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.

Coexistence of room temperature magneto-chiral dichroism and magneto-electric coupling in a chiral nanomagnet

We report herein on the magneto-chiral dichroism (MChD), investigated through near infrared light absorption, of a chiral nanomagnet showing room temperature magneto-electric coupling. The MChD signal associated with the YbIII center is driven by the magnetic dipole allowed character of the 2F7/2 ← 2F5/2 electronic transition (|ΔJ| = 1). Magnetic field and temperature dependence studies reveal an MChD signal that follows the material magnetization and persists at room temperature. These results represent the first evidence of the coexistence of magneto-chiral dichroism and magneto-electric coupling at room temperature in a molecular nanomagnet and pave the way for further studies where magneto-chiral anisotropy and magneto-electric coupling interact.

Magnetoelectric Coupling in a Mn4Na-Organic Complex under Pulsed Magnetic Fields up to 73 T

Research on the magnetoelectric (ME) effect (or spin-electric coupling) in molecule-based magnetic materials is a relatively nascent but promising topic. Molecule-based magnetic materials have diverse magnetic functionalities that can be coupled to electrical properties. Here we investigate a realization of ME coupling that is fundamental but not heavily studied─the coupling of magnetic spin level crossings to changes in electric polarization. A mixed-valence Mn4Na complex with a total ground-state spin S = 5/2 under zero magnetic field and S = 17/2 under high magnetic field undergoes a cascade of ground-state level crossings of the Sz states with increasing magnetic field. Magnetization and electrical polarization measurements under pulsed magnetic fields up to 73 T show that each spin level crossing is accompanied by a significant change in electric polarization that is an even function of the applied magnetic field. A molecular Hamiltonian describing antiferromagnetic exchange in a distorted tetrahedron of three MnIII and one MnII ions matches the data well. We conclude that the ME coupling is caused by magnetostriction within the polar molecule as it distorts to lower its magnetic exchange energy.

Investigating the influence of oriented external electric fields on modulating spin-transition temperatures in Fe(II) SCO complexes: a theoretical perspective

Spin-crossover complexes, valued for their bistability, are extensively studied due to their numerous potential applications. A primary challenge in this molecular class is to identify effective methods to adjust the spin-transition temperature, which frequently falls outside the desired temperature range. This typically necessitates intricate chemical design and synthesis or the use of stimuli such as light or pressure, each introducing its own set of challenges for integrating these molecules into end-user applications. In this work, we aim to address this challenge using an oriented external electric field (OEEF) as one stimulus to modulate the spin-transition temperatures. For this purpose, we have employed both periodic and non-periodic calculations on three well-characterised Fe(II) SCO complexes, namely [Fe(phen)2(NCS)2] (1, phen = 1,10-phenanthroline), [Fe(bt)2(NCS)2] (2, bt = 2,2'-bi-2-thiazoline) and [Fe(py)2phen(NCS)2] (3, py = pyridine) possessing a similar structural motif of {FeN4N'2}. To begin with, DFT calculations employing the TPSSh functional were performed on complexes 1 to 3, and the estimated low-spin (LS) and high-spin (HS) gaps are 24.6, 15.3 and 15.4 kJ mol-1, and these are in the range expected for Fe(II) SCO complexes. In the next step, an OEEF was applied in the molecule along the pseudo-C2 axis that bisects two coordinated -NCS groups. Application of an OEEF was found to increase the Fe-ligand bond length and found to affect the spin-transition at the particular applied OEEF. While the HS state of 1 becomes the ground state at an applied field of 0.514 V Å-1, the LS state lies at a higher energy of 1.3 kJ mol-1. Similarly, complexes 2 and 3 also show the HS ground state at an applied field of 0.514 V Å-1, where the LS state stays at higher energies of 6.13 and 11.62 kJ mol-1, respectively. It is found that the overall change in enthalpy (ΔHHL) and entropy (ΔSHL) for the spin transition in the presence of OEEFs decreases upon increasing the strength of the applied field. The computed spin-transition temperature (T1/2) using DFT was found to be in close agreement with the experimentally reported values. It is estimated that on increasing the strength of the applied electric field, the T1/2 increases significantly. While the DFT computed T1/2 values for the optimised geometry of 1, 2 and 3 were found to be 134.6 K, 159.9 K and 111.4 K respectively, at the applied field of 0.6425 V Å-1T1/2 increases up to 187.3 K, 211.0 K and 184.4 K respectively, unveiling an hitherto unknown strategy to tune the T1/2 values. A limited benchmarking was performed with five additional exchange-correlation functionals: PBE, BLYP, B3LYP*, B3LYP, and PBE0. These functionals were found to be unsuitable for predicting the correct SCO behaviour for complex 2, and their behaviour under various electric fields did not improve. This emphasises the importance of choosing the correct functional at zero OEEF prior to testing them under various electric fields. Furthermore, calculations were performed with complex 1 adsorbed on the Au(111) surface. The formation of an Au-S bond during adsorption significantly stabilises the low-spin (LS) state, hindering the observation of spin-crossover (SCO) behaviour. Nonetheless, the application of an OEEF reduces this gap and brings the T1/2 value closer to the desired temperature. This offers a novel post-fabrication strategy for attaining SCO properties at the interface.

