A Study of Magnetic Relaxation in Dysprosium(III) Single‐Molecule Magnets

Structures and Single-Molecule Magnet Behavior of Dy3 and Dy4 Clusters Constructed by Different Dysprosium(III) Salts

Using the Schiff base ligand H2L-pyra (N'-(2-hydroxybenzoyl)pyrazine-2-carbohydrazonamide) with multiple dentate sites, the trinuclear DyIII-based complex [Dy3(HL-pyra)2(L-pyra)2(CH3COO)3]·2H2O (1) was synthesized. By analyzing the fragmented assembly process and fine-tuning the bridging anions, complex [Dy4(HL-pyra)2(L-pyra)4(NO3)2(H2O)2]·8H2O (2) with different nuclear numbers was successfully synthesized. Magnetic studies demonstrated that 1 did not exhibit magnetic relaxation behavior under the external field; however, 2 exhibited zero-field single-molecule magnetic relaxation behavior with an effective energy barrier (Ueff) of 197.44 K. This is attributed to the improved anisotropy of the single ion after the normalization of the crystal structure, thus realizing the molecular magnetic switching. Moreover, magnetic dilution analysis of 2 demonstrated that the weak magnetic interaction between metal ions inhibited the occurrence of quantum tunneling of magnetization (QTM), resulting in high-performance single-molecule magnet (SMM) behavior. The reasons for the magnetic difference between these two complexes were analyzed using ab initio calculation and magneto-structural correlations. This study provides a reasonable prediction of the ideal configuration of the approximately parallelogram DyIII-based SMMs, thus offering an effective approach for synthesizing Dy4 complexes with excellent properties.

Constructing high axiality mononuclear dysprosium molecular magnets via a regulation-of-co-ligands strategy

Two lanthanide complexes with formulae [DyIII(LN5)(pentafluoro-PhO)3] (1) and [DyIII(LN5)(2,6-difluoro-PhO)2](BPh4) (2) (LN5 = 2,14-dimethyl-3,6,10,13,19-pentaazabicyclo[13.3.1]nonadecal (19),2,13,15,17-pentaene) were structurally and magnetically characterized. DyIII ions lie in the cavity of a five coordinate nitrogen macrocycle, and in combination with the introduction of multi-fluorinated monodentate phenoxyl coligands a high axiality coordination symmetry is built. Using the pentafluorophenol co-ligand, complex 1 with a D2d coordination environment, is obtained and displays moderate single-molecule magnets (SMMs) behavior. When difluorophenol co-ligands were used, a higher local axisymmetric pentagonal bipyramidal coordination geometry was observed in complex 2, which displays apparent slow magnetic relaxation behavior with a hysteresis temperature of up to 5 K. Further magnetic studies of diluted samples combined with ab initio calculations indicate that the high axiality plays a crucial role in suppressing quantum tunneling of magnetization (QTM) and consequently results in good slow magnetic relaxation behavior. Different fluoro-substituted phenoxyl co-ligands have phenoloxy oxygen atoms with different electrostatic potentials as well as a different number of phenoloxy coligands along the magnetic axis, resulting in different ligand field strengths and coordination symmetries.

Inductive detection of temperature-induced magnetization dynamics of molecular spin systems

The development and technological applications of molecular spin systems require versatile experimental techniques to characterize and control their static and dynamic magnetic properties. In the latter case, bulk spectroscopic and magnetometric techniques, such as AC magnetometry and pulsed electron paramagnetic resonance, are usually employed, showing high sensitivity, wide dynamic range, and flexibility. They are based on creating a nonequilibrium state either by changing the magnetic field or by applying resonant microwave radiation. Another possible source of perturbation is a laser pulse that rapidly heats the sample. This approach has proven to be one of the most useful techniques for studying the kinetics and mechanism of chemical and biochemical reactions. Inspired by these works, we propose an inductive detection of temperature-induced magnetization dynamics as applied to the study of molecular spin systems and describe the general design and construction of a particular induction probehead, taking into account the constraints imposed by the cryostat and electromagnet. To evaluate the performance, several coordination compounds of VO2+, Co2+, and Dy3+ were investigated using low-energy pulses of a terahertz free electron laser of the Novosibirsk free electron laser facility as a heat source. All measured magnetization dynamics were qualitatively or quantitatively described using a proposed basic theoretical model and compared with the data obtained by alternating current magnetometry. Based on the results of the research, the possible scope of applications of inductive detection and its advantages and disadvantages in comparison with standard methods are discussed.

