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

## TL;DR

This paper theoretically demonstrates that transverse domain walls in spin valves with planar-transverse polarizers can achieve high velocities and ultra-high differential mobility at low current densities, enabling energy-efficient magnetic nanodevices.

## Contribution

It reveals the stable high-velocity traveling-wave motion of TDWs with planar-transverse polarizers and explains existing simulation results analytically, highlighting potential for low-energy magnetic device applications.

## Key findings

- TDWs reach velocities of 10^3 m/s at current densities below 10^7 A/cm^2
- Stable traveling-wave motion persists with strong planar-transverse polarizers
- External transverse magnetic fields can further enhance TDW velocity

## Abstract

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 $10^7$ $\mathrm{A/cm^2}$. 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.