Role of Magnetic Exchange Interactions in the Magnetization Relaxation of {3d–4f} Single‐Molecule Magnets: A Theoretical Perspective

Combined density functional and ab initio calculations are performed on two isomorphous tetranuclear {Ni₃^IIILn^III} star‐type complexes [Ln=Gd ( 1 ), Dy ( 2 )] to shed light on the mechanism of magnetic exchange in 1 and the origin of the slow magnetization relaxation in complex 2 . DFT calculations correctly reproduce the sign and magnitude of the J values compared to the experiments for complex 1 . Acute ?Ni?O?Gd bond angles present in 1 instigate a significant interaction between the 4f_xyz orbital of the Gd^III ion and 3d orbital of the Ni^II ions, leading to rare and strong antiferromagnetic Ni???Gd interactions. Calculations reveal the presence of a strong next‐nearest‐neighbour Ni???Ni antiferromagnetic interaction in complex 1 leading to spin frustration behavior. CASSCF+RASSI‐SO calculations performed on complex 2 suggest that the octahedral environment around the Dy^III ion is neither strong enough to stabilize the m_J |±15/2〉 as the ground state nor able to achieve a large ground‐state–first‐excited‐state gap. The ground‐state Kramers doublet for the Dy^III ion is found to be the m_J |±13/2〉 state with a significant transverse anisotropy, leading to very strong quantum tunneling of magnetization (QTM). Using the POLY_ANISO program, we have extracted the J_NiDy interaction as ?1.45 cm^?1. The strong Ni???Dy and next‐nearest‐neighbour Ni???Ni interactions are found to quench the QTM to a certain extent, resulting in zero‐field SMM behavior for complex 2 . The absence of any ac signals at zero field for the structurally similar [Dy(AlMe₄)₃] highlights the importance of both the Ni???Dy and the Ni???Ni interactions in the magnetization relaxation of complex 2 . To the best of our knowledge, this is the first time that the roles of both the Ni???Dy and Ni???Ni interactions in magnetization relaxation of a {3d–4f} molecular magnet have been established.     

Supramolecular “Double‐Propeller” Dimers of Hexanuclear CuII/LnIII Complexes: A {Cu3Dy3}2 Single‐Molecule Magnet

Propelling magnetism : Supramolecular organization leads to a remarkable dodecanuclear {Cu₃Dy₃}₂ cluster with a “double–propeller” shape (see picture). The linkages of the CuDy units, both intramolecular and supramolecular, appear to be responsible for a drastic change in the single molecule magnetic behavior.

     

Tuning the Magnetization Dynamic Properties of Nd⋅⋅⋅Fe and Nd⋅⋅⋅Co Single‐Molecular Magnets by Introducing 3 d–4 f Magnetic Interactions

By using paramagnetic [Fe(CN)₆]^3? anions in place of diamagnetic [Co(CN)₆]^3? anions, two field‐induced mononuclear single‐molecular magnets, [Nd(18‐crown‐6)(H₂O)₄][Co(CN)₆] ? 2 H₂O ( 1 ) and [Nd(18‐crown‐6)(H₂O)₄][Fe(CN)₆] ? 2 H₂O ( 2 ), have been synthesized and characterized. Single‐crystal X‐ray diffraction analysis revealed that compounds 1 and 2 were ionic complexes. The Nd^III ions were located inside the cavities of the 18‐crown‐6 ligands and were each bound by four water molecules on either side of the crown ether. Magnetic investigations showed that these compounds were both field‐induced single‐molecular magnets. By comparing the slow relaxation behaviors of compounds 1 and 2 , we found significant differences between the direct and Raman processes for these two complexes, with a stronger direct process in compound 2 at low temperatures. Complete active space self‐consistent field (CASSCF) calculations were also performed on two [Nd(18‐crown‐6)(H₂O)₄]³⁺ fragments of compounds 1 and 2 . Ab initio calculations showed that the magnetic anisotropies of the Nd^III centers in complexes 1 and 2 were similar to each other, which indicated that the difference in relaxation behavior was not owing to the magnetic anisotropy of Nd^III. Our analysis showed that the magnetic interaction between the Nd^III ion and the low‐spin Fe^III ion in complex 2 played an important role in enhancing the direct process and suppressing the Raman process of the single‐molecular magnet.     

