  We explore the nematic order of model goethite nanorods in an external
magnetic field within Onsager-Parsons density functional theory. The goethite
rods are represented by monodisperse, charged spherocylinders with a permanent
magnetic moment along the rod main axis, forcing the particles to align
parallel to the magnetic field at low field strength. The intrinsic diamagnetic
susceptibility anisometry of the rods is negative which leads to a preferred
perpendicular orientation at higher field strength. It is shown that these
counteracting effects may give rise to intricate phase behavior, including a
pronounced stability of biaxial nematic order and the presence of reentrant
phase transitions and demixing phenomena. The effect of the applied field on
the nematic-to-smectic transition will also be addressed.
