  Use of a spin polarized current for the manipulation of magnetic domain walls
in ferromagnetic nanowires has been the subject of intensive research for many
years. Recently, due to technological advancements, creating nano-contacts with
special characteristics is becoming more and more prevalent. We now present a
full quantum investigation of the magnetoresistance and the spin transfer
torque in a domain wall, which is embedded in a nano-contact of Ni$_{80}$Fe$_
{20}$, where the size of the domain wall becomes a relevant tunable parameter.
The dependence on the domain wall width as well as the spatial dependence of
the torque along the domain wall can be analyzed in complete detail. The
magnetoresistance drops with increasing domain wall width as expected, but also
shows characteristic modulations and points of resonant spin-flip transmission.
The spin transfer torque has both significant in-plane and out-of-plane
contributions even without considering relaxation. A closer inspection
identifies contributions from the misalignment of the spin density for short
domain walls as well as an effective gauge field for longer domain walls, both
of which oscillate along the domain wall.