A Linear 3d–4f Tetranuclear CoIII2DyIII2 Single‐Molecule Magnet: Synthesis,Structure, and Magnetic Properties

A linear tetranuclear 3d–4f Co₂Dy₂ cluster assembled from a polydentate Schiff base exhibits single‐molecule magnet (SMM) behavior with an anisotropic barrier of 33.8 K. Due to the presence of diamagnetic cobalt(III) ions, the tetranuclear cluster of 1 behaves magnetically like a dinuclear Dy₂ system. However, the diamagnetic segment might efficiently minimize undesirable intermolecular magnetic interactions, thereby improving the performance of the SMM behavior of 1 . This discrete complex presents us with a unique opportunity to study the magnetic properties and to probe the dynamics of magnetization in a magnetically isolated Dy₂ system.     

Probing the Origin of Magnetic Anisotropy in a Dinuclear {MnIIICuII} Single‐Molecule Magnet: The Role of Exchange Anisotropy

Using ab initio calculations all the components of the magnetic anisotropy in a dinuclear [Mn^IIICu^IICl(5‐Br‐sap)₂(MeOH)] single‐molecule magnet (SMM) have been computed. These calculations reveal that apart from the single‐ion anisotropy, the exchange anisotropy also plays a crucial role in determining the sign as well as the magnitude of the cluster anisotropy. Developed magneto‐structural correlations suggest that a large ferromagnetic exchange can in fact reduce the ground‐state anisotropy, which is an integral component in the design of SMMs.     

A Heterometallic FeII–DyIII Single‐Molecule Magnet with a Record Anisotropy Barrier

A record anisotropy barrier (319 cm^?1) for all d‐f complexes was observed for a unique Fe^II‐Dy^III‐Fe^II single‐molecule magnet (SMM), which possesses two asymmetric and distorted Fe^II ions and one quasi‐D_5h Dy^III ion. The frozen magnetization of the Dy^III ion leads to the decreased Fe^II relaxation rates evident in the Mössbauer spectrum. Ab initio calculations suggest that tunneling is interrupted effectively thanks to the exchange doublets.     

Tuning the Magnetic Interactions and Relaxation Dynamics of Dy2 Single‐Molecule Magnets

Efficient modulation of single‐molecule magnet (SMM) behavior was realized by deliberate structural modification of the Dy₂ cores of [Dy₂( a ′ povh )₂(OAc)₂(DMF)₂] ( 1 ) and [Zn₂Dy₂( a′povh )₂(OAc)₆] ? 4 H₂O ( 2 ; H₂ a ′ povh =N′‐[amino(pyrimidin‐2‐yl)methylene]‐o‐vanilloyl hydrazine). Compound 1 having fourfold linkage between the two dysprosium ions shows high‐performance SMM behavior with a thermal energy barrier of 322.1 K, whereas only slow relaxation is observed for compound 2 with only twofold connection between the dysprosium ions. This remarkable discrepancy is mainly because of strong axiality in 1 due to one pronounced covalent bond, as revealed by experimental and theoretical investigations. The significant antiferromagnetic interaction derived from bis(μ₂‐O) and two acetate bridging groups was found to be crucial in leading to a nonmagnetic ground state in 1 , by suppressing zero‐field quantum tunneling of magnetization.     

