  Due to its non-local nature, calculating the demagnetizing field remains the
biggest challenge in understanding domain structures in ferromagnetic
materials. Analytical descriptions of demagnetizing effects typically
approximate domain walls as uniformly magnetized ellipsoids, neglecting both
the smooth rotation of magnetization from one domain to the other and the
interaction between the two domains. Here, instead of the demagnetizing field,
we compute analytically the demagnetizing energy of a straight domain wall
described by the classical $\tanh$ magnetization profile in a thin film with
perpendicular magnetic anisotropy. We then use our expression for the
demagnetizing energy to derive an improved version of the 1D model of
field-driven domain wall motion, resulting in accurate expressions for
important properties of the domain wall such as the domain wall width and the
Walker breakdown field. We verify the accuracy of our analytical results by
micromagnetic simulations.
