM layers. Meanwhile, the dampinglike torque is dominated by the tunneling electrons that experience the lowest barrier height. We propose a device of the form FM/(S)/MI/(S)/FM that takes advantage of these characteristics and allows for tuning the spin-torque magnitudes over a wide range just by rotation of the magnetization of the insulating layer.

Figure 1

(a) Schematic structure of a SFTJ of the form FM/MI/FM. The magnetization vector on each layer is rotated by an angle $\theta$ in $xz$ plane. Subscripts L, R, and B stands for left, right, and barrier, respectively. The atomic layers, represented by green crosses, are enumerated from 1 to 3 in the barrier $\left(N_B=3\right)$. Subscripts next to left (right) interface are denoted $a$ $\left(b\right)$ in the barrier and $\alpha$ $\left({\alpha }^{\prime }\right)$ in the lead. (b) Potential profile describing the averaged on-site energies $({\epsilon }_L^0,{\epsilon }_B^0$, and ${\epsilon }_R^0)$ and exchange splittings $({\Delta }_L,{\Delta }_B$, and ${\Delta }_R)$. $\text{eV}={\mu }_R-{\mu }_L$, with $\mu$ the chemical potential in the lead. $E_F=0$ $\text{eV}$ refers to Fermi energy level. For negative bias, the electron flow density $\left(J_e\right)$ goes from reference layer (left) to free layer (right). (c) Density of states at zero bias for ${\epsilon }_R^0=+5$ and $-1$ $\text{eV}$ cases.

Figure 2

Bias dependence of nonequilibrium (a) Slonczewski, $T_{\parallel }$, and (b) fieldlike, $T_{\perp }-T_{\perp }^0$, spin-torque components, for NM/MI/FM (main panels) and FM/I/FM (insets) structures, with ${\theta }_R=\pi /2,{\theta }_{L\left(B\right)}=0$ and ${\epsilon }_B^0=+9$ eV for different values of spin averaged on-site energies in the leads $\left({\epsilon }_L^0={\epsilon }_R^0\right)$. ${\Delta }_L=0$ and ${\Delta }_{R\left(B\right)}=+2$ $\text{eV}$ in p-SFTJs (former). ${\Delta }_B=0$ and ${\Delta }_{L\left(R\right)}=+2$ $\text{eV}$ in MTJs (latter). $N_B=N_I=N_{\mathrm{MI}}=3$ and the hopping parameter is $t=-1$ eV. In all cases, the magnitudes of the torques are given in $\mu \text{eV}/\Lambda$, where $\Lambda$ denotes the interfacial unit area.

Figure 3

MTJ and p-SFTJ efficiencies for the nonequilibrium (a) Slonczewski and (b) fieldlike spin-torque components as a function of ${\epsilon }_{L\left(R\right)}^0$ and $V=-1.0$ V. Similar parameters as in Fig. 2 are considered. In (b), the MTJ magnitude is multiplied by 10 to fit in the graph. Insets refer to the torque efficiencies of the p-SFTJ as a function of barrier thickness $\left(N_B=N_{\mathrm{MI}}\right)$, given in numbers of atomic layers, for $V=-1.0$ V and ${\epsilon }_{L\left(R\right)}^0=+3$ eV. The magnitudes of the torque efficiencies are given in units of $h/e$.

Figure 4

Angular dependence of nonequilibrium (a) Slonczewski torque, (b) fieldlike torque, and (c) electron flow density, for FM/MI/FM structure (s-SFTJ) with $V=+1.0$ V and four values of the spin-averaged on-site energy. (d) Bias dependence of the spin-torque components for 1/4 band filling case $({\epsilon }_{L\left(R\right)}^0=+3$ $\text{eV})$. Left- (right-) hand insets compare the s-SFTJ solutions with a MTJ (p-SFTJ) structure with parameters similar to those given in Fig. 2. The magnetization of the barrier is rotated by an angle ${\theta }_B$ while the magnetization of the leads are kept perpendicular to each other, ${\theta }_{L\left(R\right)}=\pi /2\left(0\right)$. ${\Delta }_{L\left(R\right)\left(B\right)}=+2$ eV in s-SFTJ.

Figure 5

MTJ and p-SFTJ efficiencies for the nonequilibrium (a) Slonczewski and (b) fieldlike spin-torque components as a function of bias. Three p-SFTJ structures of the form NM/MI/S/FM are studied, where the thickness of MI is fixed to $N_{\mathrm{MI}}=3$ and of S to $N_S=0,1$, or 2 monolayers. The barrier thickness of the MTJ is set to $N_I=3$. Insets refer to the bias dependence of the nonequilibrium (top) Slonczewski and (bottom) fieldlike torque. In all cases, ${\epsilon }_{L\left(R\right)}^0=+5$ $\text{eV},{\epsilon }_B^0=+9$ $\text{eV},{\theta }_R=\pi /2,{\theta }_{L\left(B\right)}=0$, and t = −1 eV. ${\epsilon }_S^0=+7$ eV, ${\Delta }_{R\left(B\right)}=+2$ $\text{eV}$, and ${\Delta }_{L\left(S\right)}=0$ in p-SFTJs. ${\Delta }_{L\left(R\right)}=+2$ $\text{eV}$ and ${\Delta }_B=0$ in MTJs.

Figure 6

Bias dependence of the spin-torque components for 1/4 band filling case $({\epsilon }_{L\left(R\right)}^0=+3$ $\text{eV})$. Left (right) panels compare the s-SFTJ system of the form FM/S/MI/S/FM with a MTJ (p-SFTJ) structure of the form FM/I/FM (NM/MI/S/FM), where the thicknesses of I, MI, and S are fixed to $N_{I\left(\text{MI}\right)\left(S\right)}=5\left(3\right)\left(1\right)$. Top (bottom) panels refer to the nonequlibrium Slonczewski (fieldlike) component. The magnetization of the leads are kept perpendicular to each other, ${\theta }_{L\left(R\right)}=\pi /2\left(0\right)$. Left (right) panels refer to the configuration where ${\theta }_B=0(3\pi /2)$. Two MTJ structures are displayed on left panels, ${\epsilon }_B^0=+7$ eV and ${\epsilon }_B^0=+9$ eV. To fit in the graph, the former has been multiplied by 0.1 and the latter by 10. Other parameters are similar to previous figures.