In this work we compute the torque field present in a ferromagnet in contact with a metallic nanowire when a skyrmion is present. If the nanowire is narrow enough, then the current is carried by a single conduction band. In this regime the classical torque model breaks down and we show that a skyrmion driven by spin transfer torque moves in a different direction than predicted by the classical model. However, the amount of charge current required to move a skyrmion with a certain velocity in the single-band regime is similar to a classical model of torque where it is implicitly assumed current transport by many conduction bands. The single-band regime is more efficient creating spin current from charge current because of the perfect polarization of the single band but is less efficient creating torque from spin current. Nevertheless, it is possible to take profit of the single-band regime to move skyrmions even with no net charge or spin current flowing between the device contacts. We have also been able to recover the classical limit considering an ensemble of only a few electronic states. In this limit we have discovered that electron diffusion needs to be considered even in ballistic nanowires due the effect of the skyrmion structure on the electron current.

• Received 25 June 2020
• Revised 15 September 2020
• Accepted 15 September 2020

DOI:https://doi.org/10.1103/PhysRevB.102.125436