1
|
Heully-Alary F, Pradines B, Suaud N, Guihéry N. Physical origin of the anisotropic exchange tensor close to the first-order spin-orbit coupling regime and impact of the electric field on its magnitude. J Chem Phys 2024; 161:054310. [PMID: 39105550 DOI: 10.1063/5.0218707] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2024] [Accepted: 07/18/2024] [Indexed: 08/07/2024] Open
Abstract
This article follows earlier studies on the physical origin of magnetic anisotropy and the means of controlling it in polynuclear transition metal complexes. The difficulties encountered when focusing a magnetic field on a molecular object have led to consider the electric field as a more appropriate control tool. It is therefore fundamental to understand what governs the sensitivity of magnetic properties to the application of an electric field. We have already studied the impact of the electric field on the isotropic exchange coupling and on the Dzyaloshinskii-Moriya interaction (DMI). Here, we focus on the symmetric exchange anisotropy tensor. In order to obtain significant values of anisotropic interactions, we have carried out this study on a model complex that exhibits first-order spin-orbit coupling. We will show that (i) large values of the axial parameter of symmetric exchange can be reached when close to the first-order spin-orbit coupling regime, (ii) both correlated energies and wave functions must be used to achieve accurate values of the symmetric tensor components when the DMI is non-zero, and (iii) finally, an interferential effect between the DMI and the axial parameter of symmetric exchange occurs for a certain orientation of the electric field, i.e., the latter decreases in magnitude as the former increases. While DMI is often invoked as being involved in magneto-electric coupling, isotropic exchange and the symmetrical anisotropic tensor also contribute. Finally, we provide a recipe for generating significant anisotropic interactions and a significant change in magnetic properties under an electric field.
Collapse
Affiliation(s)
- Flaurent Heully-Alary
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France
| | - Barthélémy Pradines
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France
| | - Nicolas Suaud
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France
| | - Nathalie Guihéry
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse, France
| |
Collapse
|
2
|
Sergentu DC, Le Guennic B, Maurice R. The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes. Phys Chem Chem Phys 2024; 26:6844-6861. [PMID: 38328993 DOI: 10.1039/d3cp04943d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/09/2024]
Abstract
The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of magnitude or smaller than the various anisotropic terms, which generates a complex set of levels characterized by spin mixing. Although the model multispin Hamiltonian in the absence of local orbital momentum, , is considered good enough to map the experimental energies at zero field and in the strong-exchange limit, theoretical works pointed out limitations of this simple model. This work revives the use of ĤMS from a new theoretical perspective, detailing point-by-point a strategy to correctly map the computational energies and wave functions onto ĤMS, thus validating it regardless of the exchange limit. We will distinguish two cases, based on experimentally characterized dicobalt(II) complexes from the literature. If centrosymmetry imposes alignment of the various rank-2 tensors constitutive of ĤMS in the first case, the absence of any symmetry element prevents such alignment in the second case. In such a context, the strategy provided herein becomes a powerful tool to rationalize the experimental magnetic data, since it is capable of fully and rigorously extracting the multispin model without any assumption on the orientation of its constitutive tensors. Furthermore, the strategy allows to question the use of the spin Hamiltonian approach by explicitly controlling the projection norms on the model space, which is showcased in the second complex where local orbital momentum could have occurred (distorted octahedra). Finally, previous theoretical data related to a known dinickel(II) complex is reinterpreted, clarifying initial wanderings regarding the weak exchange limit.
Collapse
Affiliation(s)
- Dumitru-Claudiu Sergentu
- Univ Rennes, CNRS ISCR (Institut des Sciences Chimiques de Rennes) - UMR 6226, 35000 Rennes, France.