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.

Search for Toroidal Ground State and Magnetoelectric Effects in Molecular Spin Triangles with Antiferromagnetic Exchange

Using first-principles methods and spin models, we investigate the magnetic properties of transition-metal trimers Cr₃ and Cu₃. We calculate exchange coupling constants and zero-field splitting parameters using density functional theory and, with these parameters, determine the ground spin state as well as thermodynamic properties via spin models. Results for Cr₃ indicate uniaxial magnetic anisotropy with a magnetic easy axis aligned along the 3-fold rotational symmetry axis and a mostly isotropic exchange interaction. The Cu₃ molecule lacks rotational symmetry and our results show strong antisymmetric interactions for three distinct exchange couplings within the molecule. We are able to reproduce experimental findings on magnetic susceptibility and magnetization of Cr₃ with the first-principles spin-Hamiltonian parameters. Our results show no presence of a toroidal ordering of spins for Cr₃ and a finite toroidal moment for Cu₃ in the ground state. We apply an external electric field up to 0.08 V/Å to each system to reveal the field dependence of exchange coupling as magnetoelectric effects. Finally, we scan the parameter space of a spin Hamiltonian to gain insights into which parameters would lead to a sizable toroidal moment in such systems.

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.

Direct observation of electric field-induced magnetism in a molecular magnet

We report the direct observation of an electrically-induced magnetic susceptibility in the molecular nano- magnet [Fe₃O(O₂CPh)₆(py)₃]ClO₄·py, an Fe₃ trimer. This magnetoelectric effect results from the breaking of spatial inversion symmetry due to the spin configurations of the antiferromagnetic trimer. Both static and very low frequency electric fields were used. Fractional changes of the magnetic susceptibility of 11 ppb[Formula: see text] per kVm^-1 for the temperature range 8.5 < T < 13.5 K were observed for applied electric fields up to 62 kV m^-1. The changes in susceptibility were measured using a tunnel diode oscillator operating at liquid helium temperatures while the sample is held at a higher regulated temperature.

Inherent Spin-Polarization Coupling in a Magnetoelectric Vortex

Solid-state materials are currently being explored as a platform for the manipulation of spins for spintronics and quantum information science. More broadly, a wide spectrum of ferroelectric materials, spanning from inorganic oxides to polymeric systems such as PVDF, present a different approach to explore quantum phenomena in which the spins are set and manipulated with electric fields. Using dilute Fe³⁺-doped ferroelectric PbTiO₃-SrTiO₃ superlattices as a model system, we demonstrate intrinsic spin-polarization control of spin directionality in complex ferroelectric vortices and skyrmions. Electron paramagnetic resonance (EPR) spectra show that the spins in the Fe³⁺ ion are strongly coupled to the local polarization and preferentially aligned perpendicular to the ferroelectric polar c axis in this complex vortex structure. The effect of polarization-spin directionality is corroborated by first-principles calculations, demonstrating the variation of the spin directionality with the polar texture and offering the potential for future quantum analogues of macroscopic magnetoelectric devices.

