Spin-Phonon Coupling and Slow-Magnetic Relaxation in Pristine Ferrocenium

Synergy of Experiment and Broadened Exploration of Ab Initio Calculations for Understanding of Lanthanide-Pentacyanidocobaltate Molecular Nanomagnets and Their Optical Properties

We present a synergistic experimental-theoretical methodology for the investigation of lanthanide-based single-molecule magnets (SMMs), demonstrated using the example of novel heterometallic molecules incorporating Nd3+/Ce3+ ions combined with three different, rarely explored, pentacyanidocobaltate(III) metalloligands, [CoIII(CN)5(azido/nitrito-N/iodido)]3-. The theoretical part of our approach broadens the exploration of ab initio calculations for lanthanide(III) complexes toward the convenient simulations of such physical characteristics as directional dependences of Helmholtz energy, magnetization, susceptibility, and their thermal and field evolution, as well as light absorption and emission bands. This work was conducted using newly designed SlothPy software (https://slothpy.org). It is introduced as an open-source Python library for simulating various physical properties from first-principles based on results of electronic structure calculations obtained within popular quantum chemistry packages. The computational results were confronted with spectroscopic and ac/dc-magnetic data, the latter analyzed using previously designed relACs software. The combination of experimental and computational methods gave insight into phonon-assisted magnetic relaxation mechanisms, disentangling them from the temperature-independent quantum tunneling of magnetization and emphasizing the role of local-mode processes. This study provides an understanding of the changes in lanthanide(III) magnetic anisotropy introduced with pentacyanidocobaltates(III) modifications, theoretically exploring also potential applications of reported compounds as anisotropy switches or optical thermometers.

Unravelling the role of spin-vibrational coupling in designing high-performance pentagonal bipyramidal Dy(iii) single ion magnets

At the cutting edge of high-performance single-molecule magnets (SMMs) lie lanthanide-based complexes, renowned for their potent magnetic anisotropy. SMMs containing one metal centre are defined as single-ion magnets (SIMs). The performance of SMMs is measured generally via the barrier height for magnetisation reversal (Ueff) and blocking temperature (TB), below which the magnetisation is fully frozen. To enhance the Ueff and TB values in lanthanide-based SMMs, the static crystal field splitting of mJ levels has been effectively adjusted through ligand design, leveraging the oblate/prolate ground state 4f electron density shape. However, the maximum fine-tuning achievable through ligand design, known as the axial limit, has already been reached in this class of compounds. This necessitates new design principles to enhance SMM characteristics to better suit end-user applications. Among other avenues that can be explored to improve SMM characteristics, a deeper understanding of spin-phonon coupling is critical to advancing TB values. However, there are only a handful of examples where this has been deciphered. In this work, using a combination of DFT and ab initio CASSCF calculations, we have performed spin-phonon calculations on five classes of pentagonal bipyramidal Dy(iii) SIMs exhibiting TB values in the range of 4.5 K to 36 K ([Dy(bbpen)Br] (1, H2bbpen = N,N'-bis(2-hydroxybenzyl)-N,N'-bis(2-methylpyridyl)ethylenediamine), [Dy(OCMe3)Br(THF)5][BPh4] (2) [Dy(OSiMe3)Br(THF)5] [BPh4] (3), [Dy(LN5)(Ph3SiO)2](BPh4)·CH2Cl2 (4) and [L2Dy(H2O)5][I]3·L2·H2O (5, L = tBuPO(NHiPr)2)). Unlike the method employed elsewhere for the calculation of spin-phonon coupling, in this work, we have employed a set of criteria and intuitively selected vibrational modes to perform the spin-phonon coupling analysis. The approach provided here not only reduces the computational cost significantly but also suggests chemical intuition to improve the performance of this class of compounds. Our calculations reveal that low-energy vibrational modes govern the magnetisation relaxation in these SIMs. A flexible first coordination sphere found on some of the complexes was found to be responsible for low-energy vibrations that flip the magnetisation, reducing the TB values drastically (complexes 2 and 3). On the other hand, a rigid first coordination sphere and a stiff ligand framework move the spin-vibrational coupling that causes the relaxation to lie beyond the secondary coordination sphere, resulting in an increase in TB values. Our calculations also reveal that not only the atoms in the first coordination sphere but also those in the secondary coordination sphere affect the performance of the SMMs. Learning from this exercise, we have undertaken several in silico models based on these vibrations to improve the TB values. Some of these predictions were correlated with literature precedents, offering confidence in the methodology employed. To this end, our comprehensive investigation, involving twenty-three molecules/models and five sets of geometries for pentagonal bipyramidal Dy(iii) single-ion magnets (SIMs), unveils a treasure trove of chemically sound design clues, poised to enhance the TB values in this fascinating molecular realm.

