the exchange-correlation potential. Test calculations were also done using the PBE GGA potential. [@PBE96] They showed that the use of GGA slightly increases exchange splitting of Mn $d$ states but has only minor effect on Bi $p$ derived bands. Brillouin zone (BZ) integrations during the self-consistency loop were done on a 32$\times$32$\times$16 mesh using the improved tetrahedron method. [@BJA94]

Matrix elements for interband optical transitions were calculated in the dipole approximation. Then, the real part of the optical conductivity was calculated using the tetrahedron method and the imaginary part was obtained using the Kramers-Kronig relations.

We found that a very dense $k$ mesh should be used in order to achieve convergence of the conductivity below 0.3 eV. For instance, the in-plane conductivity spectrum calculated on the 32$\times$32$\times$16 mesh shows a broad peak centered at 0.18 eV. The peak shifts to $\sim$0.10 eV ($\sim$1000 cm$^{-1}$), becomes narrower, and its height doubles when a denser 80$\times$80$\times$48 mesh with almost 40000 symmetry inequivalent $k$ points in BZ is used. The use of even denser 128$\times$128$\times$48 ($\sim$10$^6$ $k$ points) mesh still leads to a small ($<$0.01 eV) shift of the peak position and 10% increase of its height. However, since calculations on such a 