A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound

High-Frequency EPR Studies of New 2p-3d Complexes Based on a Triazolyl-Substituted Nitronyl Nitroxide Radical: The Role of Exchange Anisotropy in a Cu-Radical System

Using the 1-(m-tolyl)-1H-1,2,3-triazole-4-(4,4,5,5-tetramethylimidazoline-1-oxyl-3-oxide) (TlTrzNIT) radical and metal β-diketonate complexes [M(hfac)₂(H₂O)₂], where hfac is hexafluoroacetylacetonato, three new 2p-3d heterospin complexes were synthesized. Their structures were solved using single crystal X-ray diffraction data, and magnetic investigation was performed by DC and AC measurements and multifrequency EPR spectroscopy. Compounds 1 and 2 are isostructural complexes with molecular formula [M₃(TlTrzNIT)₂(hfac)₆] (M^II = Mn or Cu) while compound 3 is the mononuclear [Co(TlTrzNIT)(hfac)₂] complex. In all complexes, the radical acts as a bidentate ligand through the oxygen atom of the nitroxide moiety and the nitrogen atom from the triazole group. Furthermore, in compounds 1 and 2, the TlTrzNIT is bridge-coordinated between two metal centers, leading to the formation of trinuclear complexes. The fitting of the static magnetic behavior reveals antiferromagnetic and ferromagnetic intramolecular interactions for complexes 1 and 2, respectively. The EPR spectra of 1 are well described by an isolated ferrimagnetic S = ¹³/₂ (= ⁵/₂ - ¹/₂ + ⁵/₂ - ¹/₂ + ⁵/₂) ground state with a biaxial zero-field splitting (ZFS) interaction characterized, respectively, by 2nd order axial and rhombic parameters, D and E, such that E/D is close to the maximum of 0.33. Meanwhile, EPR spectra for 2 are explained in terms of a ferromagnetic model with weakly anisotropic Cu-radical exchange interactions, giving rise to an isolated S = ⁵/₂ (= 5 × ¹/₂) ground state with both an anisotropic g tensor and a weak ZFS interaction. Complex 2 represents one of only a few examples of Cu-radical moieties with measurable exchange anisotropy.

Strong Relativistic Effects in Lanthanide-Based Single-Molecule Magnets

Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the nonrelativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO]+ molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the M J states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlation. We demonstrate that this interplay affects the resonances between the spin and vibrational transitions and, therefore, the spin relaxation time.

Ligand Fluorination to Mitigate the Raman Relaxation of DyIII Single-Molecule Magnets: A Combined Terahertz, Far-IR and Vibronic Barrier Model Study

The fast Raman relaxation process via a virtual energy level has become a puzzle for how to chemically engineer single-molecule magnets (SMMs) with better performance. Here, we use the trifluoromethyl group to systematically substitute the methyl groups in the axial position of the parent bis-butoxide pentapyridyl dysprosium(III) SMM. The resulting complexes-[Dy(OL^A )₂ py₅ ][BPh₄ ] (L^A =CH(CF₃ )₂ ^- 1, CH₂ CF₃ ^- 2, CMe₂ CF₃ ^- 3)-show progressively enhanced T_B ^hys (@100 Oe s^-1 ) from 17 K (for 3), 20 K (for 2) to 23 K (for 1). By experimentally identifying the varied under barrier relaxation energy in the 5-500 cm^-1 regime, we are able to identify that the C-F bond related vibration energy of the axial ligand ranging from 200 to 350 cm^-1 is the key variant for this improvement. Thus, this finding not only reveals a correlation between the structure and the Raman process but also provides a paradigm for how to apply the vibronic barrier model to analyze multi-phonon relaxation processes in lanthanide SMMs.

