First-principle studies of spin-electric coupling in a $\{Cu_3\}$ single molecular magnet

We report on a study of the electronic and magnetic properties of the triangular antiferromagnetic $\{Cu_3\}$ single-molecule magnet, based on spin density functional theory. Our calculations show that the low-energy magnetic properties are correctly described by an effective three-site spin $s=1/2$ Heisenberg model, with an antiferromagnetic exchange coupling $J \approx 5$ meV. The ground state manifold of the model is composed of two degenerate spin $S=1/2$ doublets of opposite chirality. Due to lack of inversion symmetry in the molecule these two states are coupled by an external electric field, even when spin-orbit interaction is absent. The spin-electric coupling can be viewed as originating from a modified exchange constant $δJ$ induced by the electric field. We find that the calculated transition rate between the chiral states yields an effective electric dipole moment $d = 3.38\times 10^{-33} {\rm C\ m} \approx e 10^{-4}a$, where $a$ is the Cu separation. For external electric fields ${\varepsilon} \approx 10^8$ V/m this value corresponds to a Rabi time $τ\approx 1$ ns and to a $δJ$ of the order of a few $μ$eV.