Description of molecular nanomagnets by the multiorbital Hubbard model with correlated hopping

We present a microscopic description of molecular magnets by the multiorbital Hubbard model, which includes the correlated hopping term, i.e., the dependence of the electron hopping amplitude between orbitals on the degree of their occupancy. In the limit of large Coulomb on-site interaction, we derive the spin Hamiltonian using the perturbation theory. We determine the magnetic coupling constant between two ions 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 diagonalization of the multiorbital Hubbard model. The procedure we use can be applied to various nanomagnets, but we perform the final calculations for the molecular ring ${\text{Cr}}_8$. We show that the correlated hopping can reduce the antiferromagnetic exchange between ions, which is essential for a proper description of ${\mathrm{Cr}}_8$.

Figure 1

The total exchange couplings: $\mathrm{\Gamma }$ derived from perturbation theory (solid line) and ${\mathrm{\Gamma }}^{*}$ derived from the exact diagonalization calculations (dots) in ${\mathrm{Cr}}_8$ as a function of the CH parameter $a$ for $U=5.98\text{eV}, J=0.26\text{eV}$, and the set of $t_{m{m}^{\prime }}^{i{i}^{\prime }}$ amplitudes reported in Ref. [19] with the corrected value of $t_{11}^{ij}=-0.131\text{eV}$. The intersection points of the dashed lines indicate that the experimental value $\mathrm{\Gamma }=1.46\text{meV}$ is attained for either $a\approx 0.05$ or $a\approx 0.06$, as obtained with the perturbation or exact diagonalization calculations, respectively.

Figure 2

The curves corresponding to the constant value of the superexchange coupling $\mathrm{\Gamma }(U,J)=1.46\text{meV}$ in ${\mathrm{Cr}}_8$ obtained from the perturbation calculus as a function of the interacting couplings $U$ and $J$ for the amplitudes $t_{m{m}^{\prime }}^{i{i}^{\prime }}$ reported in Ref. [19] with the corrected value of $t_{11}^{ij}=-0.131\text{eV}$ and for the following set of the CH parameters: $a=0.0,0.02,0.04,0.05$ (top to bottom). The intersection point of the dashed lines indicates that the experimental value $\mathrm{\Gamma }=1.46\text{meV}$ is attained for $U=5.98\text{eV}$ and $J=0.26\text{eV}$ (the values reported in [19]) when $a\approx 0.05$.