Theory of calculating eigenmodes spectrum for gyrotropic resonators when using scalar potentials formalism is developed. Equations for calculating splitting of resonant frequencies of gyromagnetic and gyroelectric cylinder resonators in magnetic field are derived. Theoretical results are compared to the experimentally obtained figures for microwave gyromagnetic resonators made of barium hexaferrite. Example of a resonator made of indium antimonide demonstrates the possibility of using magnetized semiconductor resonators cooled to liquid nitrogen temperature to achieve the same characteristics offered by resonators made of magnetically firm hexaferrites when designing unidirectional microwave devices
