Phase shift of spin waves traveling through a 180° Bloch-domain wall

We describe a spin wave traveling through a 180 degrees Bloch-domain wall. The resulting linearized Bloch equations have the same form as for a spin wave propagating past a negative effective field well. The field varies slowly relative to the wavelength of the considered spin waves. A Wentzel-Kramers-Brillouin (WKB) approximation is used to estimate the phase shift and is compared to known exact results.