Dinuclear Fluoride Single-Bridged Lanthanoid Complexes as Molecule Magnets: Unprecedented Coupling Constant in a Fluoride-Bridged Gadolinium Compound

A new synthetic method allows isolating fluoride-bridged complexes Bu₄N{[M(3NO₂,5Br-H₃L^1,1,4)]₂(μ-F)} (M = Dy, 1; M = Ho, 2; M = Gd, 3) and Bu₄N{[Dy(3Br,5Cl-H₃L^1,2,4)]₂(μ-F)}·2H₂O, 4·2H₂O. The crystal structures of 1·5CH₃C₆H₅,·2·2H₂O·0.75THF, 3, and 4·2H₂O·2THF show that all of them are dinuclear compounds with linear single fluoride bridges and octacoordinated metal centers. Magnetic susceptibility measurements in the temperature range of 2–300 K reveal that the Gd^III ions in 3 are weakly antiferromagnetically coupled, and this constitutes the first crystallographically and magnetically analyzed gadolinium complex with a fluoride bridge. Variable-temperature magnetization demonstrates a poor magnetocaloric effect for 3. Alternating current magnetic measurements for 1, 2, and 4·2H₂O bring to light that 4·2H₂O is an SMM, 1 shows an SMM-like behavior under a magnetic field of 600 Oe, while 2 does not show relaxation of the magnetization even under an applied magnetic field. In spite of this, 2 is the first fluoride-bridged holmium complex magnetically analyzed. DFT and ab initio calculations support the experimental magnetic results and show that apparently small structural differences between 1 and 4·2H₂O introduce important changes in the dipolar interactions, from antiferromagnetic in 1 to ferromagnetic in 4·2H₂O.

Dinuclear linear fluoride single-bridged Dy^III, Ho^III, and Gd^III complexes are systematically obtained from mononuclear aquo-complexes, with the Dy^III ones showing slow relaxation of the magnetization and the Gd^III one revealing a weak AF coupling through the Gd−F−Gd bridge.

Importance of an Axial LnIII-F Bond across the Lanthanide Series and Single-Molecule Magnet Behavior in the Ce and Nd Analogues

The recently reported compound [Dy^IIILF](CF₃SO₃)₂·H₂O (L = 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraaza-cyclododecane) displays a strong axial magnetic anisotropy, due to the short axial Dy–F bond, and single-molecule magnet (SMM) behavior. Following our earlier [Dy^IIILF]²⁺ work, herein we report the systematic structural and magnetic study of a family of [Ln^IIILF](CF₃SO₃)₂·H₂O compounds (Ln(III) = 1-Ce, 2-Pr, 3-Nd, 4-Eu, 5-Tb, 6-Ho, 7-Er, 8-Tm, and 9-Yb). From this series, the Ce(III) and Nd(III) analogues show slow relaxation of the magnetization under an applied direct current magnetic field, which is modeled using a Raman process. Complete active space self-consistent field theoretical calculations are employed to understand the relaxation pathways in 1-Ce and 3-Nd and also reveal a large tunnel splitting for 5-Tb. Additional computational studies on model compounds where we remove the axial F^– ligand, or replace F^– with I^–, highlight the importance of the F^– ligand in creating a strong axial crystal field for 1-Ce and 3-Nd and for promoting the SMM behavior. Importantly, this systematic study provides insight into the magnetic properties of these lighter lanthanide ions.

The structural and magnetic properties of a family of [Ln^IIILF](CF₃SO₃)₂·H₂O (L = 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraaza-cyclododecane) compounds are reported. In addition to the previously reported Dy(III) analogue, we find that the Ce(III) and Nd(III) analogues show slow relaxation of the magnetization due to the strong axial magnetic anisotropy created by the axial F⁻ ligand. AC magnetic susceptibility data and CASSCF theoretical calculations are employed to understand the single-molecule magnet behavior of 1-Ce and 3-Nd.

Chemical control of spin-lattice relaxation to discover a room temperature molecular qubit

