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.

Quantifying superparamagnetic signatures in nanoparticle magnetite: a generalized approach for physically meaningful statistics and synthesis diagnostics

Magnetization is a common measurable for characterizing bulk, nanoscale, and molecular materials, which can be quantified to high precision as a function of an applied external field. These data provide detailed information about a material's electronic structure, phase purity, and impurities, though interpreting this data can be challenging due to many contributing factors. In sub-single-domain particles of a magnetic material, an inherently time-dependent rotation of the entire particle spin becomes possible. This phenomenon, known as superparamagnetism (SPM), simultaneously represents a very early size-dependent property to be considered, while being one of the least explored in the current quantum materials era. This discrepancy is, at least in part, due to the need for models with less built-in complexity that can facilitate the generation of comparative data. In this work, we map an extensive dataset of variable-size SPM Fe₃O₄ (magnetite) to an intrinsic statistical model for their field-dependence. By constraining the SPM behavior to a probabilistic model, the data are apportioned to several decorrelated sources. From this, there is strong evidence that standard measures such as saturation magnetization, M_S, are poor comparative parameters, being dependent on experimental knowledge and measurement of the magnetic mass. In contrast, parameters of the intrinsic probability distribution, such as the maximum susceptibility, χ_max, are far better suited to describe the SPM behavior itself and do not propagate unknown magnetic mass error. By confining the data fitting to intrinsic variables of the model distribution, scaling parameters, and linear contributions, we find greater value in magnetic data, ultimately aiding potential synthesis diagnostics and prediction of new properties and functionality.

Size-Tunable Magnetite Nanoparticles from Well-Defined Iron Oleate Precursors

The synthesis of iron oxide nanoparticles with control over size and shape has long been an area of research, with iron oleate being arguably the most successful precursor. Issues with reproducibility and versatility in iron oleate-based syntheses remain, however, in large part due to the mutable nature of its structure and stoichiometry. In this work, we characterize two new forms of iron oleate precursor that can be isolated in large quantities, show long-term stability, and have well-defined stoichiometry, leading to reproducible and predictable reactivity. Synthesis with these precursors is shown to produce iron oxide nanoparticles in a tunable size range of 4-16 nm with low size dispersity and properties consistent with magnetite in the superparamagnetic size regime.

Strong Electronic and Magnetic Coupling in M4 (M = Ni, Cu) Clusters via Direct Orbital Interactions between Low-Coordinate Metal Centers

We present an extensive study of tetranuclear transition-metal cluster compounds M₄(NP^tBu₃)₄ and [M₄(NP^tBu₃)₄][B(C₆F₅)₄] (M = Ni, Cu; ^tBu = tert-butyl), which feature low-coordinate metal centers and direct metal-metal orbital overlap. X-ray diffraction, electrochemical, magnetic, spectroscopic, and computational analysis elucidate the nature of the bonding interactions in these clusters and the impact of these interactions on the electronic and magnetic properties. Direct orbital overlap results in strongly coupled, large-spin ground states in the [Ni₄(NP^tBu₃)₄]^+/0 clusters and fully delocalized, spin-correlated electrons. Correlated electronic structure calculations confirm the presence of ferromagnetic ground states that arise from direct exchange between magnetic orbitals, and, in the case of the neutral cluster, itinerant electron magnetism similar to that in metallic ferromagnets. The cationic nickel cluster also possesses large magnetic anisotropy exemplified by a large, positive axial zero-field splitting parameter of D = +7.95 or +9.2 cm^-1, as determined by magnetometry or electron paramagnetic resonance spectroscopy, respectively. The [Ni₄(NP^tBu₃)₄]⁺ cluster is also the first molecule with easy-plane magnetic anisotropy to exhibit zero-field slow magnetic relaxation, and under a small applied field, it exhibits relaxation exclusively through an Orbach mechanism with a spin relaxation barrier of 16 cm^-1. The S = ¹/₂ complex [Cu₄(NP^tBu₃)₄]⁺ exhibits slow magnetic relaxation via a Raman process on the millisecond time scale, supporting the presence of slow relaxation via an Orbach process in the nickel analogue. Overall, this work highlights the unique electronic and magnetic properties that can be realized in metal clusters featuring direct metal-metal orbital interactions between low-coordinate metal centers.

