Electronic pressure on the ferromagnetic domain wall

The scattering of electron by a domain wall in a nano-wire is studied perturbatively to the lowest order. The correction to the thermodynamic potential of the electron system due to scattering is calculated from the phase shift. The wall profile is determined by taking account of this correction, and the result indicates that the wall in a ferromagnet with a small exchange coupling can be squeezed to be very thin to lower the electron energy.