Manifestation of spin selection rules on the quantum tunneling of magnetization in a single-molecule magnet

Macroscopic Quantum Tunneling of a Topological Ferromagnet

The recent advent of topological states of matter spawned many significant discoveries. The quantum anomalous Hall (QAH) effect is a prime example due to its potential for applications in quantum metrology, as well as its influence on fundamental research into the underlying topological and magnetic states and into axion electrodynamics. Here, electronic transport studies on a (V,Bi,Sb)₂ Te₃ ferromagnetic topological insulator nanostructure in the QAH regime are presented. This allows access to the dynamics of an individual ferromagnetic domain. The domain size is estimated to be in the 50-100 nm range. Telegraph noise resulting from the magnetization fluctuations of this domain is observed in the Hall signal. Careful analysis of the influence of temperature and external magnetic field on the domain switching statistics provides evidence for quantum tunneling (QT) of magnetization in a macrospin state. This ferromagnetic macrospin is not only the largest magnetic object in which QT is observed, but also the first observation of the effect in a topological state of matter.

Slowing magnetic relaxation with open-shell diluents

Strategies for slowing magnetic relaxation via local environmental design are vital for developing next-generation spin-based technologies (e.g., quantum information processing). Herein, we demonstrate a technique to do so via chemical design of a local magnetic environment. We show that embedding the open-shell complex (Ph₄P)₂[Co(SPh)₄] in solid-state matrices of the isostructural, open-shell species (Ph₄P)₂[M(SPh)₄] (M = Ni²⁺, S = 1; M = Fe²⁺, S = 2; M = Mn²⁺, S = 5 2 ) will slow magnetic relaxation for the embedded [Co(SPh)₄]^2- ion by three orders of magnitude. Magnetometry, electron paramagnetic resonance (EPR), and computational analyses reveal that integer spin and large, positive zero-field splitting (D) values for the diluent produce a quiet, local magnetic field that slows relaxation rates for the embedded Co molecules. These results will enable the investigation of magnetic systems for which strictly diamagnetic congeners are either synthetically inaccessible or are not isostructural.

Spectroscopic Investigation of a Metal-Metal-Bonded Fe6 Single-Molecule Magnet with an Isolated S = 19/2 Giant-Spin Ground State

The metal-metal-bonded molecule [Bu₄N][(^HL)₂Fe₆(dmf)₂] (Fe₆) was previously shown to possess a thermally isolated spin S = ¹⁹/₂ ground state and found to exhibit slow magnetization relaxation below a blocking temperature of ∼5 K [J. Am. Chem. Soc. 2015, 137, 13949-13956]. Here, we present a comprehensive spectroscopic investigation of this unique single-molecule magnet (SMM), combining ultrawideband field-swept high-field electron paramagnetic resonance (EPR) with frequency-domain Fourier-transform terahertz EPR to accurately quantify the spin Hamiltonian parameters of Fe₆. Of particular importance is the near absence of a 4th-order axial zero-field splitting term, which is known to arise because of quantum mechanical mixing of spin states on account of the relatively weak spin-spin (superexchange) interactions in traditional polynuclear SMMs such as the celebrated Mn₁₂-acetate. The combined high-resolution measurements on both powder samples and an oriented single crystal provide a quantitative measure of the isolated nature of the spin ground state in the Fe₆ molecule, as well as additional microscopic insights into factors that govern the quantum tunneling of its magnetization. This work suggests strategies for improving the performance of polynuclear SMMs featuring direct metal-metal bonds and strong ferromagnetic spin-spin (exchange) interactions.

Insights into Molecular Magnetism in Metal-Metal Bonded Systems as Revealed by a Spectroscopic and Computational Analysis of Diiron Complexes

A pair of bimetallic compounds featuring Fe-Fe bonds, [Fe(ⁱPrNPPh₂)₃FeR] (R = PMe₃, ≡N^tBu), have been investigated using High-Frequency Electron Paramagnetic Resonance (HFEPR) as well as field- and temperature-dependent ⁵⁷Fe nuclear γ resonance (Mössbauer) spectroscopy. To gain insight into the local site electronic structure, we have concurrently studied a compound containing a single Fe(II) in a geometry analogous to that of one of the dimer sites. Our spectroscopic studies have allowed for the assessment of the electronic structure via the determination of the zero-field splitting and ⁵⁷Fe hyperfine parameters for the entire series. We also report on our efforts to correlate structure with physical properties in metal-metal bonded systems using ligand field theory guided by quantum chemical calculations. Through the insight gained in this study, we discuss strategies for the design of single-molecule magnets based on polymetallic compounds linked via direct metal-metal bonds.

