Ultra-high differential mobility and velocity of N\'{e}el walls in spin valves with planar-transverse polarizers under low perpendicularly injected currents

Transverse domain wall (TDW) dynamics in long and narrow spin valves with perpendicular current injection is theoretically investigated. We demonstrate that stable traveling-wave motion of TDWs with finite velocity survives for strong enough planar-transverse polarizers. For typical ferromagnetic materials (for example, Co) and achievable spin polarization ($P=0.6$), TDWs acquire a velocity of ${10}^3$ m/s under a current density below ${10}^7$ $\mathrm{A}\mathrm{/}\mathrm{c}{\mathrm{m}}^2$. This efficiency is comparable with that of perpendicular polarizers. More importantly, in this case the wall has ultra-high “differential mobility” around the onset of stable wall excitation. Our results open new possibilities for developing magnetic nanodevices based on TDW propagation with low energy consumption. Also, analytics for parallel and perpendicular polarizers perfectly explains existing simulation findings. Finally, further boosting of TDWs by external uniform transverse magnetic fields is investigated and turns out to be efficient.