Magnetic force theorem
In order to characterize the magnetic structure of a material it is often useful to try and map the system onto an Heisenberg model: a lattice of localized atomic moments interacting via the exchange coupling J_ij.
In order to get these couplings from a DFT calculation we make use of the magnetic force theorem: after we find a localized basis set (Wannier functions), we tilt one of the spins of the lattice and calculate the perturbative correction to the total energy [1].
That difference in energy can be related to an underlying Heisenberg model.
In our group, we developed an inhouse code that is numerically particularly stable by recasting the integration in the complex plane into a sum over Matsubara frequencies.
- X. Zhu, A. Edström, and C. Ederer, external pageMagnetic exchange interactions in SrMnO3, Phys. Rev. B 101, 064401 (2020).