Dipolar ferromagnetic phase transition in Fe₃O₄ nanoparticle arrays observed by Lorentz microscopy and electron holography

Dipolar ferromagnetism formed in Fe₃O₄ nanoparticle arrays is revealed by Fresnel Lorentz microscopy and electron holography. Dipolar domain walls do not lie preferentially along macrograin boundaries but depend on the overall shape of the assembly, meaning magnetostatic energy dominates. The domain structures are imaged at different temperatures for both monolayer and bilayer arrays. The domain wall contrast in the monolayer region is visible until 575 °C, and the magnetic order parameter steeply drops toward the temperature. In the bilayer region, finer and more complicated domains are formed.