Antisymmetric Exchange in a Real Copper Triangular Complex.

The antisymmetric exchange, also known as the Dzyaloshinskii-Moriya interaction (DMI), is an effective interaction that may be at play in isolated complexes (with transition metals or lanthanides, for instance), nanoparticles, and highly correlated materials with adequate symmetry properties. While many theoretical works have been devoted to the analysis of single-ion zero-field splitting and to a lesser extent to symmetric exchange, only a few ab initio studies deal with the DMI. Actually, it originates from a subtle interplay between weak electronic interactions and spin-orbit couplings. This article aims to highlight the origin of this interaction from theoretical grounds in a real tri-copper(II) complex, capitalizing on previous methodological studies on bi-copper(II) model complexes. By tackling this three-magnetic-center system, we will first show that the multispin model Hamiltonian is appropriate for trinuclear (and likely for higher nuclearity) complexes, then that the correct application of the permutation relationship is necessary to explain the outcomes of the ab initio calculations, and finally, that the model parameters extracted from a binuclear model transfer well to the trinuclear complex. For a more theory-oriented purpose, we will show that the use of a simplified structural model allows one to perform more demanding electronic structure calculations. On this simpler system, we will first check that the previous transferability is still valid, prior to performing more advanced calculations on the derived two-magnetic-center model system. To this end, we will explain in detail the physics of the DMI in the copper triangle of interest, before advocating further theory/experiment efforts.

Extraction of giant Dzyaloshinskii-Moriya interaction from ab initio calculations: First-order spin-orbit coupling model and methodological study.

The Dzyaloshinskii-Moriya interaction is expected to be at the origin of interesting magnetic properties, such as multiferroicity, skyrmionic states, and exotic spin orders. Despite this, its theoretical determination is far from being established, neither from the point of view of ab initio methodologies nor from that of the extraction technique to be used afterward. Recently, a very efficient way to increase its amplitude has been demonstrated near the first-order spin-orbit coupling regime. Within the first-order regime, the anisotropic spin Hamiltonian involving the Dzyaloshinskii-Moriya operator becomes inappropriate. Nevertheless, in order to approach this regime and identify the spin Hamiltonian limitations, it is necessary to characterize the underlying physics. To this end, we have developed a simple electronic and spin-orbit model describing the first-order regime and used ab initio calculations to conduct a thorough methodological study.

How to create giant Dzyaloshinskii-Moriya interactions? Analytical derivation and ab initio calculations on model dicopper(II) complexes.

This paper is a theoretical "proof of concept" on how the on-site first-order spin-orbit coupling (SOC) can generate giant Dzyaloshinskii-Moriya interactions in binuclear transition metal complexes. This effective interaction plays a key role in strongly correlated materials, skyrmions, multiferroics, and 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-of-the-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 rule the orientation and magnitude of this interaction, (ii) increased values can be obtained by choosing more covalent complexes, and (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."

Ising-type Magnetic Anisotropy and Slow Relaxation of the Magnetization in Four-Coordinate Amido-Pyridine FeII Complexes.

A family of four-coordinate FeII 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-1. 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 (Ueff) of 27 cm-1 could be evidenced for one of them.