Building Molecular Nanomagnets by Encapsulating Lanthanide Ions in Boron Nitride Nanotubes: Ab Initio Investigation.

Lanthanide-based single-ion magnets have attracted much interest due to their great potential for information storage at the level of one molecule. Among various strategies to enhance magnetization blocking in such complexes, the synthesis of axially symmetric compounds is regarded as the most promising. Here, we investigate theoretically the magnetization blocking of several lanthanide ions (Tb3+, Dy3+, Ho3+, Er3+, and Tm3+) encapsulated in highly symmetric zigzag boron nitride nanotubes (BNNTs) of different diameters with ab initio methodology. We found that Tb3+@(7,0)BNNT, Dy3+@(7,0)BNNT, and Tm3+@(5,0)BNNT are suitable SIM candidates, while the other investigated complexes from this series show no signs of magnetization blocking owing to a hard competition between contributions to the crystal field of the lanthanide ion from neighboring and more distant atoms of the nanotube.

Increasing the Magnetic Blocking Temperature of Single-Molecule Magnets.

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

A High-Performance Single-Molecule Magnet Utilizing Dianionic Aminoborolide Ligands.

The first example of a homoleptic f-block borolide sandwich complex is presented and shown to be a high-performance single-molecule magnet (SMM). The bis(borolide) complex [K(2.2.2)][[1-(piperidino)-2,3,4,5-tetraphenylborolyl]2Dy] (1) features an unusual example of an anionic Ln3+ metallocene that supports short metal-ligand bonds and a high degree of linearity around the central Dy3+ ion, resulting in comparatively large barriers to magnetization reversal (Ueff = 1600 cm-1 for the most linear orientation) and, importantly, a high blocking temperature (TB, defined as T(τ100s)) of 66 K. These metrics put complex 1 among the very best performing SMMs reported to date and highlight the potential of dianionic borolide ligands to increase ligand field axiality, compared to monoanionic cyclic ligands, to ultimately maximize magnetic anisotropy in f-block-based SMMs.

Mechanisms of Luminescence in Lanthanide Complexes: A Crucial Role of Metal-Ligand Covalency.

A current understanding of the luminescence of lanthanide complexes is based on the phenomenological Judd-Ofelt (JO) theory. However, the mechanisms of electric-dipole transitions lying at its basis were never subjected to a rigorous analysis. Here, we investigate the contributions to the electric-dipole transitions in the Er3+ 4S3/2 → 4I15/2 band of an erbium trensal complex using state-of-the-art ab initio calculations. We find that the conventional JO mechanism based on the electrostatic crystal field yields only a quarter of the integral intensity of this band. Accordingly, three quarters of it is contributed by covalent binding of erbium and ligand orbitals via three major mechanisms, the 4f ligand and ligand-ligand electric-dipole transitions and covalent enhancement of the hybridization of 4f and even empty orbitals of erbium. We expect that these findings will inspire the design of efficient rare-earth luminescent materials.

Coexistence of Spin-Lattice Relaxation and Phonon-Bottleneck Processes in GdIII -Phthlocyaninato Triple-Decker Complexes under Highly Diluted Conditions.

Gd3+ complexes have been shown to undergo unusual slow magnetic relaxation processes similar to those of single-molecule magnets (SMMs), even though Gd3+ does not exhibit strong magnetic anisotropy. To reveal the origin of the slow magnetic relaxation of Gd3+ complexes, we have investigated the magnetic properties and heat capacities of two Gd3+ -phthalocyaninato triple-decker complexes, one of which has intramolecular Gd3+ -Gd3+ interactions and the other does not. It was found that the Gd3+ -Gd3+ interactions accelerate the magnetic relaxation processes. In addition, magnetically diluted samples, prepared by doping a small amount of the Gd3+ complexes into a large amount of diamagnetic Y3+ complexes, underwent dual magnetic relaxation processes. A detailed dynamic magnetic analysis revealed that the coexistence of spin-lattice relaxation and phonon-bottleneck processes is the origin of the dual magnetic relaxation processes.

