Unraveling the magnetoelectric effect using electric field-controlled magnetic anisotropy: a theoretical study

This article highlights the microscopic origin of the magnetoelectric effect, which could enable crucial control of magnetic properties using electric fields. In particular, it explains the influence of electric fields on the magnetic anisotropy of a Ni(II) complex characterized by significant uniaxial anisotropy and notable rhombicity. Our findings reveal that the electric field's effect on the axial anisotropy parameter primarily arises from atomic displacements, whereas for the rhombic parameter, it is driven by electronic structure changes. While recent observations show that electric fields applied in the direction of the molecular dipole moment induce a greater variation in D than fields applied perpendicular to it due to greater atomic displacement, here we demonstrate a striking exception: applying the electric field in the molecular direction associated with an almost zero dipole moment causes a variation in D seven times greater than that induced in the direction of a large permanent dipole moment (∼10 Debye). This observation reveals a previously unknown magnetoelectric coupling mechanism. We demonstrate that the magnetoelectric effect inducing variations of the zero-field splitting parameters is dictated by the nature of electronic excitations involved in the spin-orbit couplings that produce the magnetic anisotropy, more specifically in the orientation of the orbitals involved in these excitations, rather than by the dipole moment's magnitude. However, as the variation of D is essentially governed by the impact of field-induced geometric changes on the energy of the orbitals involved in these excitations, one may expect larger responses if one of these orbitals points in the direction of the dipole moment. Besides, as this behavior can be rationalized using crystal field theory, it offers a general principle that can help the design of molecules with predictable magnetoelectric responses.