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

Abstract

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".

Antisymmetric Exchange in a Real Copper Triangular Complex

“…The general expression of H ̂ MS (coupled) is available elsewhere. , In this 4 × 4 matrix, J ab discriminates the diagonal elements of the triplet components from that of the singlet. The axial parameter D potentially affects differently the diagonal elements of all components (singlet and triplet) in the magnetic axes frame, while the rhombic E parameter couples the M S = ±1 components and d ab couples the components of the triplet with the singlet, e.g.…”

“…The extraction of both GS and MS Hamiltonians parameters from the effective Hamiltonian theory has been practiced many times and has proven to be particularly efficient for binuclear complexes. The validity of the MS model for two S = 1/2 spins has already been demonstrated by comparing the analytical and numerical matrices, and all parameters J , D , and | d z | could easily be extracted. , We will therefore not further detail the procedure here.…”

“…also affect these energies. Two recent papers , were dedicated to the identification of the main chemical ingredients that govern both the magnitude and orientation of the DMI through analytical derivations and ab initio calculations. An analytical formula was proposed that reproduces very well the magnitude of the DMI components far from the first-order SOC regime.…”

“…An analytical formula was proposed that reproduces very well the magnitude of the DMI components far from the first-order SOC regime. One important conclusion of ref was that an efficient way to increase the DMI is to approach the first-order SOC regime, i.e. , to design complexes where some on-site d orbitals are almost degenerate.…”

Antisymmetric Spin Exchange in a μ-1,2-Peroxodicopper(II) Complex with an Orthogonal Cu–O–O–Cu Arrangement and S = 1 Spin Ground State Characterized by THz-EPR

“…Antisymmetric or Dzyaloshinskii–Moriya (DM) exchange results from the concerted action of single-ion spin–orbit coupling (SOC) and exchange coupling between ground and excited states of different paramagnetic ions in a noninversion-symmetric environment. 17 − 19 …”