Magnetization relaxation in the single-ion magnet DySc2N@C80: quantum tunneling, magnetic dilution, and unconventional temperature dependence

Quantum tunneling and relaxation of magnetization in single molecule magnet DySc₂N@C₈₀ is thoroughly studied as a function of magnetic dilution, temperature, and magnetic field.

Relaxation of magnetization in endohedral metallofullerenes DySc₂N@C₈₀ is studied at different temperatures, in different magnetic fields, and in different molecular arrangements. Magnetization behavior and relaxation are analyzed for powder sample, and for DySc₂N@C₈₀ diluted in non-magnetic fullerene Lu₃N@C₈₀, adsorbed in voids of a metal–organic framework, and dispersed in a polymer. The magnetic field dependence and zero-field relaxation are also studied for single-crystals of DySc₂N@C₈₀ co-crystallized with Ni(ii) octaethylporphyrin, as well as for the single crystal diluted with Lu₃N@C₈₀. Landau–Zener theory is applied to analyze quantum tunneling of magnetization in the crystals. The field dependence of relaxation rates revealed a dramatic dependence of the zero-field tunneling resonance width on the dilution and is explained with the help of an analysis of dipolar field distributions. AC magnetometry is used then to get access to the relaxation of magnetization in a broader temperature range, from 2 to 87 K. Finally, a theoretical framework describing the spin dynamics with dissipation is proposed to study magnetization relaxation phenomena in single molecule magnets.

Construction of Giant-Spin Hamiltonians from Many-Spin Hamiltonians by Third-Order Perturbation Theory and Application to an Fe3 Cr Single-Molecule Magnet

A general giant-spin Hamiltonian (GSH) describing an effective spin multiplet of an exchange-coupled metal cluster with dominant Heisenberg interactions was derived from a many-spin Hamiltonian (MSH) by treating anisotropic interactions at the third order of perturbation theory. Going beyond the existing second-order perturbation treatment allows irreducible tensor operators of rank six (or corresponding Stevens operator equivalents) in the GSH to be obtained. Such terms were found to be of crucial importance for the fitting of high-field EPR spectra of a number of single-molecule magnets (SMMs). Also, recent magnetization measurements on trigonal and tetragonal SMMs have found the inclusion of such high-rank axial and transverse terms to be necessary to account for experimental data in terms of giant-spin models. While mixing of spin multiplets by local zero-field splitting interactions was identified as the major origin of these contributions to the GSH, a direct and efficient microscopic explanation had been lacking. The third-order approach developed in this work is used to illustrate the mapping of an MSH onto a GSH for an S=6 trigonal Fe3 Cr complex that was recently investigated by high-field EPR spectroscopy. Comparisons between MSH and GSH consider the simulation of EPR data with both Hamiltonians, as well as locations of diabolical points (conical intersections) in magnetic-field space. The results question the ability of present high-field EPR techniques to determine high-rank zero-field splitting terms uniquely, and lead to a revision of the experimental GSH parameters of the Fe3 Cr SMM. Indeed, a bidirectional mapping between MSH and GSH effectively constrains the number of free parameters in the GSH. This notion may in the future facilitate spectral fitting for highly symmetric SMMs.

General magnetic transition dipole moments for electron paramagnetic resonance

We present general expressions for the magnetic transition rates in electron paramagnetic resonance (EPR) experiments of anisotropic spin systems in the solid state. The expressions apply to general spin centers and arbitrary excitation geometry (Voigt, Faraday, and intermediate). They work for linear and circular polarized as well as unpolarized excitation, and for crystals and powders. The expressions are based on the concept of the (complex) magnetic transition dipole moment vector. Using the new theory, we determine the parities of ground and excited spin states of high-spin (S=5/2) Fe(III) in hemin from the polarization dependence of experimental EPR line intensities.