Two C3‐Symmetric Dy3III Complexes with Triple Di‐μ‐methoxo‐μ‐phenoxo Bridges,Magnetic Ground State,and Single‐Molecule Magnetic Behavior

Two series of isostructural C₃‐symmetric Ln₃ complexes Ln₃ ? [BPh₄] and Ln₃ ? 0.33[Ln(NO₃)₆] (in which Ln^III=Gd and Dy) have been prepared from an amino‐bis(phenol) ligand. X‐ray studies reveal that Ln^III ions are connected by one μ₂‐phenoxo and two μ₃‐methoxo bridges, thus leading to a hexagonal bipyramidal Ln₃O₅ bridging core in which Ln^III ions exhibit a biaugmented trigonal‐prismatic geometry. Magnetic susceptibility studies and ab initio complete active space self‐consistent field (CASSCF) calculations indicate that the magnetic coupling between the Dy^III ions, which possess a high axial anisotropy in the ground state, is very weakly antiferromagnetic and mainly dipolar in nature. To reduce the electronic repulsion from the coordinating oxygen atom with the shortest Dy?O distance, the local magnetic moments are oriented almost perpendicular to the Dy₃ plane, thus leading to a paramagnetic ground state. CASSCF plus restricted active space state interaction (RASSI) calculations also show that the ground and first excited state of the Dy^III ions are separated by approximately 150 and 177 cm^?1, for Dy₃ ? [BPh₄] and Dy₃ ? 0.33[Dy(NO₃)₆], respectively. As expected for these large energy gaps, Dy₃ ? [BPh₄] and Dy₃ ? 0.33[Dy(NO₃)₆] exhibit, under zero direct‐current (dc) field, thermally activated slow relaxation of the magnetization, which overlap with a quantum tunneling relaxation process. Under an applied H_dc field of 1000 Oe, Dy₃ ? [BPh₄] exhibits two thermally activated processes with U_eff values of 34.7 and 19.5 cm^?1, whereas Dy₃ ? 0.33[Dy(NO₃)₆] shows only one activated process with U_eff=19.5 cm^?1.     

A {Nb6P2W12}‐Based Hexameric Manganese Cluster with Single‐Molecule Magnet Properties

By deliberately using a metastable polyanion [(NbO₂)₆P₂W₁₂O₅₆]^12? ( 1 ), which was formed in situ, we have discovered the unprecedented hexameric cluster {Mn₁₅(Nb₆P₂W₁₂O₆₂)₆} ( 2 ), in which the six polyanions [Nb₆P₂W₁₂O₆₁]^10? are alternately connected by four intriguing trinuclear {Mn^III₃} moieties and four {Mn^II} linkers. This discovery is the first in which the phosphoniobotungstate has been made accessible by using transition‐metal ions; furthermore, polyanion 2 represents the largest niobotungstate cluster reported to date. Analysis by means of electrospray ionization mass spectrometry (ESI‐MS ) provides insight into the self‐assembly process, and the peaks observed relate to the different charge states of the parent cluster, thus confirming the stability of 2 . In addition, magnetic‐susceptibility measurements reveal that each {Mn^III₃} subunit is a separate single‐molecule magnet (SMM). This discovery results from the exploration of the reverse effect of metastable polyanion 1 possessing high reactivity, thereby turning a disadvantage into an advantage. This finding could define a new synthetic strategy for the design and synthesis of magnetic polyoxometalate (POM) clusters.     

Rational Electrostatic Design of Easy‐Axis Magnetic Anisotropy in a ZnII–DyIII–ZnII Single‐Molecule Magnet with a High Energy Barrier

