  Magnetic domain walls are pinned strongly by abrupt changes in magnetic
anisotropy. When driven into oscillation by a spin-polarized current, locally
pinned domain walls can be exploited as tunable sources of short-wavelength
spin waves. Here, we develop an analytical framework and discrete Heisenberg
model to describe the static and dynamic properties of pinned domain walls with
a head-to-tail magnetic structure. We focus on magnetic domain walls that are
pinned by 90$^\circ$ rotations of uniaxial magnetic anisotropy. Our model
captures the domain wall response to a spin-transfer torque that is exerted by
an electric current. Model predictions of the domain wall resonance frequency
and its evolution with magnetic anisotropy strength and external magnetic field
are compared to micromagnetic simulations.
