Ferromagnetic Fréedericksz transition in ferromagnetic nematic filaments

Barium hexaferrite nanoplates at sufficiently high concentrations in 1-butanol spontaneously form a ferromagnetic nematic phase due to the interplay between Onsager excluded volume effects and magnetic dipole-dipole interactions [Nat Comm, 7: 10394, 2016]. We have discovered a rich variety of ferromagnetic structures, such as droplets, toroids, and filaments, which form in the isotropic background when the concentration of the nanoplates is within the isotropic-nematic phase coexistence region. Here, we demonstrate a Fréedericksz transition in such ferromagnetic filaments. In the absence of applied magnetic field, the local magnetization direction of the filaments is parallel to their long axes. When a magnetic field is applied parallel to the magnetization direction, the existing alignment of the nanoplates is reinforced and the shape of the filaments remain unchanged. However, when a sufficiently strong magnetic field is applied antiparallel to the magnetization direction, an undulation instability sets in and the filaments form wavy structures. A simple model was developed to describe the defomation of the filaments close to the transition points.