  We have developed a circularly polarized dielectric rutile (TiO$_2$) cavity
with a high quality-factor that can generate circularly polarized microwaves
from two orthogonal linearly polarized microwaves with a phase difference of
$\pm\pi/2$ using a hybrid coupler. Using this cavity, we have established a new
methodology to measure the microwave Hall conductivity of a small single
crystal of metals in the skin-depth region. Based on the cavity perturbation
technique, we have shown that all components of the surface impedance tensor
can be extracted under the application of a magnetic field by comparing the
right- and left-handed circularly polarization modes. To verify the validity of
the developed method, we performed test measurements on tiny Bi single crystals
at low temperatures. As a result, we have successfully obtained the surface
impedance tensor components and confirmed that the characteristic field
dependence of the ac Hall angle in the microwave region is consistent with the
expectation from the dc transport measurements. These results demonstrate a
significant improvement in sensitivity compared to previous methods. Thus, our
developed technique allows more accurate microwave Hall measurements, opening
the way for new approaches to explore novel topological quantum materials, such
as time-reversal symmetry-breaking superconductors.
