Instability threshold of a nematic liquid crystal in a biased rotating magnetic field

It is shown that a nematic liquid crystal in the presence of a magnetic field vector rotating on the surface of a right circular cone can have an equilibrium state in which the director rotates synchronously with the applied field. For field cone angles of less than 54.7^∘{}, this state is stable at all angular frequencies. At larger angles a stability limit exists at a finite rotation speed. Two types of instability modes are predicted, depending upon the field cone angle. The implications of these results for torque-magnetometer and electron-resonance-spectroscopy studies are discussed.