Size and fluctuation effects on the dynamics of linear domain walls in an Ising ferromagnet

Approaching the Curie temperature of ${\mathrm{LiTbF}}_4$ ellipsoids of thicknesses between 0.5 and 7 mm up to ${\mathit{T}}_{\mathit{c}}$-T=3×${10}^{\mathrm{-}4}$ ${\mathit{T}}_{\mathit{c}}$, the first clear evidence for critical fluctuations and macroscopic size effects on the domain-wall relaxation is presented. An analog to the Landau-Lifshitz model proposed recently and additional optical data on the domain width suggest associating both phenomena with the existence of linear (Bulaevskii-Ginzburg) walls and with domain branching near the surface.