The second quantum revolution harnesses exquisite quantum control for a slate of diverse applications including sensing, communication, and computation. Of the many candidates for building quantum systems, molecules offer both tunability and specificity, but the principles to enable high temperature operation are not well established. Spin-lattice relaxation, represented by the time constant T ₁, is the primary factor dictating the high temperature performance of quantum bits (qubits), and serves as the upper limit on qubit coherence times (T ₂). For molecular qubits at elevated temperatures (>100 K), molecular vibrations facilitate rapid spin-lattice relaxation which limits T ₂ to well below operational minimums for certain quantum technologies. Here we identify the effects of controlling orbital angular momentum through metal coordination geometry and ligand rigidity via π-conjugation on T ₁ relaxation in three four-coordinate Cu²⁺ S = ½ qubit candidates: bis(N,N'-dimethyl-4-amino-3-penten-2-imine) copper(ii) (Me₂Nac)₂ (1), bis(acetylacetone)ethylenediamine copper(ii) Cu(acacen) (2), and tetramethyltetraazaannulene copper(ii) Cu(tmtaa) (3). We obtain significant T ₁ improvement upon changing from tetrahedral to square planar geometries through changes in orbital angular momentum. T ₁ is further improved with greater π-conjugation in the ligand framework. Our electronic structure calculations reveal that the reduced motion of low energy vibrations in the primary coordination sphere slows relaxation and increases T ₁. These principles enable us to report a new molecular qubit candidate with room temperature T ₂ = 0.43 μs, and establishes guidelines for designing novel qubit candidates operating above 100 K.

Unequal sensitivities of energy levels in a high-symmetry Ho3+ complex towards lattice distortions

High-resolution inelastic neutron scattering has been used to study low-energy magnetic transitions in a Ho³⁺ complex. This complex crystallises in the high-symmetry space group P4/m and has near-perfect D_4d symmetry, which has allowed for the determination of all relevant spin-Hamiltonian parameters. Static and dynamic inhomogeneity in the crystal lattice manifests as a temperature-dependent broadening of the observed magnetic excitations. By implementing distributions in the spin-Hamiltonian parameters, it is possible to reproduce with great accuracy the observed magnetic transition spectrum. This reveals the range to which extraneous perturbations of the crystal field affect low-energy electronic states, such as those involved in quantum tunnelling of magnetisation, in atomic clock transitions, or in spintronics.

A mononuclear nine-coordinated Dy(iii) complex exhibiting field-induced single-ion magnetism behaviour

A new mononuclear Dy(iii) complex, with the formula [Dy(Hcpt)₃]·2H₂O (1), has been successfully prepared via self-assembly between Dy(iii) ions and 2-cyano-N′-(1-(pyridin-2-yl)amido)acetyl (Hcpt) ligand. X-ray diffraction study shows that the Dy(iii) ion is nine-coordinated by three Hcpt ligands with a tridentate chelating mode, leading to an approximately monocapped square-antiprismatic (C_4v) geometry. Magnetic data analysis demonstrates that 1 performs field-induced slow magnetic relaxation with a relaxation barrier of 97.90 K, due to the quantum tunneling effect suppressed upon a static dc field of 2000 Oe. To deeply understand the magnetic behaviors, the relaxation mechanisms and magneto-structure relationship are rationally discussed using ab initio calculations as well.

Reaction of Dy(iii) ion with tridentate acylhydrazone ligand leads to a field-induced Dy(iii) SIM, of which the magneto-structural correlation is elucidated by the magnetic and theoretical studies.

An intermetallic molecular nanomagnet with the lanthanide coordinated only by transition metals

Magnetic molecules known as molecular nanomagnets (MNMs) may be the key to ultra-high density data storage. Thus, novel strategies on how to design MNMs are desirable. Here, inspired by the hexagonal structure of the hardest intermetallic magnet SmCo₅, we have synthesized a nanomagnetic molecule where the central lanthanide (Ln) Er^III is coordinated solely by three transition metal ions (TM) in a perfectly trigonal planar fashion. This intermetallic molecule [Er^III(Re^ICp₂)₃] (ErRe₃) starts a family of molecular nanomagnets (MNM) with unsupported Ln-TM bonds and paves the way towards molecular intermetallics with strong direct magnetic exchange interactions-a promising route towards high-performance single-molecule magnets.

Stereoisomeric coordination polymers based on facial and meridional six-coordinate dysprosium(III )

Due to the small differences in the chemical properties of facial (fac) and meridional (mer) stereoisomers, selective synthesis of one of the isomers is challenging, especially for lanthanide complexes. By using a flexible bidentate phosphine oxide ligand, we managed to isolate three stereoisomeric 2D and 3D coordination polymers, in which six-coordinate Dy(III) ions possess fac- or mer-Cl₃O₃ coordination environments. Structural studies indicate that the stereochemistry differences result from their various supramolecular interactions (e.g., hydrogen bonding and π⋯π stacking). Magnetic property measurements reveal the different static and dynamic magnetic behaviours of the three stereoisomers. Ab initio CASSCF calculations were then performed which indicated that their distinct magnetic behaviours arise from their fac/mer configurations. Compared to fac-Dy(III), mer-Dy(III) possesses more axial ground-state KDs and higher first excited KDs.

