Designing Quantum Spaces of Higher Dimensionality from a Tetranuclear Erbium-Based Single-Molecule Magnet.

The spin relaxation of an Er3+ tetranuclear single-molecule magnet, [Er(hdcCOT)I]4, (hdcCOT = hexahydrodicyclopentacyclooctatetraenide dianion), is modeled as a near-tetrahedral arrangement of Ising-type spins. Combining evidence from single-crystal X-ray diffraction, magnetometry, and computational techniques, the slow spin relaxation is interpreted as a consequence of symmetry restrictions imposed on quantum tunneling within the cluster core. The union of spin and spatial symmetries describe a ground state spin-spin coupled manifold wherein 16 eigenvectors generate the 3D quantum spin-space described by the vertices of a rhombic dodecahedron. Analysis of the experimental findings in this context reveals a correlation between the magnetic transitions and edges connecting cubic and octahedral subsets of the eigenspace convex hull. Additionally, the model is shown to map to a theoretically proposed quantum Cayley network, indicating an underexplored synergy between mathematical descriptions of molecular spin interactions and quantum computing configuration spaces.

Dipolar Coupling as a Mechanism for Fine Control of Magnetic States in ErCOT-Alkyl Molecular Magnets.

The design of molecular magnets has progressed greatly by taking advantage of the ability to impart successive perturbations and control vibronic transitions in 4fn systems through the careful manipulation of the crystal field. Herein, we control the orientation and rigidity of two dinuclear ErCOT-based molecular magnets: the inversion-symmetric bridged [ErCOT(µ-Me)(THF)]2 (2) and the nearly linear Li[(ErCOT)2(µ-Me)3] (3). The conserved anisotropy of the ErCOT synthetic unit facilitates the direction of the arrangement of its magnetic anisotropy for the purposes of generating controlled internal magnetic fields, improving control of the energetics and transition probabilities of the electronic angular momentum states with exchange biasing via dipolar coupling. This control is evidenced through the introduction of a second thermal barrier to relaxation operant at low temperatures that is twice as large in 3 as in 2. This barrier acts to suppress through-barrier relaxation by protecting the ground state from interacting with stray local fields while operating at an energy scale an order of magnitude smaller than the crystal field term. These properties are highlighted when contrasted against the mononuclear structure ErCOT(Bn)(THF)2 (1), in which quantum tunneling of the magnetization processes dominate, as demonstrated by magnetometry and ab initio computational methods. Furthermore, far-infrared magnetospectroscopy measurements reveal that the increased rigidity imparted by successive removal of solvent ligands when adding bridging methyl groups, along with the increased excited state purity, severely limits local spin-vibrational interactions that facilitate magnetic relaxation, manifesting as longer relaxation times in 3 relative to those in 2 as temperature is increased.

Coordination Modes and Binding Patterns in Lanthanum Phosphoramide Complexes.

A monoanionic phosphoramide ligand is introduced, which forms a series of lanthanum complexes with the ligand in both anionic and neutral forms. Stoichiometric control alone provides monometallic complexes with either two or three phosphoramide ligands. Alternatively, a combination of anionic and neutral proteo ligands featuring intramolecular hydrogen bonding can be obtained. The anionic form of the ligand binds lanthanum as a bi- or monodentate ligand, depending on the steric demand at the metal center, while the protonated ligand binds exclusively through the phosphoramide oxygen donor.

A Four-Coordinate Pr4+ Imidophosphorane Complex.

The imidophosphorane ligand, [NPtBu3]- (tBu = tert-butyl), enables isolation of a pseudo-tetrahedral, tetravalent praseodymium complex, [Pr4+(NPtBu3)4] (1-Pr), which is characterized by a suite of physical characterization methods including single-crystal X-ray diffraction, electron paramagnetic resonance, and L3-edge X-ray near-edge spectroscopies. Variable-temperature direct-current magnetic susceptibility data, supported by multiconfigurational quantum chemical calculations, demonstrate that the electronic structure diverges from the isoelectronic Ce3+ analogue, driven by increased crystal field. The four-coordinate environment around Pr4+ in 1-Pr, which is unparalleled in reported extended solid systems, provides a unique opportunity to study the interplay between crystal field splitting and spin-orbit coupling in a molecular tetravalent lanthanide within a pseudo-tetrahedral coordination geometry.

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

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

Intuitive Control of Low-Energy Magnetic Excitations via Directed Dipolar Interactions in a Series of Er(III)-Based Complexes.

Dipolar coupling is rarely invoked as a driving force for slow relaxation dynamics in lanthanide-based single-molecule magnets, though it is often the strongest mechanism available for mediating inter-ion magnetic interactions in such species. Indeed, for multinuclear lanthanide complexes, the magnitude and anisotropy of the dipolar interaction can be considerable given their ability to form highly directional, high-moment ground states. Herein, we present a mono-, di-, and trinuclear erbium-based single-molecule magnet sequence, ([Er-TiPS2COT]+)n (n = 1-3), wherein a drastic reduction in the allowedness of magnetic relaxation pathways is rationalized within the framework of the dipole-dipole interactions between angular momentum quanta. The resulting design principles for multinuclear molecular magnetism arising from intramolecular dipolar coupling interactions between highly anisotropic magnetic states present a nuanced justification of the relaxation dynamics in complex manifolds of individual quantized transitions. Experimental evidence for the validity of this model is provided by coupling the relaxation dynamics to an AC magnetic field across an unprecedented frequency range for molecular magnetism (103-10-5 Hz). The combination of slow dynamics and multiple, low-energy transitions leads to a number of noteworthy phenomena, including a lanthanide single-molecule magnet with three well-defined relaxation processes observable at a single temperature.

Million-fold Relaxation Time Enhancement across a Series of Phosphino-Supported Erbium Single-Molecule Magnets.

Maintaining strong magnetic anisotropy in the presence of collective spin interactions has become a defining challenge in the advancement of single-molecule magnet (SMM) research. Herein we demonstrate effective decoupling of these often competing design goals in a series of new phosphino-supported SMMs containing the anisotropic [Er(COT)]+ (COT2- = cyclooctatetraene dianion) subunit. Across this series, a magnetic nuclearity increase from 1 to 2 and subsequent optimization of the relative local anisotropy axis orientation results in dramatic improvements to the long time scale behavior. Specifically, we observe a 6 orders of magnitude increase in relaxation time at 2 K and a consequent open magnetic hysteresis up to 6 K. This drastic scaling of the magnetic dynamics tracks monotonically with the introduction and approach to parallel of the angle between intramolecular anisotropy axes. These results illustrate the powerful implications of fully controlling direction and magnitude of anisotropy in the design of scalable SMMs.