Insights into Single-Molecule-Magnet Behavior from the Experimental Electron Density of Linear Two-Coordinate Iron Complexes

A breakthrough in the study of single-molecule magnets occurred with the discovery of zero-field slow magnetic relaxation and hysteresis for the linear iron(I) complex [Fe(C(SiMe₃)₃)₂]^- (1), which has one of the largest spin-reversal barriers among mononuclear transition-metal single-molecule magnets. Theoretical studies have suggested that the magnetic anisotropy in 1 is made possible by pronounced stabilization of the iron d _z² orbital due to 3d _z²-4s mixing, an effect which is predicted to be less pronounced in the neutral iron(II) complex Fe(C(SiMe₃)₃)₂ (2). However, experimental support for this interpretation has remained lacking. Here, we use high-resolution single-crystal X-ray diffraction data to generate multipole models of the electron density in these two complexes, which clearly show that the iron d _z² orbital is more populated in 1 than in 2. This result can be interpreted as arising from greater stabilization of the d _z² orbital in 1, thus offering an unprecedented experimental rationale for the origin of magnetic anisotropy in 1.

Isolation and characterization of a high-spin mixed-valent iron dinitrogen complex

We report a rare example of a mixed-valence iron compound with an FeNNFe core, which gives insight into the structural, spectroscopic, and magnetic influences of single-electron reductions and oxidations. In the new compound, the odd electron is localized as judged from Mössbauer spectra at 80 K and infrared spectra at room temperature, and the backbonding into the N2 unit is intermediate between diiron(i) and diiron(0) congeners. Magnetic susceptibility and relaxation studies on the series of FeNNFe compounds show significant magnetic anisotropy, but through-barrier pathways enable fairly rapid magnetic relaxation.

A linear cobalt(II) complex with maximal orbital angular momentum from a non-Aufbau ground state

Orbital angular momentum is a prerequisite for magnetic anisotropy, although in transition metal complexes it is typically quenched by the ligand field. By reducing the basicity of the carbon donor atoms in a pair of alkyl ligands, we synthesized a cobalt(II) dialkyl complex, Co(C(SiMe2ONaph)3)2 (where Me is methyl and Naph is a naphthyl group), wherein the ligand field is sufficiently weak that interelectron repulsion and spin-orbit coupling play a dominant role in determining the electronic ground state. Assignment of a non-Aufbau (dx2–y2, dxy)3(dxz, dyz)3(dz2)1 electron configuration is supported by dc magnetic susceptibility data, experimental charge density maps, and ab initio calculations. Variable-field far-infrared spectroscopy and ac magnetic susceptibility measurements further reveal slow magnetic relaxation via a 450–wave number magnetic excited state.

Large Anisotropy Barrier in a Tetranuclear Single-Molecule Magnet Featuring Low-Coordinate Cobalt Centers

The tetranuclear cobalt cluster compound [Co₄(μ-NP^tBu₃)₄][B(C₆F₅)₄] (^tBu = tert-butyl) was synthesized by chemical oxidation of Co₄(NP^tBu₃)₄ with [FeCp₂][B(C₆F₅)₄] and magnetically characterized to study the effect of electronic communication between low-coordinate metal centers on slow magnetic relaxation in a transition metal cluster. The dc magnetic susceptibility data reveal that the complex exhibits a well-isolated S = ⁹/₂ ground state, which persists even to 300 K and is attributed to the existence of direct metal-metal orbital overlap. The ac magnetic susceptibility data further reveals that the complex exhibits slow magnetic relaxation in the absence of an applied field, and that the relaxation dynamics can be fit with a combination of Orbach, quantum tunneling, and Raman relaxation processes. The effective spin reversal barrier for this molecule is 87 cm^-1, the largest reported to date for a transition metal cluster, and arises due to the presence of a large easy-axis magnetic anisotropy. The complex additionally exhibits waist-restricted magnetic hysteresis and magnetic blocking below 3.6 K. Taken together, these results indicate that coupling of low-coordinate metal centers is a promising strategy to enhance magnetic anisotropy and slow magnetic relaxation in transition metal cluster compounds.