Hydrogen-Bonded Framework of a Cobalt(II) Complex Showing Superior Stability and Field-Induced Slow Magnetic Relaxation

A unique hydrogen-bonded organic-inorganic framework (HOIF) constructed from a mononuclear cobalt(II) complex, [Co(MCA)₂·(H₂O)₂] (HMCA = 4-imidazolecarboxylic acid), via multiple hydrogen-bonding interactions was synthesized and structurally characterized. The Co(II) center in the HOIF features a highly distorted octahedral coordination environment. Remarkably, the Co^II HOIF showed permanent porosity with superior stability as established by combined thermogravimetric analysis (TGA), variable-temperature infrared spectra (IR), variable-temperature powder X-ray diffraction data (PXRD), and a CO₂ isotherm. Structural studies reveal that short multiple hydrogen bonds should be responsible for the superior thermal and chemical stability of a HIOF. Magnetic investigations reveal the large easy-plane magnetic anisotropy of the Co²⁺ ions with the fitted D values being 22.1 (magnetic susceptibility and magnetization data) and 29.1 cm^-1 (reduced magnetization data). In addition, the HOIF exhibits field-induced slow magnetic relaxation at low temperature with an effective energy barrier of U_eff = 45.2 cm^-1, indicative of a hydrogen-bonded framework single-ion magnet of the compound. The origin of the significant magnetic anisotropy of the complex was also understood from computational studies. In addition, BS-DFT calculations indicate that the superexchange interactions between the neighboring Co^II ions are non-negligible antiferromagnetism with J_Co-Co = -0.5 cm^-1. The foregoing results provide not only a carboxylate-imidazole ligand approach toward a stable HOIF but also a promising way to build a robust single-ion magnet via hydrogen-bond interactions.

Analysis of vibronic coupling in a 4f molecular magnet with FIRMS

Vibronic coupling, the interaction between molecular vibrations and electronic states, is a fundamental effect that profoundly affects chemical processes. In the case of molecular magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in molecular magnets and qubits, respectively. The study of vibronic coupling is challenging, and most experimental evidence is indirect. Here we employ far-infrared magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H₃trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an "envelope effect" in the vibronic coupling Hamiltonian, which we calculate fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C₃ symmetry of the molecule. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in molecules.

Extreme -Tensor Anisotropy and Its Insensitivity to Structural Distortions in a Family of Linear Two-Coordinate Ni(I) Bis-N-heterocyclic Carbene Complexes

We report a new series of homoleptic Ni(I) bis-N-heterocyclic carbene complexes with a range of torsion angles between the two ligands from 68° to 90°. Electron paramagnetic resonance measurements revealed a strongly anisotropic g-tensor in all complexes with a small variation in g_∥ ∼ 5.7-5.9 and g_⊥ ∼ 0.6. The energy of the first excited state identified by variable-field far-infrared magnetic spectroscopy and SOC-CASSCF/NEVPT2 calculations is in the range 270-650 cm^-1. Magnetic relaxation measured by alternating current susceptibility up to 10 K is dominated by Raman and direct processes. Ab initio ligand-field analysis reveals that a torsion angle of <90° causes the splitting between doubly occupied d_xz and d_yz orbitals, which has little effect on the magnetic properties, while the temperature dependence of the magnetic relaxation appears to have no correlation with the torsion angle.

