Dynamics of domains and walls in soft magnetic films

General equations are derived to describe the simultaneous nonuniform planar rotations of the magnetization vector and displacements of curved domain walls and their junctions in soft magnetic films. These equations take into account effects of exchange stiffness, magnetic anisotropy, external and either long- or short-range demagnetizing fields, wall energy, and dissipation. The case of a matched film pair using the capacitor or transmission-surface approximation for its short-range demagnetizing energy is considered. The theory is founded on energy and dissipation functionals including domain and wall terms. The constraint of wall-normal magnetization continuity across a domain wall is handled by a method of implementing d´Alembert´s virtual work principle without introducing Lagrange multipliers. The result is a set of coupled equations expressing the dynamic torque balance at points inside domains, the wall-domain constraint due to wall-normal magnetization continuity, an additional boundary condition coupling domain magnetization and wall curves, and the wall velocity.