Two novel trinuclear complexes [ZnCl(μ‐L)Ln(μ‐L)ClZn][ZnCl₃(CH₃OH)]?3 CH₃OH (Ln^III=Dy ( 1 ) and Er ( 2 )) have been prepared from the compartmental ligand N,N′‐dimethyl‐N,N′‐bis(2‐hydroxy‐3‐formyl‐5‐bromo‐benzyl)ethylenediamine (H₂L). X‐ray studies reveal that Ln^III ions are coordinated by two [ZnCl(L)]^? units through the phenoxo and aldehyde groups, giving rise to a LnO₈ coordination sphere with square‐antiprism geometry and strong easy‐axis anisotropy of the ground state. Ab initio CASSCF+RASSI calculations carried out on 1 confirm that the ground state is an almost pure M_J=±15/2 Kramers doublet with a marked axial anisotropy, the magnetic moment is roughly collinear with the shortest Dy?O distances. This orientation of the local magnetic moment of the Dy^III ion in 1 is adopted to reduce the electronic repulsion between the oblate electron shape of the M_J=±15/2 Kramers doublet and the phenoxo‐oxygen donor atoms involved in the shortest Dy?O bonds. CASSCF+RASSI calculations also show that the ground and first excited states of the Dy^III ion are separated by 129 cm^?1. As expected for this large energy gap, compound 1 exhibits, in a zero direct‐current field, thermally activated slow relaxation of the magnetization with a large U_eff=140 K. The isostructural Zn–Er–Zn species does not present significant SMM behavior as expected for the prolate electron‐density distribution of the Er^III ion leading to an easy‐plane anisotropy of the ground doublet state.     

Analysis of the Role of Peripheral Ligands Coordinated to ZnII in Enhancing the Energy Barrier in Luminescent Linear Trinuclear Zn‐Dy‐Zn Single‐Molecule Magnets

Three new Dy complexes have been prepared according to a complex‐as‐ligand strategy. Structural determinations indicate that the central Dy ion is surrounded by two LZn units (L^2? is the di‐deprotonated form of the N₂O₂ compartmental N,N′‐2,2‐dimethylpropylenedi(3‐methoxysalicylideneiminato) Schiff base. The Dy ions are nonacoordinate to eight oxygen atoms from the two L ligands and to a water molecule. The Zn ions are pentacoordinate in all cases, linked to the N₂O₂ atoms from L, and the apical position of the Zn coordination sphere is occupied by a water molecule or bromide or chloride ions. These resulting complexes, formulated (LZnX)‐Dy‐(LZnX), are tricationic with X=H₂O and monocationic with X=Br or Cl. They behave as field‐free single‐molecule magnets (SMMs) with effective energy barriers (U_eff) for the reversal of the magnetization of 96.9(6) K with τ₀=2.4×10^?7 s, 146.8(5) K with τ₀=9.2×10^?8 s, and 146.1(10) K with τ₀=9.9×10^?8 s for compounds with Zn?OH₂, Zn?Br, and Zn?Cl motifs, respectively. The Cole–Cole plots exhibit semicircular shapes with α parameters in the range of 0.19 to 0.29, which suggests multiple relaxation processes. Under a dc applied magnetic field of 1000 Oe, the quantum tunneling of magnetization (QTM) is partly or fully suppressed and the energy barriers increase to U_eff=128.6(5) K and τ₀=1.8×10^?8 s for 1 , U_eff=214.7 K and τ₀=9.8×10^?9 s for 2 , and U_eff=202.4 K and τ₀=1.5×10^?8 s for 3 . The two pairs of largely negatively charged phenoxido oxygen atoms with short Dy?O bonds are positioned at opposite sides of the Dy³⁺ ion, which thus creates a strong crystal field that stabilizes the axial M_J=±15/2 doublet as the ground Kramers doublet. Although the compound with the Zn?OH₂ motifs possesses the larger negative charges on the phenolate oxygen atoms, as confirmed by using DFT calculations, it exhibits the larger distortions of the DyO₉ coordination polyhedron from ideal geometries and a smaller U_eff value. Ab initio calculations support the easy‐axis anisotropy of the ground Kramers doublet and predict zero‐field SMM behavior through Orbach and TA‐QTM relaxations via the first excited Kramers doublet, which leads to large energy barriers. In accordance with the experimental results, ab initio calculations have also shown that, compared with water, the peripheral halide ligands coordinated to the Zn²⁺ ions increase the barrier height when the distortions of the DyO₉ have a negative effect. All the complexes exhibit metal‐centered luminescence after excitation into the UV π–π* absorption band of ligand L^2? at λ=335 nm, which results in the appearance of the characteristic Dy^III (⁴F_9/2→⁶H_J/2; J=15/2, 13/2) emission bands in the visible region.     

