Current-induced switching in $\mathrm{Py}∕\mathrm{Cu}∕\mathrm{Py}$ spin valves

Current-induced switching in $\mathrm{Py}∕\mathrm{Cu}∕\mathrm{Py}$ spin valves with the Cu spacer thickness varying between 20 and 30 monolayers is described theoretically in terms of a multiscale approach based on ab initio calculations using the fully relativistic screened Korringa-Kohn-Rostoker method and the Landau-Lifshitz-Gilbert equation. It is found that in all investigated cases a perpendicular arrangement of the magnetic slabs is lowest in energy and that therefore the critical current refers to a switching from this initial magnetic configuration to a collinear magnetic configuration, the switching time being about $30\mathrm{ps}$. Because the twisting energy as well as the corresponding sheet resistance, both of them entering as key quantities the expression for the current, can be viewed layer resolved, very clear conclusions can be drawn with respect to possible reductions of the critical current.

Figure 1

Twisting energy $\Delta E(\Theta ;m)$, sheet resistance $r(\Theta ;m)$ (top row), reduced current $I_0(\Theta ;m)$, and magnetoresistance $MR(\Theta ;m)$ (bottom row) for $m=20\mathrm{ML}$ of Cu.

Figure 2

Expansion coefficients $a_s$ [see Eq. (3)] for $s⩽3$ versus the number of spacer layers.

Figure 3

Reduced critical current $I_0(\Theta ;m)$ (top) and minimal time $t({\Theta }_i,{\Theta }_j;m)$ (bottom) versus the number of Cu spacer layers.