Ultrahard magnetism from mixed-valence dilanthanide complexes with metal-metal bonding

Magnetic effects of lanthanide bonding Lanthanide coordination compounds have attracted attention for their persistent magnetic properties near liquid nitrogen temperature, well above alternative molecular magnets. Gould et al. report that introducing metal-metal bonding can enhance coercivity. Reduction of iodide-bridged terbium or dysprosium dimers resulted in a single electron bond between the metals, which enforced alignment of the other valence electrons. The resultant coercive fields exceeded 14 tesla below 50 and 60 kelvin for the terbium and dysprosium compounds, respectively. —JSY

The interpretation and prediction of lanthanide single-ion magnet from ab initio electronic structure calculation: The capability and limit

Single-molecule magnet (SMM) is a fascinating system holding the potential of being revolutionary micro-electronic device in information technology. However current SMMs are still far away from real-life application due to...

Metal–metal bond in lanthanide single-molecule magnets

This review surveys recent critical advances in lanthanide SMMs, highlighting the influences of metal–metal bonds on the magnetization dynamics.

Opening Magnetic Hysteresis via Improving Planarity of Equatorial Coordination by Hydrogen Bonding

Through a mixed-ligand strategy, the structural change from a discrete dinuclear DyIII cluster to a one-dimensional polymeric chain was achieved, maintaining the two magnetic entities with the same {Dy(dppbO2)2(H2O)5} (dppbO2...

An experimental and theoretical study of the magnetic relaxation in heterometallic coordination polymers based on 6-methyl-2-oxonicotinate and lanthanide(iii) ions with square antriprismatic environment

Two isostructural lanthanide(iii)-based coordination polymers with square antiprismatic environment are described. Magnetic properties are studied from experimental and theoretical viewpoints to analyze their SIM behavior.

Rare-earth based tetrapyrrolic sandwiches: chemistry, materials and applications

This review summarises advances in chemistry of tetrapyrrole sandwiches with rare earth elements and highlights the current state of their use in single-molecule magnetism, organic field-effect transistors, conducting materials and nonlinear optics.

A dysprosium single molecule magnet outperforming current pseudocontact shift agents

A common criterion for designing performant single molecule magnets and pseudocontact shift tags is a large magnetic anisotropy. In this article we present a dysprosium complex chemically designed to exhibit strong easy-axis type magnetic anisotropy that is preserved in dichloromethane solution at room temperature. Our detailed theoretical and experimental studies on the magnetic properties allowed explaining several features typical of highly performant SMMs. Moreover, the NMR characterization shows remarkably large chemical shifts, outperforming the current state-of-the art PCS tags.

A robust dysprosium(iii) single molecule magnet with large uniaxial magnetic anisotropy induces pseudocontact shifts at almost doubled distance compared to standard shift agents.

Understanding the Magnetic Anisotropy for Linear Sandwich [Er(COT)]+-based Compounds: A Theoretical Investigation

A series of linear sandwich single-ion magnets containing [Er(COT)]+ fragment were selected to probe the magneto-structural correlations using ab initio methods. For prolate shaped ErIII ion, an equatorially coordinating geometry...

Tuning chain topologies and magnetic anisotropy in one-dimensional cobalt(II) coordination polymers via distinct dicarboxylates

Based on a terpyridine derivative and two different dicarboxylate ligands, two new cobalt(II) coordination polymers, namely [Co(pytpy)(DClbdc)]n (1) and [Co(pytpy)(ndc)]n (2) (pytpy = 4'-(4-Pyridyl)-2,2':6',2''-terpyridine, H2DClbc = 2,5-Dichloroterephthalic acid, and H2ndc...

Single-Molecule Magnets beyond a Single Lanthanide Ion: The Art of Coupling

The promising future of storing and processing quantized information at the molecular level has been attracting the study of Single-Molecule Magnets (SMMs) for almost three decades. Although some recent breakthroughs are mainly about the SMMs containing only one lanthanide ion, we believe SMMs can tell a much deeper story than the single-ion anisotropy. Here in this Perspective, we will try to draw a unified picture of SMMs as a delicately coupled spin system between multiple spin centres. The hierarchical couplings will be presented step-by-step, from the intra-atomic hyperfine coupling, to the direct and indirect intra-molecular couplings with neighbouring spin centres, and all the way to the inter-molecular and spin–phonon couplings. Along with the discussions on their distinctive impacts on the energy level structures and thus magnetic behaviours, a promising big picture for further studies is proposed, encouraging the multifaceted developments of molecular magnetism and beyond.

