Analytic form of transverse head-to-head domain walls in thin cylindrical wires

• Diameter-dependent analytic form of transverse domain walls in soft-magnetic nanowires.
• Magnetostatic model based on the demagnetizing factors of oblate and prolate spheroids.
• Calibration of the model with micromagnetic simulations.
• Excellent agreement between analytic form and numerical results.
• Linearization of the equations for simple, approximate solutions.

The static problem of a one-dimensional, transverse head-to-head domain wall structure in a thin soft-magnetic nanowire with circular cross-section is treated within the framework of micromagnetic theory. An analytic form of the domain wall profile is derived, which yields that the domain wall profile depends on the wire radius. The analysis is performed by decomposing the magnetostatic energy into a monopolar and a dipolar term. We present a model in which the dipolar term of the magnetostatic energy resulting from the transverse magnetization in the center of the domain wall is calculated with Osborn's formulas for homogeneously magnetized ellipsoids [Phys. Rev. 67 (1945) 351] [22]. The analytic results agree almost perfectly with simulation data as long as the wire diameter is sufficiently small to prevent inhomogeneities of the magnetization along the cross-section. Owing to the recently demonstrated negligible Döring mass of these walls, our results should also apply to the dynamic case, where domain walls are driven by spin-transfer toque effects and/or an axial magnetic field.