The ligand spin problem: downfolding the Heisenberg Hamiltonian

In some structures, the spin magnetic momentum on the ligand are . They are however, not due to the spin splitting of the ligand atom, but the hybridization to the orbitals of surrounding atoms (often transitional metals). The refore, the spin will move with the

In these cases, a “downfolding” method could be used to used to get an effective Heisenberg model with only the transitional metal spins as independent variables from the exchange parameters with both transitional metal spins and ligand spins.

Usage:

To do the downfolding, one has to first generate the Heisenberg Hamiltonian with both the transitional metal and the ligands as magnetic elements, e.g. in CrI3,

wann2J.py --elements Cr I ....

The result is saved to TB2J_results directory. Then run the downfolding to get the Cr only effective exchange parameters, e.g.

TB2J_downfold.py --inpath TB2J_results --outpath TB2J_results_downfold --metals Cr --ligands I

will generate the downfolded result to TB2J_results_downfold.