In this Perspective, we draw a unified picture for single-molecule magnets as delicately coupled spin systems, discuss the hierarchical couplings (from intra-atomic to inter-molecular) and their distinctive impacts on the magnetic behaviours.

Tunable Cr4+ Molecular Color Centers

The inherent atomistic precision of synthetic chemistry enables bottom-up structural control over quantum bits, or qubits, for quantum technologies. Tuning paramagnetic molecular qubits that feature optical-spin initialization and readout is a crucial step toward designing bespoke qubits for applications in quantum sensing, networking, and computing. Here, we demonstrate that the electronic structure that enables optical-spin initialization and readout for S = 1, Cr(aryl)₄, where aryl = 2,4-dimethylphenyl (1), o-tolyl (2), and 2,3-dimethylphenyl (3), is readily translated into Cr(alkyl)₄ compounds, where alkyl = 2,2,2-triphenylethyl (4), (trimethylsilyl)methyl (5), and cyclohexyl (6). The small ground state zero field splitting values (<5 GHz) for 1-6 allowed for coherent spin manipulation at X-band microwave frequency, enabling temperature-, concentration-, and orientation-dependent investigations of the spin dynamics. Electronic absorption and emission spectroscopy confirmed the desired electronic structures for 4-6, which exhibit photoluminescence from 897 to 923 nm, while theoretical calculations elucidated the varied bonding interactions of the aryl and alkyl Cr⁴⁺ compounds. The combined experimental and theoretical comparison of Cr(aryl)₄ and Cr(alkyl)₄ systems illustrates the impact of the ligand field on both the ground state spin structure and excited state manifold, laying the groundwork for the design of structurally precise optically addressable molecular qubits.

Significantly Enhancing the Single-Molecule-Magnet Performance of a Dinuclear Dy(III) Complex by Utilizing an Asymmetric Auxiliary Organic Ligand

In this work, we employed an asymmetric auxiliary organic ligand (1,1,1-trifluoroacetylacetone, Htfac) to further regulate the magnetic relaxation behavior of series of Dy₂ single-molecule magnets (SMMs) with a N1,N3-bis(3-methoxysalicylidene)diethylenetriamine (H₂L) ligand. Fortunately, an air-stable Dy₂ complex, [Dy₂(L)₂(tfac)₂] (1; Htfac = 1,1,1-trifluoroacetylacetone) was obtained at room temperature. A structural analysis indicated that some Dy-O or Dy-N bond lengths for 1 are not in the range of those for the complexes [Dy^III₂(L)₂(acac)₂]·2CH₂Cl₂ (Dy₂-acac; Hacac = acetylacetone) and [Dy^III₂(L)₂(hfac)₂] (Dy₂-hfac; Hhfac = hexafluoroacetylacetone), although the electron-withdrawing ability of tfac^- is stronger than that of acac^- but weaker than that of hfac^-. Additionally, the Dy-O3/O3a (the two O atoms bridged to Dy^III ions) bond lengths are also affected by the asymmetrical Htfc ligand. This indicated that the charge distribution of the coordination atoms around Dy^III has been modified in 1, which leads to the fine-tuning of the magnetic relaxation behavior of 1. Magnetic studies indicated that the values of effective energy barrier (U_eff) for 1 and its diluted sample (2) are 234.8(3) and 188.0(6) K, respectively, which are both higher than the reported value of 110 K for the complex Dy₂-hfac. More interestingly, 1 exhibits a magnetic hysteresis opening when T < 2.5 K at zero field, while the hysteresis loops of 2 are closed at a zero dc field. This discrepancy is due to the weak intramolecular exchange coupling in 2, which cannot overcome the QTM of the single Dy^III ion. Ab initio calculations for 1 revealed that the charge distributions of the coordination atoms around Dy^III ions were regulated and the intramolecular exchange coupling was indeed improved when the asymmetrical Htfc was employed as a ligand for the synthesis of this kind of Dy₂ SMM.

