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

Static properties and current-induced dynamics of pinned $90$ degree magnetic domain walls under applied fields: an analytic approach