Polyanisotropic Magnetoelectric Coupling in an Electrically Controlled Molecular Spin Qubit

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.

Room-temperature Magnetocapacitance Spanning 97K Hysteresis in Molecular Material

Magnetic capacitor, as a new type of device, has broad application prospects in fields such as magnetic field sensing, magnetic storage, magnetic field control, power electronics and so on. Traditional magnetic capacitors are mostly assembled by magnetic and capacitive materials. Magnetic capacitor made of a single material with intrinsic properties is very rare. This intrinsic property is magnetocapacitance (MC). The studies on MC effect have mainly focused on metal oxides so far. No study was reported in molecular materials. Herein, two complexes: (CETAB)2[CuCl4] (1) and (CETAB)2[CuBr4] (2) (CETAB=(2-chloroethyl)trimethylammonium) are reported. There exist strong H-Br and Br-Br interactions and other weak interactions in complex 2, so the phase transition energy barrier is high, resulting in the widest thermal hysteresis loop on a molecular level to date. Furthermore, complexes 1 and 2 show large MC parameters of 0.247 and 1.614, respectively, which is the first time to observe MC effect in molecular material.

Ab Initio Design of Molecular Qubits with Electric Field Control

Current scalable quantum computers require large footprints and complex interconnections due to the design of superconducting qubits. While this architecture is competitive, molecular qubits offer a promising alternative due to their atomic scale and tuneable properties through chemical design. The use of electric fields to precisely, selectively and coherently manipulate molecular spins with resonant pulses has the potential to solve the experimental limitations of current molecular spin manipulation techniques such as electron paramagnetic resonance (EPR) spectroscopy. EPR can only address a macroscopic ensemble of molecules, defeating the inherent benefits of molecule-based quantum information. Hence, numerous experiments have been performed using EPR in combination with electric fields to demonstrate coherent spin manipulation. In this work, we explore the underlying theory of spin-electric coupling in lanthanide molecules, and outline ab initio methods to design molecules with enhanced electric field responses. We show how structural distortions arising from electric fields generate coupling elements in the crystal field Hamiltonian within a Kramers doublet ground state and demonstrate the impact of molecular geometry on this phenomenon. We use perturbation theory to rationalize the magnetic and electric field orientation dependence of the spin-electric coupling. We use pseudo-symmetry point groups to decompose molecular distortions to understand the role that symmetry has on spin-electric coupling. Finally, we present an analytical electric field model of structural perturbations that provides large savings in computational expense and allows for the investigation of experimentally accessible electric field magnitudes which cannot be accessed using common ab initio methods.

Electrically Induced Crystal Field Distortion in a Ferroelectric Perovskite Revealed by Electron Paramagnetic Resonance

The magnetoelectric material has attracted multidisciplinary interest in the past decade for its potential to accommodate various functions. Especially, the external electric field can drive the quantum behaviors of such materials via the spin-electric coupling effect, with the advantages of high spatial resolution and low energy cost. In this work, the spin-electric coupling effect of Mn2+-doped ferroelectric organic-inorganic hybrid perovskite [(CH3)3NCH2Cl]CdCl3 with a large piezoelectric effect was investigated. The electric field manipulation efficiency for the allowed transitions was determined by the pulsed electron paramagnetic resonance. The orientation-included Hamiltonian of the spin-electric coupling effect was obtained via simulating the angle-dependent electric field modulated continuous-wave electron paramagnetic resonance. The results demonstrate that the applied electric field affects not only the principal values of the zero-field splitting tensor but also its principal axis directions. This work proposes and exemplifies a route to understand the spin-electric coupling effect originating from the crystal field imposed on a spin ion being modified by the applied electric field, which may guide the rational screening and designing of hybrid perovskite ferroelectrics that satisfy the efficiency requirement of electric field manipulation of spins in quantum information applications.

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.

Electric control of spin transitions at the atomic scale

Electric control of spins has been a longstanding goal in the field of solid state physics due to the potential for increased efficiency in information processing. This efficiency can be optimized by transferring spintronics to the atomic scale. We present electric control of spin resonance transitions in single TiH molecules by employing electron spin resonance scanning tunneling microscopy (ESR-STM). We find strong bias voltage dependent shifts in the ESR signal of about ten times its line width. We attribute this to the electric field in the tunnel junction, which induces a displacement of the spin system changing the g-factor and the effective magnetic field of the tip. We demonstrate direct electric control of the spin transitions in coupled TiH dimers. Our findings open up new avenues for fast coherent control of coupled spin systems and expands on the understanding of spin electric coupling.

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.

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.

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.

Spin-Electric Coupling in a Cobalt(II)-Based Spin Triangle Revealed by Electric-Field-Modulated Electron Spin Resonance Spectroscopy

A cobalt(II)-based spin triangle shows a significant spin-electric coupling. [Co3 (pytag)(py)6 Cl3 ]ClO4 ⋅3 py crystallizes in the acentric monoclinic space group P21 . The intra-triangle antiferromagnetic interaction, of the order of ca. -15 cm-1 (H=-JSa Sb ), leads to spin frustration. The two expected energy-degenerate ground doublets are, however, separated by a few wavenumbers, as a consequence of magnetic anisotropy and deviations from threefold symmetry. The Co3  planes of symmetry-related molecules are almost parallel, allowing for the determination of the spin-electric properties of single crystals by EFM-ESR spectroscopy. The spin-electric effect detected when the electric field is applied in the Co3  plane was revealed by a shift in the resonance field. It was quantified as ΔgE /E=0.11×10-9  m V-1 , which in terms of frequency corresponds to approximately 0.3 Hz m V-1 . This value is comparable to what was determined for a Cu3  triangle despite the antiferromagnetic interaction being 20 times larger for the latter.

Half-Integer Spin Triangles: Old Dogs, New Tricks

Spin triangles, that is, triangular complexes of half-integer spins, are the oldest molecular nanomagnets (MNMs). Their magnetic properties have been studied long before molecular magnetism was delineated as a research field. This Review presents the history of their study, with references to the parallel development of new experimental investigations and new theoretical ideas used for their interpretation. It then presents an indicative list of spin-triangle families to illustrate their chemical diversity. Finally, it makes reference to recent developments in terms of theoretical ideas and new phenomena, as well as to the relevance of spin triangles to spintronic devices and new physics.

Hard X-ray magnetochiral dichroism in a paramagnetic molecular 4f complex

Magnetochiral dichroism (MΧD) originates in the coupling of local electric fields and magnetic moments in systems where a simultaneous break of space parity and time-reversal symmetries occurs. This magnetoelectric coupling, displayed by chiral magnetic materials, can be exploited to manipulate the magnetic moment of molecular materials at the single molecule level. We demonstrate herein the first experimental observation of X-ray magnetochiral dichroism in enantiopure chiral trigonal single crystals of a chiral mononuclear paramagnetic lanthanide coordination complex, namely, holmium oxydiacetate, at the Ho L₃-edge. The observed magnetochiral effect is opposite for the two enantiomers and is rationalised on the basis of a multipolar expansion of the matter–radiation interaction. These results demonstrate that 4f–5d hybridization in chiral lanthanoid coordination complexes is at the origin of magnetochiral dichroism, an effect that could be exploited for addressing of their magnetic moment at the single molecule level.

Magnetochiral Dichroism of chiral mononuclear lanthanoid complexes is for the first time detected by X-ray absorption measurements on single crystals of Holmium oxydiacetate, at the Ho L₃-edge. The effect is of opposite sign for the two enantiomers.