  In our previous publication [S. Ozaki and M. Ogata, Phys. Rev. Research 3,
013058], the quantization of the orbital-Zeeman (OZ) cross term in the magnetic
susceptibility, or the cross term of spin Zeeman and orbital effect, was shown
for the Kane-Mele model using the expansion around the Dirac points. In the
present study, we accurately evaluate the orbital, spin-Zeeman, and OZ cross
term of the Kane-Mele model using a recently developed formulation. This
formula is written in terms of the explicit Bloch wave functions, and enables
us to evaluate each contribution taking account of the integration over the
whole Brillouin zone and the summation over all the bands. As a result,
additional contributions such as core-electron diamagnetism are found.
Furthermore, our evaluation confirms the quantization of the OZ cross term and
reveals its behavior including the metallic case. The possibility of
experimental detection of the quantization is discussed.
