Spin-phonon coupling and magnetic relaxation in single-molecule magnets

Distortion Engineering: A Strategy to Modulate Molecular Upconversion with Molecular Cluster-Aggregates

The rational engineering of molecules is a powerful chemistry tool of pivotal importance in the fields of molecular magnetism and luminescence. Hence, systems that can be modulated via molecular engineering and composition control are expected to present extra versatility regarding the tunability of their properties. This is the case with molecular cluster aggregates (MCAs), high nuclearity molecular compounds. Herein, we demonstrate how the union of both strategies, namely, composition control and molecular engineering, can be employed to enhance molecular upconversion in MCAs. This was achieved by doping a {Gd8Er2Yb10} MCA with CeIII ions. By replacement of the optically silent GdIII ions with CeIII, the upconversion mechanism is modified due to CeIII-mediated cross-relaxation. In addition to this effect, we could also engineer the degree of metal site distortion due to the larger size of CeIII ions, relaxing the selection rules and impacting the upconversion quantum yield and luminescent thermometry. Opto-structural correlations demonstrate that the presented molecular engineering strategy can be used to enhance the performance of molecular upconverters.

Organolanthanide Single-Molecule Magnets with Heterocyclic Ligands

Lanthanide (Ln) based mononuclear single-molecule magnets (SMMs) provide probably the finest ligand regulation model for magnetic property. Recently, the development of such SMMs has witnessed a fast transition from coordination to organometallic complexes because the latter provides a fertile, yet not fully excavated soil for the development of SMMs. Especially those SMMs with heterocyclic ligands have shown the potential to reach higher blocking temperature. In this minireview, we give an overview of the design principle of SMMs and highlight those "shining stars" of heterocyclic organolanthanide SMMs based on the ring sizes of ligands, analysing how the electronic structures of those ligands and the stiffness of subsequently formed molecules affect the dynamic magnetism of SMMs. Finally, we envisaged the future development of heterocyclic Ln-SMMs.

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.

(η8-Cyclooctatetraene)(η5-fluorenyl)titanium: a processable molecular spin qubit with optimized control of the molecule-substrate interface

Depositing single paramagnetic molecules on surfaces for sensing and quantum computing applications requires subtle topological control. To overcome issues that are often encountered with sandwich metal complexes, we exploit here the low symmetry architecture and suitable vaporability of mixed-sandwich [FluTi(cot)], Flu = fluorenyl, cot = cyclooctatetraene, to drive submonolayer coverage and select an adsorption configuration that preserves the spin of molecules deposited on Au(111). Electron paramagnetic resonance spectroscopy and ab initio quantum computation evidence a d z 2 ground state that protects the spin from phonon-induced relaxation. Additionally, computed and measured spin coherence times exceed 10 μs despite the molecules being rich in hydrogen. A thorough submonolayer investigation by scanning tunneling microscopy, X-ray photoelectron and absorption spectrocopies and X-ray magnetic circular dichroism measurements supported by DFT calculations reveals that the most stable configuration, with the fluorenyl in contact with the metal surface, prevents titanium(iii) oxidation and spin delocalization to the surface. This is a necessary condition for single molecular spin qubit addressing on surfaces.

Record Quantum Tunneling Time in an Air-Stable Exchange-Bias Dysprosium Macrocycle

In recent years, dysprosium macrocycle single-molecule magnets (SMMs) have received increasing attention due to their excellent air/thermal stability, strong magnetic anisotropy, and rigid molecular skeleton. However, they usually display fast zero-field quantum tunneling of the magnetization (QTM) rate, severely hindering their data storage applications. Herein, we report the design, synthesis, and characterization of an air-stable monodecker didysprosium macrocycle integrating strong single-ion anisotropy, near-perfect local crystal field (CF) symmetry, and efficient exchange bias. These indispensable features enable clear-cut elucidation of the crucial role of very weak antiferromagnetic coupling on magnetization dynamics, creating a prominent SMM with a large effective energy barrier (Ueff) of 670 cm-1, open hysteresis loops at zero field up to 14.9 K, and a record relaxation time of QTM (τQTM), 24281 s, for all known nonradical-bridged lanthanide SMMs.