Bis-Alkoxide Dysprosium(III) Crown Ether Complexes Exhibit Tunable Air Stability and Record Energy Barrier

High-performance and air-stable single-molecule magnets (SMMs) can offer great convenience for the fabrication of information storage devices. However, the controversial requisition of high stability and magnetic axiality is hard to balance for lanthanide-based SMMs. Here, a family of dysprosium(III) crown ether complexes possessing hexagonal-bipyramidal (pseudo-D6h symmetry) local coordination geometry with tunable air stability and effective energy barrier for magnetization reversal (Ueff) are shown. The three complexes share the common formula of [Dy(18-C-6)L2][I3] (18-C-6 = 1,4,7,10,13,16-hexaoxacyclooctadecane; L = I, 1; L = OtBu 2 and L = 1-AdO 3). 1 is highly unstable in the air. 2 can survive in the air for a few minutes, while 3 remains unchanged in the air for more than 1 week. This is roughly in accordance with the percentage of buried volumes of the axial ligands. More strikingly, 2 and 3 show progressive enhancement of Ueff and 3 exhibits a record high Ueff of 2427(19) K, which significantly contributes to the 100 s blocking temperature up to 11 K for Yttrium-diluted sample, setting a new benchmark for solid-state air-stable SMMs.

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.

Effect of diamagnetic Zn(II) ions on the SMM properties of a series of trinuclear ZnDy2 and tetranuclear Zn2Dy2 (LnIII = Dy, Tb, Gd) complexes: combined experimental and theoretical studies

To study the effect of diamagnetic ions on magnetic interactions, utilizing a compartmental ligand (Z)-2-(hydroxymethyl)-4-methyl-6-((quinolin-8-ylimino)methyl)phenol (LH2), two different series of ZnII-LnIII complexes, namely the trinuclear series of [DyZn2(L)2(μ2-OAc)2(CH3OH)2]·NO3·MeOH (1), [TbZn2(L)2(μ2-OAc)2(CH3OH)2]·NO3·5MeOH·H2O (2), and [GdZn2(L)2(μ2-OAc)2(CH3OH)2]·NO3·MeOH·CHCl3 (3) and the tetranuclear series of [Dy2Zn2(LH)4(NO3)4(μ2OAc)]·NO3·MeOH·H2O (4), [Tb2Zn2(LH)4(NO3)4(μ2-OAc)]·NO3·MeOH·2H2O (5), and [Gd2Zn2(LH)4(NO3)4(μ2-OAc)]·NO3·MeOH·2H2O (6), were synthesized. Trinuclear ZnII-LnIII complexes 1-3 consist of one LnIII ion sandwiched between two peripheral ZnII ions forming a bent type ZnII-DyIII-ZnII array with an angle of 110.64°. Tetranuclear ZnII-LnIII complexes 4-6 are basically a combination of two dinuclear moieties of [LnZn(LH)2(NO3)2]+ connected by one bidentate bridging acetate ion in μ2-OAc coordination mode. The detailed magnetic analysis reveals that complexes 1 and 4 are single molecule magnets having energy barriers of 34.98 K and 46.71 K with relaxation times (τ0) of 5.05 × 10-4 s and 5.24 × 10-4 s, respectively. Ab initio calculations were employed to analyze the magnetic anisotropy and magnetic exchange interaction between the ZnII and LnIII centers with the aim of gaining better insights into the magnetic dynamics of complexes 1-6.

Luminescent Er3+ based single molecule magnets with fluorinated alkoxide or aryloxide ligands

We report the synthesis, structures, and magnetic and luminescence properties of a series of new mono- and dinuclear Er3+ complexes derived from sterically demanding aryloxide and fluorinated alkoxide ligands: [4-tBu-2,6-(Ph2CH)2C6H2O]3Er(THF) (1), [(C6F5)3CO]3Er(Me3SiOH) (2), [(C6F5)3CO]3Er[(Me3Si)2NH] (3), [(C6F5)3CO]3Er(C6H5CH3) (4), [(C6F5)3CO]3Er(o-Me2NC6H4CH3) (5) and {[Ph(CF3)2CO]2Er(μ2-OC(CF3)2Ph)}2 (6). In compounds 1, 2, and 4, the Er3+ ion is four-coordinated and adopts a distorted trigonal pyramidal geometry, while in 3, 5, and 6, the coordination geometry of Er3+ is impacted by the presence of several relatively short Er⋯F distances, making them rather 6-coordinated. All compounds behave as field-induced Single Molecule Magnets (SMMs) and exhibit an Er3+ characteristic near infrared (NIR) emission associated with the 4I13/2 → 4I15/2 transition with a remarkably long lifetime going up to 73 μs, which makes them multifunctional luminescent SMMs. The deconvolution of the NIR emission spectra allowed us to provide a direct probe of the crystal field splitting in these compounds, which was correlated with magnetic data.