An Inconspicuous Six-Coordinate Neutral DyIII Single-Ion Magnet with Remarkable Magnetic Anisotropy and Stability.

It is a crucial challenge to address both magnetic anisotropy and stability for single-molecule magnets (SMMs) used in next-generation nanodevices. Highly axial lanthanide SMMs with neutral charge and moderate coordination numbers represent promising magnetic materials. Here, using iodide ions with large volume and low surface charge density as weak donors, we report a six-coordinate neutral dysprosium SMM [Dy(Cy3PO)2I3(CH3CN)] with a certain degree of stability exhibiting a huge thermal barrier of 1062 K and hysteresis loops open up to 9 K. Through the elaborate reduction of ligand field strength, an apparent strongly axial crystal field is provided which elicits prominent crystal-field splitting and high axiality with the thermally activated relaxation via the third-excited Kramers' doublet. Moreover, the profound influence of strong equatorial ligand substitution on the electronic structure and relaxation pathway is clearly explored in DyIII analogues. The result suggests the great potential of the reducing the transverse ligand field in the improvement of SMMs performance.

Modern quantum chemistry with [Open]Molcas.

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions.

Magnetic Anisotropy in Divalent Lanthanide Compounds.

Complexes of trivalent lanthanides (Ln) are known to possess strong magnetic anisotropy, which enables them to be efficient single-molecule magnets. High-level ab initio calculations are reported for [LnO] (where Ln is terbium (Tb), dysprosium (Dy), or holmium (Ho)), which show that divalent lanthanides can exhibit equally strong magnetic anisotropy and magnetization blocking barriers. In particular, detailed calculations predict a multilevel magnetization blocking barrier exceeding 3000 K for a [DyO] complex deposited on a hexagonal boron nitride (h-BN) surface, bringing the expected performance of single-molecule magnets to a qualitatively new level compared to the current state-of-the art complexes.

Axial Elongation of Mononuclear Lanthanide Metallocenophanes: Magnetic Properties of Dysprosium- and Terbium-[1]Ruthenocenophane Complexes.

We report the first f-block-ruthenocenophane complexes 1 (Dy) and 2 (Tb) and provide a comparative discussion of their magnetic structure with respect to earlier reported ferrocenophane analogues. While axial elongation of the rare trigonal-prismatic geometry stabilizes the magnetic ground state in the case of Dy3+ and results in a larger barrier to magnetization reversal (U), a decrease in U is observed for the case of Tb3+ .

Dysprosium Single-Molecule Magnets with Bulky Schiff Base Ligands: Modification of the Slow Relaxation of the Magnetization by Substituent Change.

The synthesis, and magnetic and photoluminescence investigations of two bifunctional dysprosium complexes based on tridentate Schiff base ligands is reported. Magnetic investigations reveal a genuine single-molecule magnet (SMM) behavior, with out-of-phase signals up to 60 K, and tunable emission arising from the Schiff base ligands.

Effects of the Exchange Coupling on Dynamic Properties in a Series of CoGdCo Complexes.

