APPLICATION OF SOLITON THEORY TO FERROMAGNETIC DOMAIN-WALL DYNAMICS

Consider the dynamics of a 180° ferromagnetic domain wall pinned by a planar defect. The defect is characterized by an abrupt change in both the magnetic anisotropy and exchange energies. General algebraic expressions are obtained for the resonant domain wall oscillation frequency, the effective wall stiffness, and the coercive force. The wall oscillation frequency due to a grain boundary in iron is computed as ∼400 Mc/s. in good agreement with typical experimental values of ∼500 Mc/s. Noting that, when an effective stiffness constant is added to the Hamiltonian, the zero energy Goldstone translation mode is raised to a finite energy level, we show that this excitation energy is proportional to the fractional change in the medium characteristics and to the anisotropy constant and that it has a maximum value when the ratio of defect width to domain wall width is of order unity.