Search for toroidal ground state and magneto-electric effect in single-moleculemagnets

Using spin Hamiltonians parameterized first-principles calculations, we investigate the magnetic properties of high-symmetry transition-metal trimers, Cr3 and Cu3. We derive exchange coupling and magnetic anisotropy tensor for each trimer, showing these parameters give an accurate modeling of ground state properties. Results for Cr3 indicate uniaxial magnetic anisotropy with an easy-axis aligned along the c-axis with a mostly isotropic exchange interaction due to its high rotational symmetry. The Cu3 molecule lacks rotational symmetry and results show strong antisymmetric interactions for three distinct exchange couplings within the molecule. Diagonalizing multi-spin Hamiltonians, we obtain the ground state for these systems and show that susceptibility and magnetization simulations reproduce experimental findings. The presence of a non-collinear spin structure is investigate using the same multi-spin model and results show negligible presence of a toroidal ordering of spins for Cr3 and a finite toroidal moment for Cu3. We then scan the parameter space of the Hamiltonian to understand and to give insights into which interaction would lead to a measurable toroidal moment. We apply an external electric field and measure the corresponding change in the isotropic and full exchange coupling interaction for Cr3 and Cu3, respectively, with results indicating the presence of a magneto-electric effect. Combining the parameter sampling search for toroidal moments and the application of an electric field, results hint at the possibility of controlling the magnetic state of these system through electronic means.