Dual Structure of a Vanadyl-Based Molecular Qubit Containing a Bis(β-diketonato) Ligand

We designed [VO(bdhb)] (1') as a new electronic qubit containing an oxovanadium(IV) ion (S = 1/2) embraced by a single bis(β-diketonato) ligand [H2bdhb = 1,3-bis(3,5-dioxo-1-hexyl)benzene]. The synthesis afforded three different crystal phases, all of which unexpectedly contain dimers with formula [(VO)2(bdhb)2] (1). A trigonal form (1h) with a honeycomb structure and 46% of solvent-accessible voids quantitatively transforms over time into a monoclinic solvatomorph 1m and minor amounts of a triclinic solventless phase (1a). In a static magnetic field, 1h and 1m have detectably slow magnetic relaxation at low temperatures through quantum tunneling and Raman mechanisms. Angle-resolved electron paramagnetic resonance (EPR) spectra on single crystals revealed signatures of low-dimensional magnetic behavior, which is solvatomorph-dependent, being the closest interdimer V···V separations (6.7-7.5 Å) much shorter than intramolecular V···V distances (11.9-12.1 Å). According to 1H diffusion ordered spectroscopy (DOSY) and EPR experiments, the complex adopts the desired monomeric structure in organic solution and its geometry was inferred from density functional theory (DFT) calculations. Spin relaxation measurements in a frozen toluene-d8/CD2Cl2 matrix yielded Tm values reaching 13 μs at 10 K, and coherent spin manipulations were demonstrated by Rabi nutation experiments at 70 K. The neutral quasi-macrocyclic structure, featuring nuclear spin-free donors and additional possibilities for chemical functionalization, makes 1' a new convenient spin-coherent building block in quantum technologies.

Unravelling the Highest Magnetic Anisotropy Among all the n-Shells in 20 Metallocene

Single-molecule magnets (SMMs) with a large magnetization reversal barrier are predominated by the lanthanide systems due to their strong spin-orbit coupling (SOC). However, the transition metals have also emerged as potential contenders and the largest magnetic anisotropy has been identified for a cobalt system among any d-series-based SMMs (Bunting et al. Science 2018, 362, eaat7319). In this work, we have explored the magnetic anisotropy in highly axial ligand field systems of metallocene, having different d-subshell (3d4, 4d4, and 5d4). The wave function-based multireference methods including static and dynamic electron correlations have been employed to investigate the zero-field splitting (ZFS) parameters. Here, we report exceptionally large magnetic anisotropy for a 5d complex of [WCp2]0 with the highest energy barrier that is nearly twice as high as the previous record value for the Co complex. We have also observed that the axial ZFS parameter (D) is increasing down the group in the order of 3d < 4d < 5d, pertaining to a large SOC.

Increasing the Magnetic Blocking Temperature of Single-Molecule Magnets

The synthesis of single-molecule magnets (SMMs), magnetic complexes capable of retaining magnetization blocking for a long time at elevated temperatures, has been a major concern for magnetochemists over the last three decades. In this review, we describe basic SMMs and the different approaches that allow high magnetization-blocking temperatures to be reached. We focus on the basic factors affecting magnetization blocking, magnetic axiality and the height of the blocking barrier, which can be used to group different families of complexes in terms of their SMM efficiency. Finally, we discuss several practical routes for the design of mono- and polynuclear complexes that could be applied in memory devices.

