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When a magnetic fluid thin film is subjected to a perpendicular magnetic field H, the particles in the film agglomerate and form particle columns. With the increasing H, the columns evolve from a disordered column phase to the first-level hexagonal structural pattern and finally reach the second-level hexagonal structural pattern through a phase transition. During the transition phase, each column split into two columns. The split of a column may be attributed to the further alignment of the magnetic particles in each column under higher H’s. Hence the dipolar repulsive force in each column becomes dominant and causes the split of a column. The formation of the second-level hexagonal structure reveals that the minimum energy of the equilibrium system of magnetic fluid thin films under perpendicular magnetic fields has multiple local minima when H varies.

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