Effect of Spin-Orbit Coupling on Phonon-Mediated Magnetic Relaxation in a Series of Zero-Valent Vanadium, Niobium, and Tantalum Isocyanide Complexes

Spin-vibronic coupling leads to spin relaxation in paramagnetic molecules, and an understanding of factors that contribute to this phenomenon is essential for designing next-generation spintronics technology, including single-molecule magnets and spin-based qubits, wherein long-lifetime magnetic ground states are desired. We report spectroscopic and magnetic characterization of the isoelectronic and isostructural series of homoleptic zerovalent transition metal triad M(CNDipp)₆ (M = V, Nb, Ta; CNDipp = 2,6-diisopropylphenyl isocyanide) and show experimentally the significant increase in spin relaxation rate upon going from V to Nb to Ta. Correlated electronic calculations and first principle spin-phonon computations support the role of spin-orbit coupling in modulating spin-phonon relaxation. Our results provide experimental evidence that increasing magnetic anisotropy through spin-orbit coupling interactions leads to increased spin-vibronic relaxation, which is detrimental to long spin lifetime in paramagnetic molecules.

Tunable magnetic anisotropy in luminescent cyanido-bridged {Dy2Pt3} molecules incorporating heteroligand PtIV linkers

The interest in the generation of photoluminescence in lanthanide(III) single-molecule magnets (SMMs) is driven by valuable magneto-optical correlations as well as perspectives toward magnetic switching of emission and opto-magnetic devices linking SMMs with optical thermometry. In the pursuit of enhanced magnetic anisotropy and optical features, the key role is played by suitable ligands attached to the 4f metal ion. In this context, cyanido complexes of d-block metal ions, serving as expanded metalloligands, are promising. We report two novel discrete coordination systems serving as emissive SMMs, {[Dy^III(H₂O)₃(tmpo)₃]₂[Pt^IVBr₂(CN)₄]₃}·2H₂O (1) and {[Dy^III(H₂O)(tmpo)₄]₂[Pt^IVBr₂(CN)₄]₃}·2CH₃CN (2) (tmpo = trimethylphosphine oxide), obtained by combining Dy^III complexes with uncommon dibromotetracyanidoplatinate(IV) ions, [Pt^IVBr₂(CN)₄]^2-. They are built of analogous Z-shaped cyanido-bridged {Dy₂Pt₃} molecules but differ in the coordination number of Dy^III (C.N. = 8 in 1, C.N. = 7 in 2) and the number of coordinated tmpo ligands (three in 1, four in 2) which is related to the applied solvents. As a result, both compounds reveal Dy^III-centred slow magnetic relaxation but only 1 shows SMM character at zero dc field, while 2 is a field-induced SMM. The relaxation dynamics in both systems is governed by the Raman relaxation mechanism. These effects were analysed using ac magnetic data and the results of the ab initio calculations with the support of magneto-optical correlations based on low-temperature high-resolution emission spectra. Our findings indicate that heteroligand halogeno-cyanido Pt^IV complexes are promising precursors for emissive SMMs with the further potential of sensitivity to external stimuli that may be related to the lability of the axially positioned halogeno ligands.

Hetero-tri-spin systems: an alternative stairway to the single molecule magnet heaven?

The search for molecule-based magnetic materials has stimulated over the years the development of extremely rich coordination chemistry. Various combinations of spin carriers have been investigated and illustrated by a plethora of hetero-spin complexes: 3d-nd, 3d-4f, 2p-3d, and 2p-4f. More recently, two other classes of hetero-spin complexes have grown rapidly: compounds containing three different paramagnetic metal ions, or one radical and two different paramagnetic metal ions (all within the same molecular entity). Such new classes of systems represent a challenge both from a synthetic and theoretical point of view. Indeed, the synthetic control and the understanding of the spin topology effect on the overall magnetic behavior from first-principles is a difficult problem to be solved. The presence of different spin carriers in a single molecule makes such compounds particularly interesting because they offer the possibility of developing new magnetic properties, different from those of hetero-bi-spin or homo-spin systems. A critical overview taking the case of 2p-3d-4f complexes is the focus of this perspective paper. An original organic picture of the state-of-art in this field and new hints about the main directions that should be pursued to achieve hetero-tri-spin systems with large anisotropy barriers, low quantum tunneling of magnetization and, possibly, large blocking temperatures are provided in this article through an analysis based on numerically revisiting already published data and a critical survey of the literature reported so far. The reasons for the limited success obtained for the largely used 3d-2p-4f topology are given along with the ones explaining the failure for the 2p-4f-3d case. The still never synthesized linear 2p-3d-4f spin topology seemed to be the most promising one based on the results obtained for the unique closed hetero-tri-spin closed triangular system synthesized so far.