A trivalent 4f complex with two bis-silylamide ligands displaying slow magnetic relaxation

The best-performing single-molecule magnets (SMMs) have historically relied on pseudoaxial ligands delocalized across several coordinated atoms. This coordination environment has been found to elicit strong magnetic anisotropy, but lanthanide-based SMMs with low coordination numbers have remained synthetically elusive species. Here we report a cationic 4f complex bearing only two bis-silylamide ligands, Yb(III)[{N(SiMePh₂)₂}₂][Al{OC(CF₃)₃}₄], which exhibits slow relaxation of its magnetization. The combination of the bulky silylamide ligands and weakly coordinating [Al{OC(CF₃)₃}₄]^- anion provides a sterically hindered environment that suitably stabilizes the pseudotrigonal geometry necessary to elicit strong ground-state magnetic anisotropy. The resolution of the m_J states by luminescence spectroscopy is supported by ab initio calculations, which show a large ground-state splitting of approximately 1,850 cm^-1. These results provide a facile route to access a bis-silylamido Yb(III) complex, and further underline the desirability of axially coordinated ligands with well-localized charges for high-performing SMMs.

Single-Molecule Magnetism in Linear Fe(I) Complexes with Aufbau and Non-Aufbau Ground States

With the ongoing efforts on synthesizing mononuclear single-ion magnets (SIMs) with promising applications in high-density data storage and spintronics devices, the linear or quasi-linear Fe(I) complexes emerge as the enticing candidates possessing large unquenched angular momentum. Herein, we have studied five experimentally synthesized linear Fe(I) complexes to uncover the origin of single-molecule magnetic behavior of these complexes. To begin with, we benchmarked the methodology on the experimentally and theoretically well-studied complex [Fe(C(SiMe₃)₃)₂]^-1 (1) (SiMe₃ = trimethylsilyl), which is characterized with a large spin-reversal barrier of 226 cm^-1. Subsequently, the spin-phonon coupling coefficients are calculated for the low-frequency vibrational modes to understand the relaxation mechanism of the complex. Furthermore, the two Fe(I) complexes, that is, [Fe(cyIDep)₂]⁺¹ (2) (cyIDep = 1,3-bis(2',6'-diethylphenyl)-4,5-(CH₂)₄-imidazole-2-ylidene) and [Fe(sIDep)₂]⁺¹ (3) (sIDep = 1,3-bis(2',6'-diethylphenyl)-imidazolin-2-ylidene), are studied that are experimentally reported with no SIM behavior under ac or dc magnetic fields; however, they exhibit large opposite axial zero field splitting (-62.4 and +34.0 cm^-1, respectively) from ab initio calculations. We have unwrapped the origin of this contrasting observation between experiment and theory by probing their magnetic relaxation pathways and the pattern of d orbital splitting. Additionally, the two experimentally synthesized Fe(I) complexes, that is, [(η⁶-C₆H₆)FeAr*-3,5-Pr₂ⁱ] (4) (Ar*-3,5-Pr₂ⁱ = C₆H-2,6-(C₆H₂-2,4,6-Pr₃ⁱ)₂-3,5-Pr₂ⁱ) and [(CAAC)₂Fe]⁺¹ (5) (CAAC = cyclic (alkyl) (amino)carbene), are investigated for SIM behavior, since there is no report on their magnetic anisotropy. To this end, complex 4 presents itself as the possible candidate for SIM.

Harnessing Colossal Magnetic Anisotropy in Sandwiched 3d2-Metallocenes

Single-molecule magnets are gaining attention in recent years with the growing focus on achieving higher barriers of magnetization reversal. Metallocenes, owing to their unique sandwiched structure, assure themselves as plausible molecular systems for the development of novel single-molecule magnets (SMMs). Here in this work, we have explicitly investigated metallocenes of first-row transition elements, along with their one-electron-oxidized (cationic) and -reduced (anionic) analogues, for their magnetic anisotropies by adopting multireference ab initio calculations. Herein, we report a high magnetic anisotropy for 3d² systems among all 3d-metallocenes.

Solid polymorphism and dynamic magnetic properties of a dodecylated vanadyl–porphyrinato complex: spin–lattice relaxations modulated by phase stabilisation

Phase stabilisation elongates spin–lattice relaxation times.