- Laboratorul RA-03 (RECENT AIR), Universitatea Alexandru Ioan Cuza din Iaşi, 700506 Iaşi, Romania
- Facultatea de Chimie, Universitatea Alexandru Ioan Cuza din Iaşi, 700506 Iaşi, Romania
| | - Boris Le Guennic
- Univ Rennes, CNRS ISCR (Institut des Sciences Chimiques de Rennes) - UMR 6226, 35000 Rennes, France.
| | - Rémi Maurice
- Univ Rennes, CNRS ISCR (Institut des Sciences Chimiques de Rennes) - UMR 6226, 35000 Rennes, France.
| |
Collapse
|
3
|
Maurice R, Mallah T, Guihéry N. Magnetism in Binuclear Compounds: Theoretical Insights. TOP ORGANOMETAL CHEM 2023. [DOI: 10.1007/3418_2022_78] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
|
4
|
Pradines B, Cahier B, Suaud N, Guihéry N. Impact of the electric field on isotropic and anisotropic spin Hamiltonian parameters. J Chem Phys 2022; 157:204308. [DOI: 10.1063/5.0116709] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
One may obviously think that the best way to control magnetic properties relies on using a magnetic field. However, it is not convenient to focus a magnetic field on a small object, whereas it is much easier to do so with an electric field. Magnetoelectric coupling allows one to control the magnetization with the electric field and the polarization with the magnetic field and could therefore provide a solution to this problem. This paper aims at quantifying the impact of the electric field on both the isotropic magnetic exchange and the Dzyaloshinskii–Moriya interaction in the case of a binuclear system of S = 1/2 spins. This study follows previous studies that showed that very high Dzyaloshinskii–Moriya interaction, i.e., the antisymmetric exchange, can be generated when close to first order spin orbit coupling. We will, therefore, explore this regime in a model Cu(II) complex that exhibits a quasi-degeneracy of the [Formula: see text] and d xy orbitals. This situation is indeed the one that allows us to obtain the largest spin orbit couplings in transition metal complexes. We will show that both the magnetic exchange and the Dzyaloshinskii–Moriya interaction are very sensitive to the electric field and that it would therefore be possible to modulate and control magnetic properties by the electric field. Finally, rationalizations of the obtained results will be proposed.
Collapse
Affiliation(s)
- Barthélémy Pradines
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Benjamin Cahier
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Nicolas Suaud
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Nathalie Guihéry
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| |
Collapse
|
5
|
Lunghi A, Sanvito S. Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations. Nat Rev Chem 2022; 6:761-781. [PMID: 37118096 DOI: 10.1038/s41570-022-00424-3] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 08/15/2022] [Indexed: 11/09/2022]
Abstract
Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.
Collapse
|
6
|
Bouammali MA, Suaud N, Guihéry N, Maurice R. Antisymmetric Exchange in a Real Copper Triangular Complex. Inorg Chem 2022; 61:12138-12148. [PMID: 35895313 DOI: 10.1021/acs.inorgchem.2c00939] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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.
Collapse
Affiliation(s)
- Mohammed-Amine Bouammali
- Laboratoire de Chimie et Physique Quantiques, UMR5626, Université de Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Nicolas Suaud
- Laboratoire de Chimie et Physique Quantiques, UMR5626, Université de Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Nathalie Guihéry
- Laboratoire de Chimie et Physique Quantiques, UMR5626, Université de Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Rémi Maurice
- SUBATECH, UMR CNRS 6457, IN2P3/IMT Atlantique/Université de Nantes, 4 rue Alfred Kastler, BP 20722, 44307 Nantes Cedex 3, France.,Univ Rennes, CNRS, ISCR (Institut des Sciences Chimiques de Rennes)─UMR 6226, 35000 Rennes, France
| |
Collapse
|
7
|
Lohmiller T, Spyra CJ, Dechert S, Demeshko S, Bill E, Schnegg A, Meyer F. 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. JACS AU 2022; 2:1134-1143. [PMID: 35647586 PMCID: PMC9131480 DOI: 10.1021/jacsau.2c00139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Revised: 04/08/2022] [Accepted: 04/11/2022] [Indexed: 06/15/2023]
