Fourth-Order Magnetic Anisotropy and Tunnel Splittings in $\mathrm{M}{\mathrm{n}}_{\mathrm{12}}$ from Spin-Orbit-Vibron Interactions

From density-functional-theory based methods, we calculate the vibrational spectrum of the $\mathrm{M}{\mathrm{n}}_{\mathrm{12}}{\mathrm{O}}_{\mathrm{12}}(\mathrm{C}\mathrm{O}\mathrm{O}\mathrm{H}{)}_{16}({\mathrm{H}}_{\mathrm{2}}\mathrm{O}{)}_4$ molecular magnet. Calculated infrared intensities are in accord with experimental studies. There have been no ab initio attempts at determining which interactions account for the fourth-order anisotropy. We show that vibrationally induced distortions of the molecule contribute to the fourth-order anisotropy Hamiltonian and that the magnitude and sign of the effect ($-6.2\mathrm{K}$) is in good agreement with all experiments. Vibrationally induced tunnel splittings in isotopically pure and natural samples are predicted.

Figure 1

Calculated total and IR vibrational density of states for the ${\mathrm{M}\mathrm{n}}_{12}$ molecule. In addition, we have projected the IR active density of states onto Mn, ${\mathrm{O}}^{2-}$, COOH, and ${\mathrm{H}}_{\mathrm{2}}\mathrm{O}$ to show the origin of the IR spectrum.

Figure 2

Evolution of fourth-order anisotropy barrier [$\Delta (4)$] as a function of the number of modes included. Also shown is the total and Mn-projected calculated IR and Raman spectra. Large jumps in the barrier are due to strong Raman modes, as discussed in the text.