Half-Integer Spin Triangles: Old Dogs, New Tricks

Probing spin-electric transitions in a molecular exchange qubit

Electric fields represent an ideal means for controlling spins at the nanoscale and, more specifically, for manipulating protected degrees of freedom in multispin systems. Here we perform low-temperature magnetic far-IR spectroscopy on a molecular spin triangle (Fe3) and provide initial experimental evidence suggesting spin-electric transitions in polynuclear complexes. The co-presence of electric- and magnetic-dipole transitions, allows us to estimate the spin-electric coupling. Based on spin Hamiltonian simulations of the spectra, we identify the observed transitions and introduce the concept of a generalized exchange qubit. This applies to a wide class of molecular spin triangles, and includes the scalar chirality and the partial spin sum qubits as special cases.

Matrix effects on the magnetic properties of a molecular spin triangle embedded in a polymeric film

Molecular triangles with competing Heisenberg interactions and significant Dzyaloshinskii-Moriya interactions (DMI) exhibit high environmental sensitivity, making them potential candidates for active elements for quantum sensing. Additionally, these triangles exhibit magnetoelectric coupling, allowing their properties to be controlled using electric fields. However, the manipulation and deposition of such complexes pose significant challenges. This work explores a solution by embedding iron-based molecular triangles in a polymer matrix, a strategy that offers various deposition methods. We investigate how the host matrix alters the magnetic properties of the molecular triangle, with specific focus on the magnetic anisotropy, aiming to advance its practical applications as quantum sensors.

A Trinuclear High-Spin Iron(III) Complex with a Geometrically Frustrated Spin Ground State Featuring Negligible Magnetic Anisotropy and Antisymmetric Exchange

The trinuclear high-spin iron(III) complex [Fe₃Cl₃(saltag^Br)(py)₆]ClO₄ {H₅saltag^Br = 1,2,3-tris[(5-bromo-salicylidene)amino]guanidine} was synthesized and characterized by several experimental and theoretical methods. The iron(III) complex exhibits molecular 3-fold symmetry imposed by the rigid ligand backbone and crystallizes in trigonal space group P3̅ with the complex cation lying on a crystallographic C₃ axis. The high-spin states (S = ⁵/₂) of the individual iron(III) ions were determined by Mößbauer spectroscopy and confirmed by CASSCF/CASPT2 ab initio calculations. Magnetic measurements show an antiferromagnetic exchange between the iron(III) ions leading to a geometrically spin-frustrated ground state. This was complemented by high-field magnetization experiments up to 60 T, which confirm the isotropic nature of the magnetic exchange and negligible single-ion anisotropy for the iron(III) ions. Muon-spin relaxation experiments were performed and further prove the isotropic nature of the coupled spin ground state and the presence of isolated paramagnetic molecular systems with negligible intermolecular interactions down to 20 mK. Broken-symmetry density functional theory calculations are consistent with the antiferromagnetic exchange between the iron(III) ions within the presented trinuclear high-spin iron(III) complex. Ab initio calculations further support the absence of appreciable magnetic anisotropy (D = 0.086, and E = 0.010 cm^-1) and the absence of significant contributions from antisymmetric exchange, as the two Kramers doublets are virtually degenerate (ΔE = 0.005 cm^-1). Therefore, this trinuclear high-spin iron(III) complex should be an ideal candidate for further investigations of spin-electric effects arising exclusively from the spin chirality of a geometrically frustrated S = ¹/₂ spin ground state of the molecular system.

An Open-Cuboidal [Fe3S4] Cluster Characterized in Both Biologically Relevant Redox States

Synthetic analogues of the three common types of Fe-S clusters found in biology─diamond-core [Fe₂S₂] clusters, open-cuboidal [Fe₃S₄] clusters, and cuboidal [Fe₄S₄] clusters─have been reported in each biologically relevant redox state with one exception: the open-cuboidal [Fe₃S₄]⁺ cluster. Here, we describe the synthesis and characterization of an open-cuboidal [Fe₃S₄] cluster in both biologically relevant redox states: [Fe₃S₄]⁺ and [Fe₃S₄]⁰. Like their biological counterparts, the oxidized cluster has a spin-canted, S = ¹/₂ ground state, and the reduced cluster has an S = 2 ground state. Structural analysis reveals that the [Fe₃S₄] core undergoes substantial contraction upon oxidation, in contrast to the minimal structural changes observed for the only [Fe₃S₄] protein for which high-resolution structures are available in both redox states (Azotobacter vinelandii ferredoxin I; Av FdI). This difference between the synthetic models and Av FdI is discussed in the context of electron transfer by [Fe₃S₄] proteins.

