Electronic structure of a ${\mathrm{Mn}}_{12}$ molecular magnet: Theory and experiment

We used site-selective and element-specific resonant inelastic x-ray scattering (RIXS) to study the electronic structure and the electron interaction effects in the molecular magnet $\left[{\mathrm{Mn}}_{12}{\mathrm{O}}_{12}{\left(\mathrm{C}{\mathrm{H}}_3\mathrm{C}\mathrm{O}\mathrm{O}\right)}_{16}{\left({\mathrm{H}}_2\mathrm{O}\right)}_4\right]\bullet 2\mathrm{C}{\mathrm{H}}_3\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}\bullet 4{\mathrm{H}}_2\mathrm{O}$, and compared the experimental data with the results of local spin density approximation $+U$ electron structure calculations which include the on-site Coulomb interactions. We found a good agreement between theory and experiment for the Coulomb repulsion parameter $U=4\mathrm{eV}$. In particular, the $p\text{−}d$ band separation of $1.8\mathrm{eV}$ has been found from the RIXS spectra, which is in accordance with the calculations. Similarly, the positions of the peaks in the XPS spectra agree with the calculated densities of $p$ and $d$ states. Using the results of the electronic structure calculations, we determined the intramolecular exchange parameters, and used them for diagonalization of the ${\mathrm{Mn}}_{12}$ spin Hamiltonian. The calculated exchanges gave the correct ground state with the total spin $S=10$.

Figure 1

The comparison of Mn $L_{2,3}$ XES of ${\mathrm{Mn}}_{12}$ with spectra of reference samples.

Figure 2

RIXS spectra of ${\mathrm{Mn}}_{12}$ excited at C $K$ edge.

Figure 3

RIXS spectra of ${\mathrm{Mn}}_{12}$ excited at O $K$ edge.

Figure 4

The comparison of XPS VB and XES of constituents of ${\mathrm{Mn}}_{12}$ on the binding energy scale.

Figure 5

Mn $3s$ x-ray photoelectron spectra of ${\mathrm{Mn}}_{12}$ and manganese oxides $\mathrm{Li}\mathrm{Mn}{\mathrm{O}}_2$, ${\mathrm{La}}_{0.67}{\mathrm{Sr}}_{0.33}\mathrm{Mn}{\mathrm{O}}_3$, and ${\mathrm{Li}}_2\mathrm{Mn}{\mathrm{O}}_3$. The spectra are given on an energy scale relative to the main maxima of the high-spin components. The deconvolution of the spectrum of ${\mathrm{Mn}}_{12}$ into Gaussian functions is shown by thin solid lines. The positions of the low-spin components for each spectrum are shown by vertical lines.

Figure 6

Mn $2p$ x-ray photoelectron spectra of ${\mathrm{Mn}}_{12}$ and some manganese oxides: $\mathrm{Li}\mathrm{Mn}{\mathrm{O}}_2$, ${\mathrm{La}}_{0.67}{\mathrm{Sr}}_{0.33}\mathrm{Mn}{\mathrm{O}}_3$, and ${\mathrm{Li}}_2\mathrm{Mn}{\mathrm{O}}_3$. The deconvolution of the Mn $2p$ spectrum of ${\mathrm{Mn}}_{12}$ into Gaussian functions is shown by thin solid lines. Positions of the $2p_{3∕2}$ main lines and of the satellites are shown by the arrows.

Figure 7

Calculated projected electronic DOSs for ${\mathrm{Mn}}_{12}$ for Mn $3d$ (upper panel), different types of O $2p$ electrons (central panel), and different types of C $2p$ electrons (lower panel).

Figure 8

Calculated projected electronic DOSs for $3d$ states of different manganese atoms (a) and $2p$ states of different oxygen atoms (b) calculated with $U=4\mathrm{eV}$.

Figure 9

Sketch of ${\mathrm{Mn}}_{12}$ molecules showing positions of different Mn ions: black circles, Mn1; white circles, Mn2; and dashed circles, Mn3 (denoted by their numbers). The exchange interactions between different ions are shown by solid lines.