This paper is a theoretical "proof of concept" on how the on-site first-order spin-orbit coupling can generate giant Dzyaloshinskii-Moriya interaction in binuclear transition metal complexes. This effective interaction plays a key role in strongly correlated materials, skyrmions, multiferroics, molecular magnets of promising use in quantum information science and computing. Despite this, its determination from both theory and experiment is still in its infancy and existing systems usually exhibit very tiny magnitudes. We derive analytical formulas that perfectly reproduce both the nature and the magnitude of the Dzyaloshinskii-Moriya interaction calculated using state-ofthe-art ab initio calculations performed on model bicopper(II) complexes. We also study which geometrical structures/ligand-field forces would enable one to control the magnitude and the orientation of the Dzyaloshinskii Moriya vector in order to guide future synthesis of molecules or materials. This article provides an understanding of its microscopic origin and proposes recipes to increase its magnitude. We show that i) the on-site mixings of 3d orbitals rules the orientation and magnitude of this interaction, ii) increased values can be obtained by choosing more covalent complexes, iii) huge values (~1000 cm -1 ) and controlled orientations could be reached by approaching structures exhibiting on-site first-order SOC, i.e. displaying an "unquenched orbital momentum".

A family of four-coordinate Fe complexes formed with N,N'-chelating amido-pyridine ligands was synthesized, and their magnetic properties were investigated. These distorted tetrahedral complexes exhibit significant magnetic anisotropy with zero-field splitting parameter D ranging between -17 and -12 cm. Ab initio calculations enabled identification of the structural factors that control the nature of the magnetic anisotropy and the rationalization of the variation of D in these complexes. It is shown that a reduced N-Fe-N angle involving the chelating nitrogen atoms of the ligands is at the origin of the negative D value and that the torsion between the two N-Fe-N planes imposed by steric hindrances further increases the |D| value. Field-induced slow relaxation of magnetization was observed for the three compounds, and a single-molecule magnet behavior with an energy barrier for magnetization flipping (U) of 27 cm could be evidenced for one of them.

The magnetic anisotropy parameters of a hexacoordinate trigonally elongated Ni(II) complex with symmetry close to D3d are measured using field-dependent magnetization and High-Field and High-Frequency EPR spectroscopy (D = +2.95 cm -1 , |E/D| = 0.08 from EPR). Wavefunction based theoretical calculations reproduce fairly well the EPR experimental data and allows analysing the origin of the magnetic anisotropy of the complex. Calculations on model complexes allows getting insight into the origin of the large increase in the axial magnetic anisotropy (D) when the complex is brought to a prismatic geometry with a symmetry close to D3h .