Description of Magnetic Nanomolecules by the Extended Multi-orbital Hubbard Model: Perturbative vs Numerical Approach

We present a microscopic description of magnetic molecules by the extended multi-orbital Hubbard model. In the limit of large Coulomb on-site interaction, we derived the spin Hamiltonian using the perturbation theory. The magnetic coupling constant between two ions we determined in two different ways: a) from the expression obtained in the perturbation calculus and b) from the analysis of distances between the lowest levels of the energy spectrum obtained by the diagonalization of the Hamiltonian of the extended multi-orbital Hubbard model. In order to speed up the very long and memory-intensive process of constructing the Hamiltonian matrix, whose size was $$14400\times 14400$$ , we implemented a procedure for locating the positions of non-zero elements. This significantly reduced the time of matrix creation and made it possible to perform calculations for more model parameters. The procedure we use can be applied to various nanomagnets, but the final calculations we performed for the molecular ring Cr $$_8$$ . We showed that the intersite repulsion between electrons located on neighboring ions increases the antiferromagnetic exchange coupling between magnetic moments of these ions, but this increase can be compensated for by the effect of correlated hopping of electrons.