Effect of coordinated anions on ferromagnetically coupled Dy2 zero-field single-molecule magnets

A new hydrazone Schiff base ligand was condensed from 2-hydroxy-3-methoxybenzaldehyde and pyrimidine-4-carbohydrazide {H2L = (E)-N'-(2-hydroxy-3-methoxybenzylidene)pyrimidine-4-carbohydrazide}, which was used to assemble two new Dy2 complexes Dy2L2(DMF)2(NO3)2 (1) and Dy2L2(DMF)2(AcO)2 (2). Notably, the coordinated anions have a subtle effect on the coordination configurations of the Dy3+ ions and the magnetic properties of the two Dy2 complexes. The Dy3+ ions in 1 and 2 have the same N2O5 coordination environment but show the triangular dodecahedron and the biaugmented trigonal prism coordination configurations, respectively. Magnetic measurements revealed that both 1 and 2 have intramolecular ferromagnetic interactions between the Dy3+ ions and show single-molecule magnet behaviors at 0 Oe, with Ueff/k values of 58.2 K for 1 and 59.9 K for 2. These magnetic properties may be explained by theoretical calculations.

Single-Molecule Magnet Behavior of Confined Dy(III) in a Mixed Heteroatom-Substituted Polyoxotungstate

Two heteroatom-templated Dy(III)-confined polyoxotungstates [H2N(CH3)2]7Na7[Dy2(H2O)7(W4O9)(HPSeW15O54)(α-SeW9O33)2]·31H2O (1) and [H2N(CH3)2]14K2Na18{[Dy2(H2O)13W14O40]2[α-SeW9O33]4[HPSeW15O54]2}·44H2O (2) were synthesized by a one-pot aqueous reaction and structurally characterized. The most distinctive structural feature of complexes 1 & 2 is the simultaneous presence of both trivacant Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building blocks containing P(III)-Se(IV) heteroatoms. The trimeric polyanion of 1 can be represented as a fusion of two trivacant Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building units encapsulating the [Dy2(H2O)7(W4O9)]12+ cluster. On the other hand, hexameric polyoxoanions of 2 are described as four trivacant Keggin [α-SeW9O33]8- and two Dawson [HPSeW15O54]10-, building units anchoring a [Dy4(H2O)26W28O80]20+ cluster. The magnetic investigation revealed the presence of significant magnetic anisotropy and slow relaxation of magnetization behavior for complex 1 with a phenomenological energy barrier, Ueff = 13.58 K in the absence of an external magnetic field, and Ueff = 24.57 K in the presence of a 500 Oe external dc magnetic field. On the other hand, complex 2 favors the QTM relaxation process in the absence of an external magnetic field and shows field-induced slow relaxation of magnetization with Ueff = 11.11 K at 1500 Oe applied dc field. The in-depth analysis of magnetic relaxation dynamics shows that the relaxation process follows the Orbach as well as Raman relaxation pathways. Further, the ab initio calculation of the studied complexes confirms that the highly axial ground and first excited energy states (containing pure highest mJ states) are responsible for the observed single-molecule magnet (SMM) behavior. Remarkably, this is the first example of a mixed heteroatom-based Dy(III)-substituted polyoxotungstate with both trimeric Keggin [α-SeW9O33]8- and Dawson [HPSeW15O54]10- building units showing SMM behavior.

Tetranuclear lanthanide-based silsesquioxanes: towards a combination of a slow relaxation of the magnetization and a luminescent thermometry

Lanthanide-based silsesquioxanes constitute an emerging family of cage-like metallasilsesquioxanes with exciting optical and magnetic properties. We report here the synthesis, structures and luminescence properties of a series of tetranuclear lanthanide-silsesquioxane compounds of general formula [NEt4]2[(Ph4Si4O8)2(Ln/Ln')4(NO3)6(EtOH)2(MeCN)2]·4(MeCN) with different lanthanide ions (where Ln/Ln' = Dy3+/Eu3+ (1), Dy3+/Tb3+ (2) and Eu3+/Tb3+/Y3+ (3)) and investigate the impact of the lanthanide ions combination on magnetic and photo-luminescent properties. Compound 1 behaves as a field-induced Single Molecule Magnet (SMM) and presents temperature-dependent luminescence characteristics of Eu3+ making it an emissive thermometer working in the temperature range 293-373 K with the maximum relative sensitivity of 1.15% K-1 achieved at 293 K. Compounds 2 and 3 are paramagnets, which demonstrate a characteristic photoluminescence with Dy3+ to Tb3+ and Tb3+ to Eu3+ energy transfers, respectively.

