  We developed a new microwave Hall effect measurement method for materials in
the skin depth region at low temperatures using a cross-shaped bimodal cavity.
We analytically calculated electromagnetic fields in the cross-shaped cavity,
and the response of the cavity including the sample, whose property is
represented by the surface impedance tensor; further, we constructed the method
to obtain the Hall component of the surface impedance tensor in terms of the
change in resonance characteristics. To confirm the validity of the new method,
we applied our method to measure the Hall effect in metallic Bi single crystals
at low temperatures, and we confirmed that the microwave Hall angles coincide
with the DC Hall angle. Thus, it becomes clear that the Hall angle measurement
under cryogenic conditions becomes possible without any complicated tuning
mechanisms, and our bimodal cavity method can be used to measure the microwave
Hall effect on materials in the skin depth region. The result opens a new
approach to discuss the Hall effect in condensed matter physics such as the
microwave flux-flow Hall effect in superconductors.
