Antisymmetric Exchange in a Real Copper Triangular Complex

Abstract

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.

The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes

“…In the absence local orbital momentum, the model multispin Hamiltonian expression reads: 33,36,69 where a and b label the two magnetic centers, Ŝ a and Ŝ b are spin operators, J is the Heisenberg exchange magnetic coupling, are rank-2 tensors describing the local anisotropies, is a rank-2 tensor describing the symmetric anisotropic exchange, and d̄ is a pseudovector describing the antisymmetric component of the anisotropic exchange. In centrosymmetric complexes, the latter term of eqn (1), also referred to as the Dzyaloshinskii–Moriya interaction (DMI), 70–75 vanishes, and otherwise, may be less important than the other terms unless specific situations are encountered (exotic coordination environment and/or orbital near-degeneracy). In fact, this work does not specifically focus in the DMI, which will be later justified by comparing Ĥ eff and Ĥ MS .…”

Spin Frustrated Pyrazolato Triangular CuII Complex: Structure and Magnetic Properties, an Overview

“…The antisymmetric vector is considered equal for each pair (G 12 = G 23 = G 31 = G) and only the z-component is assumed to be non-zero (G x = G y = 0) [18,19]. It is important to remark that the antisymmetric exchange can be affected by the distortions of the triangular structure [46][47][48]. Thus, based on the structural arrangement of the Cu II triangles, we have used a model with two isotropic exchange interactions (J 1 and J 2 ) for an isosceles triangle and an antisymmetric exchange, using the Hamiltonian equation shown below:…”

Voltage-induced modulation of the magnetic exchange in binuclear Fe(iii) complex deposited on Au(111) surface

“…To address this challenge, we performed a rigorous computational study focused on the deposition of a binuclear magnetic complex over a metallic surface. Although isolated polynuclear magnetic molecules have been extensively studied through sophisticated wave function based methods (WFT), [36][37][38][39][40] this is no longer possible once they are deposited on a substrate due to the extensive size of the systems. In this sense, we employed Density Functional Theory (DFT) based methods, widely used to determine the magnetic properties of metallic complexes interacting with different substrates, [41][42][43][44][45][46] and even their transport properties in single molecule junctions architectures.…”