A Combined Synthetic, Magnetic, and Theoretical Study on Enhancing Ligand-Field Axiality for Dy(III) Single-Molecule Magnets Supported by Ferrocene Diamide Ligands

Molecular design is crucial for improving the performance of single-molecule magnets (SMMs). For dysprosium(III) SMMs, enhancing ligand-field axiality is a well-suited strategy to achieve high-performance SMMs. We synthesized a series of dysprosium(III) complexes, (NN^TIPS)DyBr(THF)₂ (1, NN^TIPS = fc(NSiⁱPr₃)₂; fc = 1,1'-ferrocenediyl, THF = tetrahydrofuran), [(NN^TIPS)Dy(THF)₃][BPh₄] (2), (NN^TIPS)DyI(THF)₂ (3), and [(NN^TBS)Dy(THF)₃][BPh₄] (4, NN^TBS = fc(NSi^tBuMe₂)₂), supported by ferrocene diamide ligands. X-ray crystallography shows that the rigid ferrocene backbone enforces a nearly axial ligand field with weakly coordinating equatorial ligands. Dysprosium(III) complexes 1-4 all exhibit slow magnetic relaxation under zero fields and possess high effective barriers (U_eff) around 1000 K, comparable to previously reported (NN^TBS)DyI(THF)₂ (5). We probed the influences of structural variations on SMM behaviors by theoretical calculations and found that the distribution of negative charges defined by r_q, i.e., the ratio of the charges on the axial ligands to the charges on the equatorial ligands, plays a decisive role. Moreover, theoretical calculations on a series of model complexes 1'-5' without equatorial ligands unveil that the axial crystal-field parameters B₂⁰ are directly proportional to the N-Dy-N angles and support the hypothesis that enhancing the ligand-field axiality could improve SMM performance.

Electron Paramagnetic Resonance Spectra of Pentagonal Bipyramidal Gadolinium Complexes

Gadolinium is a special case in spectroscopy because of the near isotropic nature of the 4f⁷ configuration of the +3 oxidation state. Gd³⁺ complexes have been studied in several symmetries to understand the underlying mechanisms of the ground state splitting. The abundance of information in Gd³⁺ spectra can be used as a probe for properties of the other rare earth ions in the same complexes. In this work, the zero-field splitting (ZFS) of a series of Gd³⁺ pentagonal bipyramidal complexes of the form [GdX₁X₂(L_eq)₅]ⁿ⁺ [n = 1, X = axial ligands: Cl^-, ^-O^tBu, ^-OArF₅ or n = 3, X = ^tBuPO(NHⁱPr)₂, L_eq = equatorial ligand: Py, THF or H₂O] with near fivefold symmetry axes along X¹-Gd-X² was investigated. The ZFS parameters were determined by fitting of room-temperature continuous wave electron paramagnetic resonance (EPR) spectra (at X-, K-, and Q-band) to a spin Hamiltonian incorporating extended Stevens operators compatible with C₅ symmetry. Examination of the acquired parameters led to the conclusion that the ZFS is dominated by the B₂⁰ term and that the magnitude of B₂⁰ is almost entirely dependent on, and inversely proportional to, the donor strength of the axial ligands. Surveying the continuous shape measure and the X¹-Gd-X² angle of the complexes showed that there is some correlation between the proximity of each complex to D_5h symmetry and the magnitude of the B₆⁵ parameter, but that the deformation of the X¹-Gd-X² angle is more significant than other distortions. Finally, the magnitude of B₂⁰ was found to be inversely proportional to the thermal barrier for the reversal of the magnetic moment (U_eff) of the corresponding isostructural Dy³⁺ complexes.

Recent Progress for Single-Molecule Magnets Based on Rare Earth Elements

Single-molecule magnets (SMMs) have attracted much attention due to their potential applications in molecular spintronic devices. Rare earth SMMs are considered to be the most promising for application owing to their large magnetic moment and strong magnetic anisotropy. In this review, the recent progress in rare earth SMMs represented by mononuclear and dinuclear complexes is highlighted, especially for the modulation of magnetic anisotropy, effective energy barrier (U_eff) and blocking temperature (T_B). The terbium- and dysprosium-based SMMs have a U_eff of 1541 cm^-1 and an increased T_B of 80 K. They break the boiling point temperature of liquid nitrogen. The development of the preparation technology of rare earth element SMMs is also summarized in an overview. This review has important implications and insights for the design and research of Ln-SMMs.

Role of molecular symmetry in the magnetic relaxation dynamics of five-coordinate Dy(III) complexes

A new family of low-coordinate mononuclear Dy^III single-molecule magnets [(Trapen^TMS)Dy(L^B)] (Trapen = tris(2-aminobenzyl)amine; TMS = SiMe₃; L^B = THF 1, pyridine 2, ONMe₃3) has been synthesized and structurally characterized by single crystal X-ray diffraction. The five-coordinate Dy^III ions exhibit distorted triangular bipyramidal geometries, among the different neutral ligands L^B on the apex and the same Trapen^TMS ligand, making the pyramid base of the trigonal bipyramid. Magnetic data analysis reveals that 1-3 are characteristic of SMM behaviors without a dc field, accompanying an unambiguous quantum tunneling of magnetization. Under an extra dc field of 500 Oe, field-induced slow magnetic relaxation behaviors occur with Raman and/or QTM processes. Ab initio calculations were also performed to rationalize the observed discrepancy in the magnetic behaviors, and the result illustrates that the SMM behavior could be effectively manipulated by the axial symmetry of the triangular bipyramidal Dy^III motifs.