Three-leaf quantum interference clovers in a trigonal single-molecule magnet

We report on a single-molecule magnet where the spatial arrangement of three manganese ions and their spin-orbit coupling tensor orientations result in threefold angular modulations of the magnetization tunneling rates and quantum interference patterns that mimic the form of a three-leaf clover. Although expected in all quantum tunneling of magnetization resonances for a trigonal molecular symmetry, the threefold modulation only appears at resonances for which a longitudinal magnetic field is applied (i.e., resonance numbers |k|>0). A sixfold transverse field modulation observed at resonance k = 0 manifests as a direct consequence of a threefold corrugation of the spin-orbit coupling energy landscape, creating an effective longitudinal field which varies the resonance condition in the presence of a transverse field. The observations allow for an association between the trigonal distortion of the local spin-orbit interactions and the spatial disposition of the constituent ions, a finding that can be extrapolated to other systems where spin-orbit coupling plays a significant role.

A family of enantiopure FeIII4 single molecule magnets: fine tuning of energy barrier by remote substituent

We report a new family of enantiopure star-shaped Fe^III₄ single-molecule magnets (SMMs). Interestingly, the SMM properties of this series of clusters can be finely tuned by the remote substituent of the ligands.

A mononuclear Fe(III) single molecule magnet with a 3/2↔5/2 spin crossover

The air stable complex [(PNP)FeCl(2)] (1) (PNP = N[2-P(CHMe(2))(2)-4-methylphenyl](2)(-)), prepared from one-electron oxidation of [(PNP)FeCl] with ClCPh(3), displays an unexpected S = 3/2 to S = 5/2 transition above 80 K as inferred by the dc SQUID magnetic susceptibility measurement. The ac SQUID magnetization data, at zero field and between frequencies 10 and 1042 Hz, clearly reveal complex 1 to have frequency dependence on the out-of-phase signal and thus being a single molecular magnet with a thermally activated barrier of U(eff) = 32-36 cm(-1) (47-52 K). Variable-temperature Mössbauer data also corroborate a significant temperature dependence in δ and ΔE(Q) values for 1, which is in agreement with the system undergoing a change in spin state. Likewise, variable-temperature X-band EPR spectra of 1 reveals the S = 3/2 to be likely the ground state with the S = 5/2 being close in energy. Multiedge XAS absorption spectra suggest the electronic structure of 1 to be highly covalent with an effective iron oxidation state that is more reduced than the typical ferric complexes due to the significant interaction of the phosphine groups in PNP and Cl ligands with iron. A variable-temperature single crystal X-ray diffraction study of 1 collected between 30 and 300 K also reveals elongation of the Fe-P bond lengths and increment in the Cl-Fe-Cl angle as the S = 5/2 state is populated. Theoretical studies show overall similar orbital pictures except for the d(z(2)) orbital, which has the most sensitivity to change in the geometry and bonding, where the quartet ((4)B) and the sextet ((6)A) states are close in energy.

Two-dimensional 3d-4f networks containing planar Co4Ln2 clusters with single-molecule-magnet behaviors

Two novel two-dimensional 3d-4f networks based on planar Co(4)Ln(2) clusters supported by rigid 4'-(4-carboxyphenyl)-2,2':6',2"-terpyridine afford the first examples of high-dimensional networks with 3d-4f clusters behaving as single-molecule magnets.

Asymmetric Berry-phase interference patterns in a single-molecule magnet

A Mn(4) single-molecule magnet displays asymmetric Berry-phase interference patterns in the transverse-field (H(T)) dependence of the magnetization tunneling probability when a longitudinal field (H(L)) is present, contrary to symmetric patterns observed for H(L)=0. Reversal of H(L) results in a reflection of the transverse-field asymmetry about H(T)=0, as expected on the basis of the time-reversal invariance of the spin-orbit Hamiltonian which is responsible for the tunneling oscillations. A fascinating motion of Berry-phase minima within the transverse-field magnitude-direction phase space results from a competition between noncollinear magnetoanisotropy tensors at the two distinct Mn sites.