Abstract
A unique type of Cu2/O2 adduct with orthogonal (close to 90°) Cu-O-O-Cu arrangement has been proposed for initial stages of O2 binding at biological type III dicopper sites, and targeted ligand design has now allowed us to emulate such an adduct in a pyrazolate-based μ-η1 :η1-peroxodicopper(II) complex (2) with Cu-O-O-Cu torsion φ of 87°, coined ⊥ P intermediate. Full characterization of 2, including X-ray diffraction (d O-O = 1.452 Å) and Raman spectroscopy (ν̃O-O = 807 cm-1), completes a series of closely related Cu2/O2 intermediates featuring μ-η1 :η1-peroxodicopper(II) cores with φ ranging from 55° (A, cis-peroxo C P; Brinkmeier A.et al., J. Am. Chem. Soc.2021, 143, 10361) via 87° (2, ⊥ P type) up to 104° (B, approaching trans-peroxo T P; Kindermann N.et al., Angew. Chem., Int. Ed.2015, 54, 1738). SQUID magnetometry revealed ferromagnetic interaction of the CuII ions and a triplet (S t = 1) ground state in 2. Frequency-domain THz-EPR has been employed to quantitatively investigate the spin systems of 2 and B. Magnetic transitions within the triplet ground states confirmed their substantial zero-field splittings (ZFS) suggested by magnetometry. Formally forbidden triplet-to-singlet transitions at 56 (2) and 157 cm-1 (B), which are in agreement with the exchange coupling strengths J iso inferred from SQUID data, are reported for the first time for coupled dicopper(II) complexes. Rigorous analysis by spin-Hamiltonian-based simulations attributed the corresponding nonzero transition probabilities and the ZFS to substantial antisymmetric (Dzyaloshinskii-Moriya) exchange d and provided robust values and orientations for the d , J , and g tensors. These interactions can be correlated with the Cu-O-O-Cu geometries, revealing a linear increase of J iso with the Cu-O-O-Cu torsion and a strong linear decrease with the Cu-O-O angle. Relevance of the ⊥ P intermediate for O2 activation at type III dicopper sites and a potential role of antisymmetric exchange in the concomitant intersystem crossing are proposed.
Collapse
Affiliation(s)
- Thomas Lohmiller
- EPR4Energy
Joint Lab, Department Spins in Energy Conversion and Quantum Information
Science, Helmholtz Zentrum Berlin für
Materialien und Energie GmbH, Albert-Einstein-Straße 16, 12489 Berlin, Germany
| | - Can-Jerome Spyra
- University
of Göttingen, Institute of Inorganic Chemistry, Tamannstrasse 4, D-37077 Göttingen, Germany
| | - Sebastian Dechert
- University
of Göttingen, Institute of Inorganic Chemistry, Tamannstrasse 4, D-37077 Göttingen, Germany
| | - Serhiy Demeshko
- University
of Göttingen, Institute of Inorganic Chemistry, Tamannstrasse 4, D-37077 Göttingen, Germany
| | - Eckhard Bill
- Max
Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470 Mülheim an der
Ruhr, Germany
| | - Alexander Schnegg
- Max
Planck Institute for Chemical Energy Conversion, Stiftstrasse 34-36, D-45470 Mülheim an der
Ruhr, Germany
| | - Franc Meyer
- University
of Göttingen, Institute of Inorganic Chemistry, Tamannstrasse 4, D-37077 Göttingen, Germany
- University
of Göttingen, International Center for Advanced Studies of
Energy Conversion (ICASEC), D-37077 Göttingen, Germany
| |
Collapse
|
8
|
Bouammali MA, Suaud N, Maurice R, Guihéry N. Extraction of giant Dzyaloshinskii-Moriya interaction from ab initio calculations: First-order spin-orbit coupling model and methodological study. J Chem Phys 2021; 155:164305. [PMID: 34717350 DOI: 10.1063/5.0065213] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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.
Collapse
Affiliation(s)
- Mohammed-Amine Bouammali
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Nicolas Suaud
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| | - Rémi Maurice
- Subatech, UMR CNRS 6457, IN2P3/IMT Atlantique/University of Nantes, 4 rue A. Kastler, 44307 Nantes Cedex 3, France
| | - Nathalie Guihéry
- Laboratoire de Chimie et Physique Quantiques, UMR5626, University of Toulouse 3, Paul Sabatier, 18 route de Narbonne, 31062 Toulouse, France
| |
Collapse
|