  A Rashba nanowire is subjected to a magnetic field that assumes opposite
signs in two sections of the nanowire, and, thus, creates a magnetic domain
wall. The direction of magnetic field is chosen to be perpendicular to the
Rashba spin-orbit vector such that there is only a partial gap in the spectrum.
Nevertheless, we prove analytically and numerically that such a domain wall
hosts a bound state whose energy is at bottom of the spectrum below the energy
of all bulk states. Thus, this magnetically-confined bound state is
well-isolated and can be accessed experimentally. We further show that the same
type of magnetic confinement can be implemented in two-dimensional systems with
strong spin-orbit interaction. A quantum channel along the magnetic domain wall
emerges with a non-degenerate dispersive band that lies energetically below the
bulk states. We show that this magnetic confinement is robust against disorder
and various parameter variations.
