Correlation effects in insulating surface nanostructures

We study the role of static and dynamical Coulomb correlation effects on the electronic and magnetic properties of individual Mn, Fe, and Co adatoms deposited on the CuN surface. For these purposes, we construct a realistic Anderson model, solve it by using the finite-temperature exact diagonalization method, and compare the calculated one-particle spectral functions with the LDA+$U$ densities of states. In contrast to Mn/CuN and Fe/CuN, the cobalt system tends to form the electronic excitations at the Fermi level. Based on the calculated magnetic response functions, transverse relaxation times for the magnetic moments of impurity orbitals are estimated. To study the effect of the dynamical correlations on the exchange interaction in nanoclusters, we solve the two-impurity Anderson model for the Mn dimer on the CuN surface. It is found that the experimental exchange interaction can be well reproduced by employing $U=3$ eV, which is two times smaller than the value used in static mean-field LDA+$U$ calculations. This suggests an important role of dynamical correlations in the interaction between adatoms on a surface. To estimate the correlated exchange interaction in the general case we derive a simple and transparent analytical expression demonstrating that the renormalization of the electronic spectrum due to dynamical correlations leads to a rescaling of the magnetic interactions compared to density functional results.

Figure 1

Schematic representation of the individual transition metal atom (Mn, Fe, and Co) on the CuN surface (top view) simulated in this work.

Figure 2

Partial one-particle spectral functions of Mn/CuN (red), Fe/CuN (gray), and Co/CuN (blue) obtained from LDA calculations.

Figure 3

Comparison of the partial spectral functions obtained from the LDA+$U$ (gray lines) and Anderson model calculations for the Mn/CuN (left) and Fe/CuN (right) systems ($U=3$ eV and $J_H=0.9$ eV).

Figure 4

Comparison of the partial spectral functions obtained from the LDA+$U$ (gray lines) and Anderson model calculations for the Co/CuN system ($U=3$ eV and $J_H=0.9$ eV).

Figure 5

Low- (left) and high-energy (right) parts of the spin-flip response functions [in ${\left(g{\mu }_B\right)}^{2}e{V}^{-1}$] calculated with $U=3$ and $J_H=0.9$ eV. The blue, red, purple, and brown lines correspond to the $xy$, $yz$ ($xz$), $3z^2-r^2$, and $x^2-y^2$ orbitals. The gray lines are examples of the fitting by using the Bloch equation, Eq. (6).

Figure 6

Schematic representation of the Mn dimer on the CuN surface (top view) simulated in this work.

Figure 7

Left: Comparison of the partial spectral functions obtained from the LDA (gray lines) and noninteracting model Hamiltonian for the Mn dimer on the CuN system. Right: Comparison of the partial spectral functions obtained from the LDA+$U$ (gray lines) and Anderson model calculations for the Mn dimer on the CuN surface with $U=3$ eV and $J_H=0.9$ eV.

Figure 8

Exchange interactions calculated in the LDA+$U$ ($U=5.88$ eV) and Anderson model ($U=3$ eV) as a function of the Fermi energy.