Axial Ligand as a Critical Factor for High-Performance Pentagonal Bipyramidal Dy(III) Single-Ion Magnets

The choice of axial ligands is of great importance for the construction of high-performance Dy-based single-molecule magnets (SMMs). Here, combining axial ligands Ph₃SiO^- (anion of triphenylsilanol) and 2,6-dichloro-4-nitro-PhO^- (the anion of 2,6-dichloro-4-nitrophenol) with a neutral macrocyclic ligand 2,14-dimethyl-3,6,10,13,19-pentaazabicyclo[13.3.1]nonadeca-1(19),2,13,15,17-pentaene (L₂^N5) generates two new pentagonal bipyramidal Dy(III) complexes [Dy^III(L₂^N5) (X)₂](BPh₄) (X = Ph₃SiO^-, 1; 2,6-dichloro-4-nitro-PhO^-, 2) with strong axial ligand fields. Magnetic characterizations show that 1 possesses a large energy barrier above 1000 K and a magnetic hysteresis up to 9 K, whereas 2 only displays field-induced peaks of alternating-current susceptibilities without the hysteresis loop, even though 2 has a similar coordination geometry with 1. Detailed Ab initio calculations indicate an apparent difference in the axial negative charge between both complexes, which is caused by the diverse electron-donating properties of the axial ligands. The present work provides an efficient strategy to enhance the SMMs' properties, which highlights that the electron-donating property of the axial ligands is especially important for constructing the high-performance Dy-based SMMs.

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.

Impact of Ligand Substituents on the Magnetization Dynamics of Mononuclear DyIII Single-Molecule Magnets

Two mononuclear Dy^III single-molecule magnets with different ligand substituents located far from the coordinating atoms, [Dy(L-NO₂)(NO₃)] (1) and [Dy(L-Me)(NO₃)] (2), and their diamagnetic-ion diluted analogues, 1' and 2', were structurally and magnetically characterized. 1 and 2 have nearly identical coordination environments of Dy^III ions with D_2d symmetry but different magnetization dynamics. No Orbach process was observed for 1 and 1' in the testing temperature and frequency range, but effective energy barriers of 575 and 829 K for 2 and 2' were obtained, respectively. The opened hysteresis loops were observed until 6 K for 1 and 10 K for 2. Ab initio calculations reveal that the energy gaps between ground and low-lying excited states of 2 are higher than those of 1 and the relaxation rate through quantum tunneling of magnetization of 2 is lower than that of 1 due to the electronic effect of the axial coordinating oxygen atoms influenced by ligand substitutions.

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.

Slow magnetic relaxation in dinuclear Co(III)-Co(II) complexes containing a five-coordinated Co(II) centre with easy-axis anisotropy

Two air-stable Co(III)-Co(II) mixed-valence complexes of molecular formulas [Co^IICo^III(L)(DMAP)₃(CH₃COO)]·H₂O·CH₃OH (1) and [Co^IICo^III(L)(4-Pyrrol)₃ (CH₃COO)]·0.5CH₂Cl₂ (2) (H₄L = 1,3-bis-(5-methyl pyrazole-3-carboxamide) propane; DMAP = 4-dimethylaminopyridine; and 4-Pyrrol = 4-pyrrolidinopyridine) were synthesized and characterized by single-crystal X-ray crystallography, high-field electron paramagnetic resonance (HFEPR) spectroscopy, and magnetic measurements. Both complexes possess one five-coordinated paramagnetic Co(II) ion and one six-coordinated Co(III) ion with octahedral geometry. Direct-current magnetic susceptibility and magnetization measurements show the easy-axis magnetic anisotropy that is also confirmed by low-temperature HFEPR measurements and theoretical calculations. Frequency- and temperature-dependent alternating-current magnetic susceptibility measurements reveal their field-assisted slow magnetic relaxation, which is a characteristic behavior of single-molecule magnets (SMMs), caused by the individual Co(II) ion. The effective energy barrier of complex 1 (49.2 cm^-1) is significantly higher than those of the other dinuclear Co(III)-Co(II) SMMs. This work hence presents the first instance of the dinuclear Co(III)-Co(II) single-molecule magnets with a five-coordinated environment around the Co(II) ion.

In silico design criteria for high blocking barrier uranium (III) SIMs

A combination of DFT and ab initio CASSCF/PT2 calculations on U(III) fictitious models and numerous reported X-ray structures unveils several geometries from coordination number 1 to 12 that can be targeted to design potential U(III) SIMs with attractive barrier heights. Among the geometries studied, the T-shaped and capped pentagonal antiprism geometries yield values exceeding 1500 cm^-1 - a value that is elusive for any uranium SIMs.

