Rapid soliton nucleation and dynamics in magnetic materials
Magnetism in solid materials is a fascinating yet complex phenomenon that encompasses vastly different length and time scales. This complexity is typically resolved by establishing equations that are valid at different scales. For example, magnetic dynamics at the atomic level can be described by a discrete system of Schrödinger equations while microscopic magnetic dynamics is described by a vectorial partial differential equation known as the Landau-Lifshitz equation. However, such a distinction of scales is challenged when considering the problem of a magnetic material that dynamically evolves to equilibrium from a randomized or paramagnetic state. Numerical modeling in both the atomic and microscopic limits was performed to understand the manner in which long-range magnetism is recovered from a paramagnetic state. Along with experimental evidence, it was found that materials with perpendicular magnetic anisotropy, which acts as an attractive mechanism, rapidly form magnetic solitons that are randomly distributed in space. This phenomenon is analogous to soliton and pattern formation in incoherent light beams via modulational instability that is operative past a critical correlation length. At later times, the magnetic solitons exhibit dynamics that include perimeter excitations, growth, merger, break-up, and eventually decay. Despite the good agreement between experiments and multiscale modeling, the applicability of either the discrete or the continuum model remains an open question. An outline of future research addressing this conundrum from a mathematical and numerical perspective will be discussed.