Auxiliary Rather Than Dominant. The Role of Direct Dy-S Coordination in Single-Molecule Magnet Unveiled via ab initio Study

The role of Dy-S coordination in a single-molecule magnet (SMM) is investigated via an ab initio study in a group of mononuclear structures. The SMM performance of this group is well interpreted via a concise criterion consisting of long quantum tunneling of magnetization (QTM) time τQTM and high effective barrier for magnetic reversal Ueff. The best SMMs in the selected group, i.e., 1Dy (CCDC refcode: PUKFAF) and 2Dy (CCDC refcode: NIKSEJ), are just those holding the longest τQTM and the highest Ueff simultaneously. Further analysis based on the crystal field model and ab initio magneto-structural exploration indicates that the influence of Dy-S coordination on the SMM performance of 1Dy is weaker than that of axial Dy-O coordination. Thus, Dy-S coordination is more likely to play an auxiliary role rather than a dominant one. However, if placed at the suitable equatorial position, Dy-S coordination could provide important support for good SMM performance. Consequently, starting from 1Dy, we built two new structures where Dy-S coordination only exists at the equatorial position and two axial positions are occupied by strong Dy-O/Dy-F coordination. Compared to 1Dy and 2Dy, these new ones are predicted to have significantly longer τQTM and higher Ueff, as well as a nearly doubled blocking temperature TB. Thus, they are probable candidates of SMM having clearly improved performance.

Intramolecular bridging strategies to suppress two-phonon Raman spin relaxation in dysprosocenium single-molecule magnets

Dy(III) bis-cyclopentadienyl (Cp) sandwich compounds exhibit extremely strong single-ion magnetic anisotropy which imbues them with magnetic memory effects such as magnetic hysteresis, and has put them at the forefront of high-performance single-molecule magnets (SMMs). Owing to the great success of design principles focused on maximising the anisotropy barrier, ever higher Ueff values have been reported leading to significant slow down of single-phonon Orbach spin relaxation. However, anisotropy-based SMM design has largely ignored two-phonon Raman spin relaxation, which is still limiting the temperatures at which a memory effect can be observed. In this work, we study the suppression of Raman relaxation through covalent bridging of the Cp ligands by alkyl chains, testing the hypothesis that increasing the rigidity of the ligand framework results in a blue shift of low frequency vibrations in the first coordination sphere of the Dy(III) ion. This reshaping of the vibrational low-energy density of states (DOS) results in lower occupation of pseudo-acoustic phonons available to drive Raman relaxation at low temperatures. We simulate Orbach and Raman spin relaxation in a series of zero-, mono-, di- and tri-bridged [Dy(Cpttt)2]+ analogues fully ab initio, using a quantum mechanics (QM)/molecular mechanics (MM) condensed phase embedding protocol in a periodic solvent matrix as a generic and experimentally testable environment model that can include (pseudo-)acoustic phononic degrees of freedom. We show that this approach can simulate magnetic relaxation dynamics in the condensed phase for the existing non-bridged [Dy(Cpttt)2]+ compound with quantitative experimental accuracy. Subsequently, we find a significant slowing down of Raman relaxation can be achieved for the singly-bridged SMM, while the introduction of further bridges leads to faster relaxation. A key result being that we find the two-phonon Raman rates correlate with the purity of the first-excited Kramers doublet in terms of its mJ = ±13/2 content. Even though the bridging design principle is successful at progressively reshaping the low-energy DOS, the introduction of linker atoms in the equatorial plane successively degrades magnetic anisotropy, suggesting the importance of refined design of the linker chemistry. The accuracy of our results emphasises the value of a generic periodic solvent embedding model, such that it permits the modelling of molecular spin dynamics in the condensed phase without knowledge of a crystal structure. This allows the study of hypothetical molecules or aggregates under real-world conditions, which we expect to have utility beyond the field of molecular magnetism.