Nickel(II)–Lanthanide(III) Magnetic Exchange Coupling Influencing Single‐Molecule Magnetic Features in {Ni2Ln2} Complexes

Four isostructural [Ni₂Ln₂(CH₃CO₂)₃(HL)₄(H₂O)₂]³⁺(Ln³⁺=Dy ( 1 ), Tb ( 2 ), Ho ( 3 ) or Lu ( 4 )) complexes and a dinuclear [NiGd(HL)₂(NO₃)₃] ( 5 ) complex are reported (where HL=2‐methoxy‐6‐[(E)‐2′‐hydroxymethyl‐phenyliminomethyl]‐phenolate). For compounds 1 – 3 and 5 , the Ni²⁺ ions are ferromagnetically coupled to the respective lanthanide ions. The ferromagnetic coupling in 1 suppresses the quantum tunnelling of magnetisation (QTM), resulting in a rare zero dc field Ni–Dy single‐molecule magnet, with an anisotropy barrier U_eff of 19 K.     

A Single‐Ion Magnet Based on a Heterometallic CoIII2DyIII Complex

We report a Co^III₂Dy^III complex, which shows single‐ion‐magnet behaviour. AC susceptibility data of this compound reveals the presence of slow relaxation of the magnetization in zero‐field below 15 K. The relaxation barrier is 88 K.     

Single‐Molecule Magnetism,Enhanced Magnetocaloric Effect,and Toroidal Magnetic Moments in a Family of Ln4 Squares

Three cationic [Ln₄] squares (Ln=lanthanide) were isolated as single crystals and their structures solved as [Dy₄(μ₄‐OH)(HL)(H₂L)₃(H₂O)₄]Cl₂?(CH₃OH)₄?(H₂O)₈ ( 1 ), [Tb₄(μ₄‐OH)(HL)(H₂L)₃(MeOH)₄]Cl₂?(CH₃OH)₄?(H₂O)₄ ( 2 ) and [Gd₄(μ₄‐OH)(HL)(H₂L)₃(H₂O)₂(MeOH)₂]Br₂?(CH₃OH)₄?(H₂O)₃ ( 3 ). The structures are described as hydroxo‐centered squares of lanthanide ions, with each edge of the square bridged by a doubly deprotonated H₂L^2? ligand. Alternating current magnetic susceptibility measurements show frequency‐dependent out‐of‐phase signals with two different thermally assisted relaxation processes for 1 , whereas no maxima in χ_M“ appears above 2.0 K for complex 2 . For 1 , the estimated effective energy barrier for these two relaxation processes is 29 and 100 K. Detailed ab initio studies reveal that complex 1 possesses a toroidal magnetic moment. The ab initio calculated anisotropies of the metal ions in complex 1 were employed to simulate the magnetic susceptibility by using the Lines model (POLY_ANISO) and this procedure yields J₁=+0.01 and J₂=?0.01 cm^?1 for 1 as the two distinct exchange interactions between the Dy^III ions. Similar parameters are also obtained for complex 1 (and 2 ) from specific heat measurements. A very weak antiferromagnetic super‐exchange interaction (J₁=?0.043 cm^?1 and g=1.99) is observed between the metal centers in 3 . The magnetocaloric effect (MCE) was estimated by using field‐dependent magnetization and temperature‐dependent heat‐capacity measurements. An excellent agreement is found for the ?ΔS_m values extracted from these two measurements for all three complexes. As expected, 3 shows the largest ?ΔS_m variation (23 J Kg^?1 K^?1) among the three complexes. The negligible magnetic anisotropy of Gd indeed ensures near degeneracy in the (2S+1) ground state microstates, and the weak super‐exchange interaction facilitates dense population of low‐lying excited states, all of which are likely to contribute to the MCE, making complex 3 an attractive candidate for cryogenic refrigeration.