  We explore magnetic behavior of kagome francisites Cu3Bi(SeO3)2O2X (X = Cl
and Br) using first-principles calculations. To this end, we propose an
approach based on the Hubbard model in the Wannier functions basis constructed
on the level of local-density approximation (LDA). The ground-state spin
configuration is determined by a Hartree-Fock solution of the Hubbard model
both in zero magnetic field and in applied magnetic fields. Additionally,
parameters of an effective spin Hamiltonian are obtained by taking into account
the hybridization effects and spin-orbit coupling. We show that only the former
approach, the Hartree-Fock solution of the Hubbard model, allows for a complete
description of the anisotropic magnetization process. While our calculations
confirm that the canted zero-field ground state arises from a competition
between ferromagnetic nearest-neighbor and antiferromagnetic
next-nearest-neighbor couplings in the kagome planes, weaker anisotropic terms
are crucial for fixing spin directions and for the overall magnetization
process. We thus show that the Hartree-Fock solution of an electronic
Hamiltonian is a viable alternative to the analysis of effective spin
Hamiltonians when a magnetic ground state and effects of external field are
considered.