Reaction of 2-hydroxy3-methoxybenzaldehyde ( o-vanillin) with 1,1,1-tris(aminomethyl)ethane, Me-C(CH2NH2)3, or with N, N', N''-trimethylphosphorothioic trihydrazide, P(S)[NMe-NH2]3, yields two tripodal LH3 and L1H3 ligands which are able to give cationic heterotrinuclear [LCoGdCoL]+ or [L1CoGdCoL1]+ complexes. The CoII ions are coordinated to these deprotonated ligands in the inner N3O3 site, while the GdIII ion is linked to three deprotonated phenoxo oxygen atoms of two anionic [LCo]- or [L1Co]- units. Air oxidation of these trinuclear complexes does not yield complexes associating CoIII and GdIII ions. With the first ligand, the structurally characterized resulting complex is the neutral mononuclear LCoIII compound, while in the second case, oxidation of the CoII ions turned out to be impossible. The [L1CoLnCoL1]+ complexes behave as single-molecule magnets with effective energy barriers for the reversal of magnetization varying from Ueff = 51.3 K, τo = 2 × 10-6 s for the yttrium complex to Ueff = 29.5, 29.4, 27.4 K and τo = 1.3 × 10-7, 1.47 × 10-7, 1.50 × 10-7 s for the gadolinium ones, depending on the used counteranions. The energy decrease is compensated by the suppression of quantum tunneling of magnetization in absence of applied field, thanks to the introduction of a ferromagnetic Co-Gd interaction. Current work also shows that uncritical use of conventional spin Hamiltonians, based on quenched orbital momenta, can be misleading and that ab initio calculations are indispensable for establishing the picture of real magnetic interaction. Ab initio calculations show that the CoII sites in the investigated compounds possess large unquenched orbital moments due to the first-order spin-orbit coupling resulting in strongly axial magnetic anisotropy. Although the CoII ions are not axial enough for showing slow relaxation of magnetization by themselves, blocking barriers of exchange type are obtained thanks to the exchange interaction with GdIII ions.

Exchange Interactions Switch Tunneling: A Comparative Experimental and Theoretical Study on Relaxation Dynamics by Targeted Metal Ion Replacement.

The magnetic relaxation and magnetization blocking barriers of tailor-made homo- and heterodinuclear compounds [Dy2 (opch)2 (OAc)2 (H2 O)2 ]⋅MeOH (1) and [DyMn(opch)2 (OAc)(MeOH)(H2 O)2 ] (2), where H2 opch is (E)-N'-(2-hydroxy-3-methoxybenzylidene)pyrazine-2-carbohydrazide, were systematically investigated and the change in single-molecule magnet behavior originating from targeted replacement of one dysprosium site in the Dy2 compound with manganese was elucidated through a combination of experimental and theoretical studies. A detailed comparative study on these closely related model compounds revealed remarkable changes of the crystal-field splitting and anisotropy of the Dy site and the total exchange spectrum due to the replacement of Dy by Mn. The blocking barriers of these two compounds, which explain their different relaxation behaviors, were analyzed. The two Ising doublets arising from the magnetic interaction in the case of 1 are strongly uniaxial, with tunneling splittings smaller than 10-6  cm-1 , and this leads to magnetic relaxation at temperatures exceeding the exchange energy (2.14 cm-1 ), which involves transition via the excited states corresponding to local transitions on the excited doublet at the Dy site. The third and fourth exchange doublets in 2 (located at 2.16 and 3.25 cm-1 , respectively) show much larger tunneling splittings (of 10-4 and 10-3  cm-1 , respectively), and thus open an important path for magnetic relaxation.

Magnetization Blocking in Fe2 III Dy2 III Molecular Magnets: Ab Initio Calculations and EPR Spectroscopy.

The magnetism and magnetization blocking of a series of [Fe2 Dy2 (OH)2 (teaH)2 (RC6 H4 COO)6 ] complexes was investigated, in which teaH3 =triethanolamine and R=meta-CN (1), para-CN (2), meta-CH3  (3), para-NO2  (4) and para-CH3  (5), by combining ab initio calculations and EPR measurements. The results of broken-symmetry DFT calculations show that in all compounds the Fe-Fe exchange interaction is antiferromagnetic and stronger by far than the Fe-Dy and Dy-Dy interactions. As a result, the lowest two exchange doublets probed by EPR spectroscopy mostly originate from the Ising interaction of the dysprosium ions in all compounds. A correct quantitative description of the splitting of these two doublets requires, however, an explicit account of the Fe-Dy and Fe-Fe interactions. Due to the inversion symmetry of the complexes, the doublets under consideration are described by a collinear Ising exchange interaction. This picture is also supported by the EPR spectra, which could be simulated with parameters close to those extracted from the calculations. The magneto-structural analysis shows an increase of the antiferromagnetic Fe-Fe exchange interaction with increasing Fe-O-Fe angle and Fe-Fe distance. For the Dy-Fe interaction, the opposite tendency is observed, that is, a decrease of antiferromagnetic exchange coupling with increasing Dy-O-Fe angle and Dy-Fe distance. The transversal g factors extracted from the ab initio calculations have values in the range of 0.01-0.2, testifying to the lack of high axiality of the ground state of the dysprosium ions. This explains the lack/poor single-molecule magnetic behavior of this series of compounds at the investigated temperatures of a few Kelvin. Due to a very small gap (fractions of a wavenumber) between the ground and first-excited exchange doublet, relaxation takes place by magnetic moment reversal at individual dysprosium sites in the considered temperature domain.