Homoleptic Rare-Earth-Metal Sandwiches with Dibenzo[a,e]cyclooctatetraene Dianions

A family of rare-earth complexes [RE(III) = Y, La, Gd, Tb, Dy, and Er] with doubly reduced dibenzo[a,e]cyclooctatetraene (DBCOT) has been synthesized and structurally characterized. X-ray diffraction analysis confirms that all products of the [RE(DBCOT)(THF)4][RE(DBCOT)2] composition consist of the anionic sandwich [RE(DBCOT)2]- and the cationic counterpart [RE(DBCOT)(THF)4]+. Within the sandwich, two elongated π decks are slightly bent toward the metal center (avg. 7.3°) with a rotation angle of 35.9-37.6°. The RE(III) ion is entrapped between the central eight-membered rings of DBCOT2- in a η8 fashion. The trends in the RE-COT bond lengths are consistent with the variations of the ionic radii of RE(III) centers. The 1H NMR spectra of the diamagnetic Y(III) and La(III) analogues illustrate the distinct solution behavior for the cationic and anionic parts in this series. Magnetic measurements for the Dy analogue reveal single-molecule magnetism, which was rationalized by considering the effect of crystal-field splitting for both building units analyzed by electronic structure calculations.

Challenges for exploiting nanomagnet properties on surfaces

Molecular complexes with single-molecule magnet (SMM) or qubit properties, commonly called molecular nanomagnets, are great candidates for information storage or quantum information processing technologies. However, the implementation of molecular nanomagnets in devices for the above-mentioned applications requires controlled surface deposition and addressing the nanomagnets' properties on the surface. This Perspectives paper gives a brief overview of molecular properties on a surface relevant for magnetic molecules and how they are affected when the molecules interact with a surface; then, we focus on systems of increasing complexity, where the relevant SMMs and qubit properties have been observed for the molecules deposited on surfaces; finally, future perspectives, including possible ways of overcoming the problems encountered so far are discussed.

A novel non-adiabatic spin relaxation mechanism in molecular qubits

The interaction of electronic spin and molecular vibrations mediated by spin-orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin-vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin-vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin-vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.

Isolation of a Bent Dysprosium Bis(amide) Single-Molecule Magnet

The isolation of formally two-coordinate lanthanide (Ln) complexes is synthetically challenging, due to predominantly ionic Ln bonding regimes favoring high coordination numbers. In 2015, it was predicted that a near-linear dysprosium bis(amide) cation [Dy{N(SiiPr3)2}2]+ could provide a single-molecule magnet (SMM) with an energy barrier to magnetic reversal (Ueff) of up to 2600 K, a 3-fold increase of the record Ueff for a Dy SMM at the time; this work showed a potential route to SMMs that can provide high-density data storage at higher temperatures. However, synthetic routes to a Dy complex containing only two monodentate ligands have not previously been realized. Here, we report the synthesis of the target bent dysprosium bis(amide) complex, [Dy{N(SiiPr3)2}2][Al{OC(CF3)3}4] (1-Dy), together with the diamagnetic yttrium analogue. We find Ueff = 950 ± 30 K for 1-Dy, which is much lower than the predicted values for idealized linear two-coordinate Dy(III) cations. Ab initio calculations of the static electronic structure disagree with the experimentally determined height of the Ueff barrier, thus magnetic relaxation is faster than expected based on magnetic anisotropy alone. We propose that this is due to enhanced spin-phonon coupling arising from the flexibility of the Dy coordination sphere, in accord with ligand vibrations being of equal importance to magnetic anisotropy in the design of high-temperature SMMs.

Understanding Single-Molecule Magnet properties of lanthanide complexes from 4f orbital splitting

We present an approach for connecting the magnetic anisotropy of lanthanide mononuclear complexes with their f-orbital splitting for both idealized and real coordination environments. Our proposal is straightforward to apply and provides sensible estimations of the energy spacing of the ground multiplet for axial magnetic systems. This energy splitting controls Single-Molecule Magnet properties of lanthanide complexes, determining key parameters such as the demagnetization energy barrier (Ueff). Importantly, this approach is consistent with the current paradigm of oblate and prolate preferences for the distribution of the f-electron density, but delivers a finer description for ions belonging to the same group (e.g. the oblates TbIII and DyIII). The model provides simple explanations for some general trends observed experimentally (e.g. the low barriers for ErIII complexes in comparison to DyIII or the large barriers observed for cyclopentadienyl DyIII complexes in comparison with other ligands based on organometallic rings), contributing as a valuable tool to expand our description of ligand field effects in lanthanide-based SMMs.

Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets

Single-molecule magnets are among the most promising platforms for achieving molecular-scale data storage and processing. Their magnetisation dynamics are determined by the interplay between electronic and vibrational degrees of freedom, which can couple coherently, leading to complex vibronic dynamics. Building on an ab initio description of the electronic and vibrational Hamiltonians, we formulate a non-perturbative vibronic model of the low-energy magnetic degrees of freedom in monometallic single-molecule magnets. Describing their low-temperature magnetism in terms of magnetic polarons, we are able to quantify the vibronic contribution to the quantum tunnelling of the magnetisation, a process that is commonly assumed to be independent of spin-phonon coupling. We find that the formation of magnetic polarons lowers the tunnelling probability in both amorphous and crystalline systems by stabilising the low-lying spin states. This work, thus, shows that spin-phonon coupling subtly influences magnetic relaxation in single-molecule magnets even at extremely low temperatures where no vibrational excitations are present.

Assembly of dysprosium(III) cubanes in a metal-organic framework with an ecu topology and slow magnetic relaxation

A dysprosium(III) metal-organic framework constructed using dysprosium(III) cubanes as secondary building units has been reported to exhibit field-induced slow magnetic relaxation behavior and an unprecedented ecu topology, which is the first example of an 8-connected Ln-cubane-based framework material and a rare Dy4-MOF showing slow magnetic relaxation.

LnIII/MnII-LnIII complexes derived from a salicylic azo dye ligand: synthesis, structures, magnetic and fluorescence properties

Two LnIII complexes Ln(HTMSA)3(H2O)2·5.5H2O (Ln = Dy (1) and Tb (2), H2TMSA = 5-azotriazolyl-3-methoxysalicylaldehyde) and two MnII-LnIII clusters [Mn(H2O)6][MnLn2(TTMSA)4(HTTMSA)2(H2O)6]·4H2O (Ln = Dy (3) and Tb (4), H2TTMSA = 5-azotetrazolyl-3-methoxysalicylaldehyde) have been synthesized and structurally characterized. Single-crystal X-ray diffraction reveals that 1 and 2 are isostructural complexes in which the LnIII ions are surrounded by six oxygen atoms from three chelate HTMSA ligands and two oxygen atoms from two coordinated water molecules forming a distorted square-anti-prismatic geometry. In complexes 3 and 4, the MnII ions adjust two LnIII mononuclear anion clusters into tri-nuclear LnIII-MnII-LnIII anion clusters, with an additional [Mn(H2O)6]2+ as a counter ion to maintain the electroneutrality of the compound. Magnetic studies reveal that all the complexes 1-4 show nonzero out-of-phase signals, indicating single-molecule magnet behavior. The photoluminescence spectra of all the complexes were investigated and are discussed in detail.

Accurate and Efficient Spin-Phonon Coupling and Spin Dynamics Calculations for Molecular Solids

Molecular materials are poised to play a significant role in the development of future optoelectronic and quantum technologies. A crucial aspect of these areas is the role of spin-phonon coupling and how it facilitates energy transfer processes such as intersystem crossing, quantum decoherence, and magnetic relaxation. Thus, it is of significant interest to be able to accurately calculate the molecular spin-phonon coupling and spin dynamics in the condensed phase. Here, we demonstrate the maturity of ab initio methods for calculating spin-phonon coupling by performing a case study on a single-molecule magnet and showing quantitative agreement with the experiment, allowing us to explore the underlying origins of its spin dynamics. This feat is achieved by leveraging our recent developments in analytic spin-phonon coupling calculations in conjunction with a new method for including the infinite electrostatic potential in the calculations. Furthermore, we make the first ab initio determination of phonon lifetimes and line widths for a molecular magnet to prove that the commonplace Born-Markov assumption for the spin dynamics is valid, but such "exact" phonon line widths are not essential to obtain accurate magnetic relaxation rates. Calculations using this approach are facilitated by the open-source packages we have developed, enabling cost-effective and accurate spin-phonon coupling calculations on molecular solids.