The coexistence of long τQTM and high Ueff as a concise criterion for a good single-molecule magnet: a theoretical case study of square antiprism dysprosium single-ion magnets

A systematic theoretical study is performed on a group of 16 square antiprism dysprosium single-ion magnets. Based on ab initio calculations, the quantum tunneling of magnetization (QTM) time, i.e., τ_QTM, and effective barrier of magnetic reversal, U_eff, are theoretically predicted. The theoretical τ_QTM is able to identify the ones with the longest QTM time with small numerical deviations. Similar results occur with respect to U_eff too. The systems possessing the best single-molecule magnet (SMM) properties here are just the ones having both the longest τ_QTM and the highest U_eff, from either experiment or theory. Thus, our results suggest the coexistence of long τ_QTM and high U_eff to be a criterion for high-performance SMMs. Although having its own limits, this criterion is easy to be applied in a large number of systems since both τ_QTM and U_eff could be predicted by theory with satisfactory efficiency and reliability. Therefore, this concise criterion could provide screened candidates for high-performance SMMs quickly and, hence, ease the burden of further exploration aiming for a higher degree of precision. This screening is important since the further exploration could easily demand tens or even hundreds of ab initio calculations for a single SMM. A semi-quantitative crystal field (CF) analysis is performed and shown here to be capable of indicating the general trends in a more chemically intuitive way. This analysis could help to identify the most important coordinating atoms for both diagonal and non-diagonal CF components. Thus, it could give some direct clues for improving the SMM properties: reducing the distance of the axial atom to the central ion, rotating the axial atom closer to the easy axis or increasing the amount of its negative charge. Correspondingly, opposite operations on the equatorial atom could give the same result.

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.

Magnetic anisotropy of transition metal and lanthanide ions in pentagonal bipyramidal geometry

The magnetic anisotropy associated with a pentagonal bipyramidal (PBP) coordination sphere is examined on the basis of experimental and theoretical investigations. The origin and the characteristics of this anisotropy are discussed in relation to the electronic configuration of the metal ions. The effects of crystal field, structural distortion, and a second-coordination sphere on the observed anisotropies for transition meal and lanthanide ions are outlined. For the Ln derivatives, we focus on compounds showing SMM-like behavior (i.e. slow relaxation of their magnetization) in order to highlight the essential chemical and structural parameters for achieving strong axial anisotropy. The use of PBP complexes to impart controlled magnetic anisotropy in polynuclear species such as SMMs or SCMs is also addressed. This review of the magnetic anisotropies associated with a pentagonal bipyramidal coordination sphere for transition metal and lanthanide ions is intended to highlight some general trends that can guide chemists towards designing a compound with specific properties.

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.

Tuning the Equatorial Negative Charge in Hexagonal Bipyramidal Dysprosium(III) Single-Ion Magnets to Improve the Magnetic Behavior

Taking advantage of the pentaethylene glycol (EO5) and deprotonation of EO5, a family of new structurally hexagonal bipyramidal Dy(III) complexes, [Dy(EO5)(2,6-dichloro-4-nitro-PhO)₂](2,6-dichloro-4-nitro-PhO) (1), [Dy(EO5-BPh₂)(2,6-dichloro-4-nitro-PhO)₂] (2), and [Dy(EO5-BPh₂)(2,6-dichloro-4-nitro-PhO)Cl] (3), were controbllably synthesized and structurally characterized. Magnetic measurements show that complex 1 is a zero-field SIM and has an observable hysteresis opening up to 4 K. Conversely, only under extra magnetic field is slow magnetic relaxation observed in 2 and 3. This considerable difference in the magnetic behavior is mainly caused by the change of the equatorial negative charge. Detailed ab initio calculations further elucidate that the quantum tunneling is induced by the presence of equatorial negative charge, and the magnetic anisotropy depends on the axial ligands. This work demonstrates that the absence of the equatorial negative charge should also be considered in the rational design of promising single molecular magnets based on the oblate ions.

Using N-Heterocyclic Carbenes as Weak Equatorial Ligands to Design Single-Molecule Magnets: Zero-Field Slow Relaxation in Two Octahedral Dysprosium(III) Complexes

We report the synthesis, structures, and magnetic investigations of two new octahedral dysprosium complexes, based on the original N-heterocyclic carbene (NHC) tridentate bis(phenoxide) ligand, of the respective formulas mer-[DyL(THF)₂Cl] (1) and mer-[DyL(THF)₃][BPh₄] (2), where L = 1,3-bis(3,5-di-tert-butyl-2-oxidophenyl)-5,5-dimethyl-3,4,5,6-tetrahydropyrimidin-1-ium chloride and THF = tetrahydrofuran. The short Dy-O distances in the axial direction in association with the weak donor ability of the NHC moiety provide a suitable environment for slow relaxation of magnetization, overcoming the previous single-molecule magnets based on NHC ligands.

A cyanometallate- and carbonate-bridged dysprosium chain complex with a pentadentate macrocyclic ligand: synthesis, structure, and magnetism

A novel one-dimensional polymeric cyanometallate- and carbonate-bridged dysprosium(iii) chain with a pentadentate macrocyclic ligand exhibits field-induced multiple-relaxation processes.