Coupling Influences SMM Properties for Pure 4 f Systems.

Increasing both the energy barrier for magnetization reversal and the coercive field of the hysteresis loop are significant challenges in the field of single-molecule magnets (SMMs). Coordination geometries of lanthanide ions and magnetic interactions between lanthanide ions are both important for guiding the magnetic behavior of SMMs. We report a high energy barrier of 657 K (457 cm-1 ) in a diamagnetic-ion-diluted lanthanide chain compound with a constrained bisphenoid symmetry (D2d ); this energy barrier is substantially higher than the barrier of 567 K (394 cm-1 ) of the non-diluted chain compound with intrachain ferromagnetic interactions. Although intrachain magnetic interaction lowers the energy barrier for magnetization reversal, it can greatly enhance the coercive fields and zero-field remanence of the hysteresis loops, which is crucial for the rational design of high-performance SMMs. Factors related to the coordination sphere of the lanthanide center, which govern the high magnetic relaxation barriers through the second excited Kramer's doublets and the magnetic interactions that affect the hysteresis loops, were revealed through ab initio calculations.

Magnetic Properties of a Terbium-[1]Ferrocenophane Complex: Analogies between Lanthanide-Ferrocenophane and Lanthanide-Bis-phthalocyanine Complexes.

A rare example of an organometallic terbium single-ion magnet is reported. A Tb3+ -[1]ferrocenophane complex displays a larger barrier to magnetization reversal than its isostructural Dy3+ analogue, which is reminiscent of trends observed for lanthanide-bis-phthalocyanine complexes. Detailed ab initio calculations support the experimental observations and suggest a significantly larger ground-state stabilization for the non-Kramers ion Tb3+ in the Tb complex than for the Kramers-ion Dy3+ in the Dy complex.

Ab Initio Crystal Field for Lanthanides.

An ab initio methodology for the first-principle derivation of crystal-field (CF) parameters for lanthanides is described. The methodology is applied to the analysis of CF parameters in [Tb(Pc)2 ]- (Pc=phthalocyanine) and Dy4 K2 ([Dy4 K2 O(OtBu)12 ]) complexes, and compared with often used approximate and model descriptions. It is found that the application of geometry symmetrization, and the use of electrostatic point-charge and phenomenological CF models, lead to unacceptably large deviations from predictions based on ab initio calculations for experimental geometry. It is shown how the predictions of standard CASSCF (Complete Active Space Self-Consistent Field) calculations (with 4f orbitals in the active space) can be systematically improved by including effects of dynamical electronic correlation (CASPT2 step) and by admixing electronic configurations of the 5d shell. This is exemplified for the well-studied Er-trensal complex (H3 trensal=2,2',2"-tris(salicylideneimido)trimethylamine). The electrostatic contributions to CF parameters in this complex, calculated with true charge distributions in the ligands, yield less than half of the total CF splitting, thus pointing to the dominant role of covalent effects. This analysis allows the conclusion that ab initio crystal field is an essential tool for the decent description of lanthanides.

Dynamic Magnetic and Optical Insight into a High Performance Pentagonal Bipyramidal DyIII Single-Ion Magnet.