Theoretical Magnetic Relaxation and Spin-Phonon Coupling Study in a Series of Molecular Engineering Designed Bridged Dysprosocenium Analogues

A detailed computational study of hypothetical sandwich dysprosium double-decker complexes, bridged by various numbers of aliphatic linkers, was performed to evaluate the effect of the structural modifications on their ground-state magnetic sublevels and assess their potential as candidates for single-molecule magnets (SMMs). The molecular structures of seven complexes were optimized using the TPSSh functional, and the electronic structure and magnetic properties were investigated using the complete active space self-consistent field method (CASSCF). Estimates of the magnetic moment blocking barrier (Ueff) and blocking temperatures (TB) are reported. In addition, a new method based on computed derivatives of effective demagnetization barriers Ueff with respect to vibrational normal modes was introduced and applied to evaluate the impact of spin-phonon coupling on the SMM properties. On the basis of the computed parameters, we have identified promising candidates with properties superior to those of the existing single-molecule magnets.

Molecular Network Approach to Anisotropic Ising Lattices: Parsing Magnetization Dynamics in Er3+ Systems with 0-3-Dimensional Spin Interactivity

We present a wide-ranging interrogation of the border between single-molecule and solid-state magnetism through a study of erbium-based Ising-type magnetic compounds with a fixed magnetic unit, using three different charge-balancing cations as the means to modulate the crystal packing environment. Properties rooted in the isolated spin Hamiltonian remain fixed, yet careful observation of the dynamics reveals the breakdown of this approximation in a number of interesting ways. First, differences in crystal packing lead to a striking 3 orders of magnitude suppression in magnetic relaxation rates, indicating a rich interplay between intermolecular interactions governed by the anisotropic Ising lattice stabilization and localized slow magnetic relaxation driven by the spin-forbidden nature of quantum tunneling of the f-electron-based magnetization. By means of diverse and rigorous physical methods, including temperature-dependent X-ray crystallography, field, temperature, and time-dependent magnetometry, and the application of a new magnetization fitting technique to quantify the magnetic susceptibility peakshape, we are able to construct a more nuanced view of the role nonzero-dimensional interactions can play in what are predominantly considered zero-dimensional magnetic materials. Specifically, we use low field susceptibility and virgin-curve analysis to isolate metamagnetic spin-flip transitions in each system with a field strength corresponding to the expected strength of the internal dipole-dipole lattice. This behavior is vital to a complete interpretation of the dynamics and is likely common for systems with such high anisotropy. This collective interactivity opens a new realm of possibility for molecular magnetic materials, where their unprecedented localized anisotropy is the determining factor in building higher dimensionality.

T1 Anisotropy Elucidates Spin Relaxation Mechanisms in an S = 1 Cr(IV) Optically Addressable Molecular Qubit

Paramagnetic molecules offer unique advantages for quantum information science owing to their spatial compactness, synthetic tunability, room-temperature quantum coherence, and potential for optical state initialization and readout. However, current optically addressable molecular qubits are hampered by rapid spin-lattice relaxation (T1) even at sub-liquid nitrogen temperatures. Here, we use temperature- and orientation-dependent pulsed electron paramagnetic resonance (EPR) to elucidate the negative sign of the ground state zero-field splitting (ZFS) and assign T1 anisotropy to specific types of motion in an optically addressable S = 1 Cr(o-tolyl)4 molecular qubit. The anisotropy displays a distinct sin2(2θ) functional form that is not observed in S = 1/2 Cu(acac)2 or other Cu(II)/V(IV) microwave addressable molecular qubits. The Cr(o-tolyl)4 T1 anisotropy is ascribed to couplings between electron spins and rotational motion in low-energy acoustic or pseudoacoustic phonons. Our findings suggest that rotational degrees of freedom should be suppressed to maximize the coherence temperature of optically addressable qubits.