Pseudo-mono-axial ligand fields that support high energy barriers in triangular dodecahedral Dy(iii) single-ion magnets

Air-stable triangular dodecahedral Dy(iii) single-ion magnets with pseudo-mono-axial linear ligand fields exhibit high energy barrier exceeding 600 K, which represent the highest energy barrier for mononuclear SMMs with triangular dodecahedron.

Effect on the geometry over the slow relaxation of the magnetization in a series of erbium(iii) complexes based on halogenated ligands

Erbium(iii) complexes based on halogenated ligands.

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...

Salen-type mononuclear dysprosium complex displays significant performance of single-molecule magnet

Three salen-type mononuclear lanthanide complexes with general formula [Ln(5-NO2salcy)(NO3)(CH3OH)2] (Ln = Dy (1), Ho (2) and Er (3)) have been designed and synthesized by reactions of N,N'-bis(5-nitrosalicylaldehyde)ethane-1,2-cyclohexanediamine (5-NO2salcyH2) with various...

Structural and magnetic studies of six-coordinated Schiff base Dy(III) complexes

With the aim to tune magnetic anisotropies of six-coordinated Dy(III) complexes, four bis-Schiff bases bearing different spacers and one mono-Schiff base were designed, which are bis(2-hydroxylnaphthalenylmethylene)hydrazine (H2L1), bis(2-hydroxylnaphthylmethylene)ethylenediamine (H2L2), bis(2-hydroxylnaphthylmethylene)-propylenediamine...

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...

Studies of the Temperature Dependence of the Structure and Magnetism of a Hexagonal-Bipyramidal Dysprosium(III) Single-Molecule Magnet

The hexagonal-bipyramidal lanthanide(III) complex [Dy(O^tBu)Cl(18-C-6)][BPh₄] (1; 18-C-6 = 1,4,7,10,13,16-hexaoxacyclooctadecane ether) displays an energy barrier for magnetization reversal (U_eff) of ca. 1000 K in a zero direct-current field. Temperature-dependent X-ray diffraction studies of 1 down to 30 K reveal bending of the Cl-Ln-O^tBu angle at low temperature. Using ab initio calculations, we show that significant bending of the O-Dy-Cl angle upon cooling from 273 to 100 K leads to a ca. 10% decrease in the energy of the excited electronic states. A thorough exploration of the temperature and field dependencies of the magnetic relaxation rate reveals that magnetic relaxation is dictated by five mechanisms in different regimes: Orbach, Raman-I, quantum tunnelling of magnetization, and Raman-II, in addition to the observation of a phonon bottleneck effect.

A Series of Novel Pentagonal-Bipyramidal Erbium(III) Complexes with Acyclic Chelating N3O2 Schiff-Base Ligands: Synthesis, Structure, and Magnetism

A series of six seven-coordinate pentagonal-bipyramidal (PBP) erbium complexes, with acyclic pentadentate [N3O2] Schiff-base ligands, 2,6-diacetylpyridine bis-(4-methoxybenzoylhydrazone) [H2DAPMBH], or 2,6-diacethylpyridine bis(salicylhydrazone) [H4DAPS], and various apical ligands in different charge states were synthesized: [Er(DAPMBH)(C2H5OH)Cl] (1); [Er(DAPMBH)(H2O)Cl]·2C2H5OH (2); [Er(DAPMBH)(CH3OH)Cl] (3); [Er(DAPMBH)(CH3OH)(N3)] (4); [(Et3H)N]+[Er(H2DAPS)Cl2]- (5); and [(Et3H)N]+[Y0.95Er0.05(H2DAPS)Cl2]- (6). The physicochemical properties, crystal structures, and the DC and AC magnetic properties of 1-6 were studied. The AC magnetic measurements revealed that most of Compounds 1-6 are field-induced single-molecule magnets, with estimated magnetization energy barriers, Ueff ≈ 16-28 K. The experimental study of the magnetic properties was complemented by theoretical analysis based on ab initio and crystal field calculations. An experimental and theoretical study of the magnetism of 1-6 shows the subtle impact of the type and charge state of the axial ligands on the SMM properties of these complexes.