Terminal Ligand and Packing Effects on Slow Relaxation in an Isostructural Set of [Dy(H2 dapp)X2 ]+ Single Molecule Magnets*

We report three structurally related single ion Dy compounds using the pentadentate ligand 2,6-bis((E)-1-(2-(pyridin-2-yl)-hydrazineylidene)ethyl)pyridine (H2 dapp) [Dy(H2 dapp)(NO3 )2 ]NO3 (1), [Dy(H2 dapp)(OAc)2 ]Cl (2) and [Dy(H2 dapp)(NO3 )2 ]Cl0.92 (NO3 )0.08 (3). The (H2 dapp) occupies a helical twisted pentagonal equatorial arrangement with two anionic ligands in the axial positions. Further influence on the electronic and magnetic structure is provided by a closely associated counterion interacting with the central N-H group of the (H2 dapp). The slow relaxation of the magnetisation shows that the anionic acetates give the greatest slowing down of the magnetisation reversal. Further influence on the relaxation properties of compounds1 and 2 is the presence of short nitrate-nitrate intermolecular ligand contact opening further lattice relaxation pathways.

The Impact of Ligand Field Symmetry on Molecular Qubit Coherence

Developing quantum bits (qubits) exhibiting room temperature electron spin coherence is a key goal of molecular quantum information science. At high temperatures, coherence is often limited by electron spin relaxation, measured by T₁. Here we develop a simple and powerful model for predicting relative T₁ relaxation times in transition metal complexes from dynamic ligand field principles. By considering the excited state origins of ground state spin-phonon coupling, we derive group theory selection rules governing which vibrational symmetries can induce decoherence. Thermal weighting of the coupling terms produces surprisingly good predictions of experimental T₁ trends as a function of temperature and explains previously confounding features in spin-lattice relaxation data. We use this model to evaluate experimental relaxation rates across S = 1/2 transition metal qubit candidates with diverse structures, gaining new insights into the interplay between spin-phonon coupling and molecular symmetry. This methodology elucidates the specific vibrational modes giving rise to decoherence, providing insight into the origin of room temperature coherence in transition metal complexes. We discuss the outlook of symmetry-based modeling and design strategies for understanding molecular coherence.

Temperature Dependence of Spin-Phonon Coupling in [VO(acac)2]: A Computational and Spectroscopic Study

Molecular electronic spins are good candidates as qubits since they are characterized by a large tunability of their electronic and magnetic properties through a rational chemical design. Coordination compounds of light transition metals are promising systems for spin-based quantum information technologies, thanks to their long spin coherence times up to room temperature. Our work aims at presenting an in-depth study on how the spin-phonon coupling in vanadyl-acetylacetonate, [VO(acac)₂], can change as a function of temperature using terahertz time-domain spectroscopy and density functional theory (DFT) calculations. Powder THz spectra were recorded between 10 and 300 K. The temperature dependence of vibrational frequencies was then accounted for in the periodic DFT calculations using unit-cell parameters measured at two different temperatures and the optimized ones, as usually reported in the literature. In this way, it was possible to calculate the observed THz anharmonic frequency shift with high accuracy. The overall differences in the spin-phonon coupling magnitudes as a function of temperature were also highlighted showing that the computed trends have to be ascribed to the anisotropic variation of cell parameters.

A Cost-Effective Semi-Ab Initio Approach to Model Relaxation in Rare-Earth Single-Molecule Magnets

We discuss a cost-effective approach to understand magnetic relaxation in the new generation of rare-earth single-molecule magnets. It combines ab initio calculations of the crystal field parameters, of the magneto-elastic coupling with local modes, and of the phonon density of states with fitting of only three microscopic parameters. Although much less demanding than a fully ab initio approach, the method gives important physical insights into the origin of the observed relaxation. By applying it to high-anisotropy compounds with very different relaxation, we demonstrate the power of the approach and pinpoint ingredients for improving the performance of single-molecule magnets.