A Theoretical Approach for Computing Magnetic Anisotropy in Single Molecule Magnets

TL;DR

This paper introduces a theoretical method to compute magnetic anisotropy parameters in single molecule magnets by treating anisotropy as a perturbation and applying it to specific compounds, revealing dependence on local anisotropy orientations.

Contribution

The paper develops a perturbative approach to calculate molecular magnetic anisotropy parameters in any eigenstate of the exchange Hamiltonian, considering local anisotropies and their orientations.

Findings

Magnetic anisotropy depends on local anisotropy orientations in Mn12Ac.

In Mn12Ac, D_M is nearly independent of core Mn(IV) anisotropy orientation.

In Fe8, molecular anisotropy shows weaker dependence on spin state.

Abstract

We present a theoretical approach to calculate the molecular magnetic anisotropy parameters, $D_M$ and $E_M$ for single molecule magnets in any eigenstate of the exchange Hamiltonian, treating the anisotropy Hamiltonian as a perturbation. Neglecting inter-site dipolar interactions, we calculate molecular magnetic anisotropy in a given total spin state from the known single-ion anisotropies of the transition metal centers. The method is applied to $Mn_{12}Ac$ and $Fe_8$ in their ground and first few excited eigenstates, as an illustration. We have also studied the effect of orientation of local anisotropies on the molecular anisotropy in various eigenstates of the exchange Hamiltonian. We find that, in case of $Mn_{12}Ac$, the molecular anisotropy depends strongly on the orientation of the local anisotropies and the spin of the state. The $D_M$ value of $Mn_{12}Ac$ is almost independent of the orientation of the local anisotropy of the core $Mn(IV)$ ions. In the case of $Fe_8$, the dependence of molecular anisotropy on the spin of the state in question is weaker.