Eight coordinated mononuclear dysprosium complexes of heptadentate aminophenol ligands: the influence of the phenol substituents and the ancillary donors on the magnetic relaxation

The mononuclear complexes [Dy(3Br,5Cl-H₃L^1,1,4)(D)]·solvate (D = H₂O, solvate = 0.25MeOH, 1W·0.25MeOH; D = Py without solvate, 1Py), and [Dy(3NO₂,5Br-H₃L^1,1,4)(H₂O)] (2W) were isolated. The crystal structures of 1W·0.25MeOH, 1Py and 2W·2CH₃C₆H₅ show that the Dy^III ion is octacoordinated, in N₄O₄ or N₅O₃ environments, with distorted geometries, between square antiprism, biaugmented trigonal prism and triangular dodecahedral. A similar environment for the metal ion is shown in the chiral crystals of the diamagnetic yttrium analogue [Y(3Br,5Cl-H₃L^1,1,4)(MeOH)] (3M), which were spontaneously resolved. Magnetic analyses of the three dysprosium complexes, and their diluted analogous 1W@Y, 1Py@Y and 2W@Y, reveal that none of them seem to relax through an Orbach mechanism at H_dc = 0. However, the three complexes show Orbach relaxation under H_dc = 1000 Oe, and 1Py is the in-field SIM with the highest energy barrier among these complexes, with a U_eff value of 358 K. Analysis of ac magnetic data shows that the electron-withdrawing substituents on the phenol rings of the aminophenol ligands, as well as the auxiliary oxygen donors from water ligands, reduce the energy barriers of the complexes, which is attributed to a charge reduction in the coordinating atoms of the aminophenol donor. Ab initio calculations support the experimental results.

Magnetic anisotropies of Ho(III) and Dy(III) single-molecule magnets experimentally determined via polarized neutron diffraction

We present the magnetic anisotropy of two isostructural pentagonal-bipyramidal complexes, [Ln(H₂O)₅(HMPA)₂]I₃·2HMPA (HMPA = hexamethylphosphoramide, Ln = Dy, Ho). Using ac magnetic susceptibility measurements, we find magnetic relaxation barriers of 600 K and 270 K for the Dy- and Ho-compounds, respectively. This difference is supported by polarized neutron diffraction (PND) measured at 5 K and 1 T which provides the first experimental evidence that the transverse elements in the magnetic anisotropy of the Ho-analogue are significant, whereas the Dy-analogue has a near-axial magnetic anisotropy with vanishing transverse contributions. The coordination geometries of the two complexes are highly similar, and we attribute the loss of strong magnetic axiality as expressed in the atomic susceptibility tensors from PND, as well as the smaller relaxation barrier in the Ho-complex compared to the Dy-complex, to the less favorable interaction of the pentagonal bipyramidal crystal field with the characteristics of the Ho(III) 4f-charge distribution.

Improving the single-molecule magnet properties of two pentagonal bipyramidal Dy3+ compounds by the introduction of both electron-withdrawing and -donating groups

Two mononuclear Dy³⁺ compounds [Dy(bmbpen-F)X] (X = Cl, 1; Br, 2) with a pentagonal bipyramidal (PBP) geometry were obtained from N,N'-bis-(5-methyl-2-hydroxybenzyl)-N,N'-bis(5-fluoro-2-methylpyridyl)ethylenediamine (H₂bmbpen-F) and dysprosium halides. The magnetic anisotropy and single-molecule magnet (SMM) behavior of these PBP compounds were regulated by introducing both electron-withdrawing F atoms into the equatorial pyridine rings and electron-donating -CH₃ groups into the axial phenolic hydroxyl rings. The results of magnetic characterization show that 1 and 2 exhibit single molecule magnet behavior with magnetization reversal barriers of 990(13) and 1189(16) K under a zero dc external field and magnetic hysteresis loops up to 26 K and 36 K, respectively. The results of ab initio calculations are consistent with the experimental observations, confirming that the simultaneous introduction of electron-withdrawing groups into the equatorial positions and electron-donating groups into the axial positions can lead to PBP Dy-SMMs with improved properties.

Slow magnetic relaxation in distorted tetrahedral Dy(III) aryloxide complexes

Three distorted tetrahedral Dy(III) aryloxide complexes, [Na(THF)₆][Dy(OAr^Ad₂tBu)₂Cl₂] (1) (OAr^Ad₂tBu = OC₆H₂Adamantyl₂-2,6-^tBu-4) and [Na(THF)₆][Dy(OMes*)₃X] (X = Cl, 2; BH₄, 3), (OMes* = OC₆H₂^tBu₃-2,4,6) exhibit easy axis magnetic anisotropy and slow magnetic relaxation at zero field, with relaxation rates 1 < 2 < 3.

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

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion's first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Methods and Models of Theoretical Calculation for Single-Molecule Magnets

Theoretical calculation plays an important role in the emerging field of single-molecule magnets (SMMs). It can not only explain experimental phenomena but also provide synthetic guidance. This review focuses on discussing the computational methods that have been used in this field in recent years. The most common and effective method is the complete active space self-consistent field (CASSCF) approach, which predicts mononuclear SMM property very well. For bi- and multi-nuclear SMMs, magnetic exchange needs to be considered, and the exchange coupling constants can be obtained by Monte Carlo (MC) simulation, ab initio calculation via the POLY_ANISO program and density functional theory combined with a broken-symmetry (DFT-BS) approach. Further application for these calculation methods to design high performance SMMs is also discussed.