Contribution from optically excited many-electron states to the superexchange interaction in Mott-Hubbard insulators

We investigated the effects of excited many-electron states in the optical control of the magnetic state in undoped Mott-Hubbard insulator. To derive the spin Hamiltonian in material under optical pumping one has used a many-electron approach based on the X-operator representation. Extending the projection operators approach on arbitrary energy spectra of the Mott-Hubbard insulator, we obtained the Hamiltonian of superexchange interaction in analytical form. The Hamiltonian includes the spin-exciton variables which are usually missing in discussion on the magnetic response to optical pumping. The superexchange is also not additive over contributions from the ground and optical excited states, and nonzero contributions to the Dzyaloshinskii-Moriya interaction are induced in insulators with different spins at the ground and excited cell states. As a test, a microscopic background for the optical induced superexchange was analyzed in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ (further La214) and ${\mathrm{FeBO}}_3$ with spins 1/2 and 5/2, respectively.

Figure 1

Configuration space of all possible cell states involved in superexchange with one hole per cell. The sectors $N_0$ and $N_{+}$ correspond to states (6) and (7), respectively.

Figure 2

Two circles (dashed line) are a sequence of intracell transitions at the light-induced superexchange $J_{ij}^{ab}$ (a) and $J_{ij}^{bb}$ (b) between $i$ and $j$ cells in Eq. (25); (c) illustrates the single circle (spin-exciton) contribution $\sim \left(t_{ij}^{a0,bA}{t}_{ji}^{b0,bA}\right)/{\mathrm{\Delta }}_{abA}$ (for cuprates), which can be reduced to the spin Hamiltonian using additional assumptions only [see Eq. (24)].

Figure 3

Sequence of intracell transitions at the superexchange $J_{ij}^{\left(a\right)}\left(l_0{\tau }_0,l_0{\mu }_0\right)$ (a), optical induced superexchange $J_{ij}^{\left(b\right)}\left(l_0{\tau }_0,l^{\prime }{\mu }_0\right)$ (b), and $J_{ij}^{\left(c\right)}\left(l^{\prime }{\tau }_0,l_0{\mu }_0\right)$ (c) in ${\mathrm{FeBO}}_3$.