Behavior of the magnetic structures of the magnetic fluid film under tilted magnetic fields

The patterns of the magnetic structure of the magnetic fluid thin film under tilted magnetic fields were taken to investigate the behavior of magnetic structures. The tilted angle θ is the angle between the direction of applied magnetic field and the normal line of the film. In our previous work, a nearly perfect ordered hexagonal structure in magnetic fluid thin film was obtained when a perpendicular magnetic field (θ = 0) was applied. By increasing θ, each column in the hexagonal structure gradually tilted to reveal a lattice of segments instead of dots on the pattern with an unchanged lattice distance d. As θ exceeding a critical value θ_c, these segments began to form longer periodic chains with an abrupt increasing of d. Hence, a transition from the magnetic hexagonal structure to a periodic chain structure at θ_c existed for magnetic fluid thin film in which the θ_c decreases exponentially as the sweeping rate increases.