Antisymmetric Spin Exchange in a μ-1,2-Peroxodicopper(II) Complex with an Orthogonal Cu-O-O-Cu Arrangement and S = 1 Spin Ground State Characterized by THz-EPR

A unique type of Cu₂/O₂ adduct with orthogonal (close to 90°) Cu-O-O-Cu arrangement has been proposed for initial stages of O₂ binding at biological type III dicopper sites, and targeted ligand design has now allowed us to emulate such an adduct in a pyrazolate-based μ-η¹ :η¹-peroxodicopper(II) complex (2) with Cu-O-O-Cu torsion φ of 87°, coined ^⊥ P intermediate. Full characterization of 2, including X-ray diffraction (d _O-O = 1.452 Å) and Raman spectroscopy (ν̃_O-O = 807 cm^-1), completes a series of closely related Cu₂/O₂ intermediates featuring μ-η¹ :η¹-peroxodicopper(II) cores with φ ranging from 55° (A, cis-peroxo ^C P; Brinkmeier A.et al., J. Am. Chem. Soc.2021, 143, 10361) via 87° (2, ^⊥ P type) up to 104° (B, approaching trans-peroxo ^T P; Kindermann N.et al., Angew. Chem., Int. Ed.2015, 54, 1738). SQUID magnetometry revealed ferromagnetic interaction of the Cu^II ions and a triplet (S _t = 1) ground state in 2. Frequency-domain THz-EPR has been employed to quantitatively investigate the spin systems of 2 and B. Magnetic transitions within the triplet ground states confirmed their substantial zero-field splittings (ZFS) suggested by magnetometry. Formally forbidden triplet-to-singlet transitions at 56 (2) and 157 cm^-1 (B), which are in agreement with the exchange coupling strengths J _iso inferred from SQUID data, are reported for the first time for coupled dicopper(II) complexes. Rigorous analysis by spin-Hamiltonian-based simulations attributed the corresponding nonzero transition probabilities and the ZFS to substantial antisymmetric (Dzyaloshinskii-Moriya) exchange d and provided robust values and orientations for the d , J , and g tensors. These interactions can be correlated with the Cu-O-O-Cu geometries, revealing a linear increase of J _iso with the Cu-O-O-Cu torsion and a strong linear decrease with the Cu-O-O angle. Relevance of the ^⊥ P intermediate for O₂ activation at type III dicopper sites and a potential role of antisymmetric exchange in the concomitant intersystem crossing are proposed.

Weak Antiferromagnetic Exchange and Ferromagnetic Alignment of FeII (S=2) Spins in Differently Charged {HAT ⋅ (FeII Cl2 )3 }n (n=2- and 3-) Assemblies of Hexaazatriphenylenes (HAT)

Hexaazatrianthracene (HATA) and hexaazatriphenylenehexacarbonitrile {HAT(CN)₆ } are reduced by metallic iron in the presence of crystal violet (CV⁺ )(Cl^- ). Anionic ligands are produced, which simultaneously coordinate three Fe^II Cl₂ to form (CV⁺ )₂ {HATA ⋅ (Fe^II Cl₂ )₃ }^2-  ⋅ 3 C₆ H₄ Cl₂ (1) and (CV⁺ )₃ {HAT(CN)_6. (Fe^II Cl₂ )₃ }^3-  ⋅ 0.5CVCl ⋅ 2.5 C₆ H₄ Cl₂ (2). High-spin (S=2) Fe^II atoms in both structures are arranged in equilateral triangles at a distance of 7 Å. An antiferromagnetic exchange is observed between Fe^II in {HATA ⋅ (Fe^II Cl₂ )₃ }^2- (1) with a Weiss temperature (Θ) of -80 K, the PHI estimated exchange interaction (J) is -4.7 cm^-1 . The {HAT(CN)₆  ⋅ (Fe^II Cl₂ )₃ }^3- assembly is obtained in 2. The formation of HAT(CN)₆ ^.3- is supported by the appearance of an intense EPR signal with g=2.0037. The magnetic behavior of 2 is described by a strong antiferromagnetic coupling between the Fe^II and HAT(CN)₆ ^.3- spins with J₁ =-164 cm^-1 (-2 J formalism) and by a weaker antiferromagnetic coupling between the Fe^II spins with J₂ =-15.4 cm^-1 . The stronger coupling results in the spins of the three Fe^II Cl₂ units to be aligned parallel to each other in the assembly. As a result, an increase of the χ_M T values is observed with the decrease of temperature from 9.82 at 300 K up to 15.06 emu ⋅ K/mol at 6 K, and the Weiss temperature is also positive being at +23 K. Thus, a change in the charge and spin state of the HAT-type ligand to ⋅3^- results in ferromagnetic alignment of the Fe^II spins, yielding a high-spin (S=11/2) system. DFT calculations showed that, due to the high symmetry and nearly degenerated LUMO of both HATA and HAT(CN)₆ , their complexes with Fe^II Cl₂ have a variety of closely lying excited high-spin states with multiplicity up to S=15/2.

Observation and deconvolution of a unique EPR signal from two cocrystallized spin triangles

A 16-line pattern has been theoretically predicted, but hitherto not reported, for the Electron Paramagnetic Resonance (EPR) spectrum of antiferromagnetically coupled CuII triangles experiencing isotropic exchange of isosceles magnetic symmetry. Now, the crystallization of such a triangular species and its X-ray structure determination in a polar space group, R3 (No. 146), has enabled its single crystal EPR study. Its detailed magnetic susceptibility, and X- and Q-band, powder and single crystal EPR spectroscopic study reveals the effect of molecular structure and of Dzyaloshinskii-Moriya interactions (DMI) on the g‖, g⊥ and A‖ parameters of the spectrum; DMI is considered for the first time in such a context. Moreover, careful analysis of the spectrum allows the deconvolution of two slightly different cocrystallized magnetic species.