The pentagonal bipyramidal single-ion magnets (SIMs) are among the most attractive prototypes of high-performance single-molecule magnets (SMMs). Here, a fluorescence-active phosphine oxide ligand CyPh2 PO (=cyclohexyl(diphenyl)phosphine oxide) was introduced into [Dy(CyPh2 PO)2 (H2 O)5 ]Br3 ⋅2 (CyPh2 PO)⋅EtOH⋅3 H2 O, and combined dynamic magnetic measurement, optical characterization, ab initio calculation, and magneto-optical correlation of this high-performance pseudo-D5h DyIII SIM with large Ueff (508(2) K) and high magnetic hysteresis temperature (19 K) were performed. This work provides a deeper insight into the rational design of promising molecular magnets.

Interplay of spin-dependent delocalization and magnetic anisotropy in the ground and excited states of [Gd2@C78]- and [Gd2@C80].

The magnetic properties and electronic structure of the ground and excited states of two recently characterized endohedral metallo-fullerenes, [Gd2@C78]- (1) and [Gd2@C80]- (2), have been studied by theoretical methods. The systems can be considered as [Gd2]5+ dimers encapsulated in a fullerene cage with the fifteen unpaired electrons ferromagnetically coupled into an S = 15/2 high-spin configuration in the ground state. The microscopic mechanisms governing the Gd-Gd interactions leading to the ferromagnetic ground state are examined by a combination of density functional and ab initio calculations and the full energy spectrum of the ground and lowest excited states is constructed by means of ab initio model Hamiltonians. The ground state is characterized by strong electron delocalization bordering on a σ type one-electron covalent bond and minor zero-field splitting (ZFS) that is successfully described as a second order spin-orbit coupling effect. We have shown that the observed ferromagnetic interaction originates from Hund's rule coupling and not from the conventional double exchange mechanism. The calculated ZFS parameters of 1 and 2 in their optimized geometries are in qualitative agreement with experimental EPR results. The higher excited states display less electron delocalization, but at the same time they possess unquenched first-order angular momentum. This leads to strong spin-orbit coupling and highly anisotropic energy spectrum. The analysis of the excited states presented here constitutes the first detailed study of the effects of spin-dependent delocalization in the presence of first order orbital angular momentum and the obtained results can be applied to other mixed valence lanthanide systems.

Hyperfine-Interaction-Driven Suppression of Quantum Tunneling at Zero Field in a Holmium(III) Single-Ion Magnet.

An extremely rare non-Kramers holmium(III) single-ion magnet (SIM) is reported to be stabilized in the pentagonal-bipyramidal geometry by a phosphine oxide with a high energy barrier of 237(4) cm-1 . The suppression of the quantum tunneling of magnetization (QTM) at zero field and the hyperfine structures originating from field-induced QTMs can be observed even from the field-dependent alternating-current magnetic susceptibility in addition to single-crystal hysteresis loops. These dramatic dynamics were attributed to the combination of the favorable crystal-field environment and the hyperfine interactions arising from 165 Ho (I=7/2) with a natural abundance of 100 %.

A Stable Pentagonal Bipyramidal Dy(III) Single-Ion Magnet with a Record Magnetization Reversal Barrier over 1000 K.

Single-molecule magnets (SMMs) with a large spin reversal barrier have been recognized to exhibit slow magnetic relaxation that can lead to a magnetic hysteresis loop. Synthesis of highly stable SMMs with both large energy barriers and significantly slow relaxation times is challenging. Here, we report two highly stable and neutral Dy(III) classical coordination compounds with pentagonal bipyramidal local geometry that exhibit SMM behavior. Weak intermolecular interactions in the undiluted single crystals are first observed for mononuclear lanthanide SMMs by micro-SQUID measurements. The investigation of magnetic relaxation reveals the thermally activated quantum tunneling of magnetization through the third excited Kramers doublet, owing to the increased axial magnetic anisotropy and weaker transverse magnetic anisotropy. As a result, pronounced magnetic hysteresis loops up to 14 K are observed, and the effective energy barrier (Ueff = 1025 K) for relaxation of magnetization reached a breakthrough among the SMMs.