Robust spin transfer torque in antiferromagnetic tunnel junctions

We theoretically study the current-induced spin torque in antiferromagnetic tunnel junctions, composed of two semi-infinite antiferromagnetic layers separated by a tunnel barrier, in both clean and disordered regimes. We find that the torque enabling electrical manipulation of the Néel antiferromagnetic order parameter is out of plane, $\sim \mathbf{n}\times \mathbf{p}$, while the torque competing with the antiferromagnetic exchange is in plane, $\sim \mathbf{n}\times (\mathbf{p}\times \mathbf{n})$. Here, $\mathbf{p}$ and $\mathbf{n}$ are the Néel order parameter direction of the reference and free layers, respectively. Their bias dependence shows behavior similar to that in ferromagnetic tunnel junctions, the in-plane torque being mostly linear in bias, while the out-of-plane torque is quadratic. Most importantly, we find that the spin transfer torque in antiferromagnetic tunnel junctions is much more robust against disorder than that in antiferromagnetic metallic spin valves due to the tunneling nature of spin transport.

Figure 1

(a) Schematic of the AF-MTJ consisting of two semi-infinite antiferromagnets spaced by a tunnel barrier. Red and blue atoms refer to the two antiferromagnetically coupled sublattices. (b) Illustration of the energy spacial profile and its alteration by the applied voltage. Dashed red and green lines represent the potential profile for two specific Fermi energies, ${\epsilon }_f=6.6$ eV and ${\epsilon }_f=1.1$ eV, as explained in the text.

Figure 2

(a) Band structure and (b) sublattice-resolved spin polarization of a two-dimensional G-type antiferromagnet for ${\mathrm{\Delta }}_{\mathrm{ex}}=0.5t$ (black curves), ${\mathrm{\Delta }}_{\mathrm{ex}}=t$ (red curves), ${\mathrm{\Delta }}_{\mathrm{ex}}=2t$ (blue curves), and $k_z=0$.

Figure 3

(a) Spacial profile of the three components of the spin density $S_x$ (blue symbols), $S_y$ (red symbols), and $S_z$ (green symbols) throughout the junction. The tunnel barrier is located between position 100 and position 103. Parameters are ${\epsilon }_f=1.1$ eV and ${\mathrm{\Delta }}_{\mathrm{ex}}=2$ eV. Spatial profiles (b, c) of $S_x$ and (d, e) of $S_y$ in the right antiferromagnet, normalized to their magnitude at the right interface, at different exchange energies ${\mathrm{\Delta }}_{\mathrm{ex}}$ and for ${\epsilon }_f=1.1$ eV (b, d) and ${\epsilon }_f=6.6$ eV (c, e). The bias voltage is 0.6 eV for all the calculations. Note that the solid blue line in (b) and (c) is not visible due to the very strong dephasing.

Figure 4

Bias dependence of (a) in-plane and (b) out-of-plane torques at an AF-MTJ, calculated in the right antiferromagnet for different exchange energies ${\mathrm{\Delta }}_{\mathrm{ex}}$ and ${\epsilon }_f=1.1$ eV.

Figure 5

(a) Spatial profile of $S_x$ in the right antiferromagnet for $\mathrm{\Gamma }=0$ (solid line), 0.2 eV (red symbols), and 0.4 eV (blue symbols) with ${\mathrm{\Delta }}_{\mathrm{ex}}=1$ eV. (b) Spatial profile of $S_x$ in the right antiferromagnet for $\mathrm{\Gamma }=0$ (solid line), 0.1 eV (red symbols), and 0.3 eV (blue symbols) with ${\mathrm{\Delta }}_{\mathrm{ex}}=2$ eV. Calculated quantities are averaged over 2000 disorder configurations.

Figure 6

(a) Spatial profile of $S_y$ in the right antiferromagnet for $\mathrm{\Gamma }=0$ (solid line), 0.2 eV (red symbols), and 0.4 eV (blue symbols) with ${\mathrm{\Delta }}_{\mathrm{ex}}=1$ eV. (b) Spatial profile of $S_y$ in the right antiferromagnet for $\mathrm{\Gamma }=0$ (solid line), 0.1 eV (red symbols), and 0.3 eV (blue symbols) with ${\mathrm{\Delta }}_{\mathrm{ex}}=2$ eV. Calculated quantities are averaged over 2000 disorder configurations.

Figure 7

Impact of disorder on the torkance components in (a) F-MTJs and (b) AF-MTJs. Black and red symbols refers to in-plane and out-of-plane components, respectively. The exchange splitting is set to ${\mathrm{\Delta }}_{\mathrm{ex}}=2$ eV, the width of the junctions is 10 monolayers, the bias voltage is 0.6 eV, and the torque computed here is the total torque.