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.

Coherent electric field manipulation of Fe3+ spins in PbTiO3

Magnetoelectrics, materials that exhibit coupling between magnetic and electric degrees of freedom, not only offer a rich environment for studying the fundamental materials physics of spin-charge coupling but also present opportunities for future information technology paradigms. We present results of electric field manipulation of spins in a ferroelectric medium using dilute ferric ion-doped lead titanate as a model system. Combining first-principles calculations and electron paramagnetic resonance (EPR), we show that the ferric ion spins are preferentially aligned perpendicular to the ferroelectric polar axis, which we can manipulate using an electric field. We also demonstrate coherent control of the phase of spin superpositions by applying electric field pulses during time-resolved EPR measurements. Our results suggest a new pathway toward the manipulation of spins for quantum and classical spintronics.

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.

Electromagnetic control of spin ordered Mn3 qubits: a density functional study

[Mn3O(O2CMe)(dpd3/2)]2 is composed of two monomers each of which contain three Mn atoms at the vertices of an equilateral triangle. A full analysis of the electronic and magnetic structure of the dimer shows that each Mn atom carries a local spin of S = 2 while other spin states are energetically much higher. This result suggests application for conventional as well as quantum tasks. A detailed analysis of the electronic and magnetic structure of the monomer, on the other hand, suggests that there are three spin states of S = 1, S = 3/2 and S = 2 per monomer which are energetically competitive. We found that while monomer-monomer interactions are very weak, the coupling of monomers via covalent linkers affects both the magnetization and electronic energy levels of monomers. In particular, the isolated monomers prefer a ground state with local spin of S = 1 on Mn atoms and an antiferromagnetically ordered structure while the dimers possess a ground state with local spin of S = 2 on Mn atoms and a ferromagnetically ordered structure. The investigation of the polarizability of both monomer and dimer is examined for antiferromagnetically ordered structures which induces a high dipole moment of 0.08 (a.u.) and 0.16 (a.u.) for monomer and dimer, respectively. The energy of the antiferromagnetic structure is also high compared to other spin-electric molecules.

Modulating magnetic anisotropy in Ln(iii) single-ion magnets using an external electric field

Single-molecule magnets have potential uses in several nanotechnology applications, including high-density information storage devices, the realisation of which lies in enhancing the barrier height for magnetisation reversal (U eff). However, Ln(iii) single-ion magnets (SIMs) that have been reported recently reveal that the maximum value of U eff values that can be obtained by modulating the ligand fields has already been achieved. Here, we have explored, using a combination of DFT and ab initio CASSCF calculations, a unique way to enhance the magnetisation reversal barrier using an oriented external electric field in three well-known Ln(iii) single-ion magnets: [Dy(Py)5(O t Bu)2]+ (1), [Er{N(SiMe3)2}3Cl]- (2) and [Dy(CpMe3)Cl] (3). Our study reveals that, for apt molecules, if the appropriate direction and values of the electric fields are chosen, the barrier height can be enhanced by twice that of the limit set by the ligand field. The application of an electric field along the equatorial direction was found to be suitable for oblate shaped Dy(iii) complexes and an electric field along the axial direction was found to enhance the barrier height for a prolate Er(iii) complex. For complexes 2 and 3, the external electric field was able to magnify the barrier height to 2-3 times that of the original complexes. However, a moderate enhancement was noticed after application of the external electric field in the case of complex 1. This novel non-chemical fine-tuning approach to modulate magnetic anisotropy is expected to yield a new generation of SIMs.

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.

Room temperature magnetoelectric coupling in a molecular ferroelectric ytterbium(III) complex

Magnetoelectric (ME) materials combine magnetic and electric polarizabilities in the same phase, offering a basis for developing high-density data storage and spintronic or low-consumption devices owing to the possibility of triggering one property with the other. Such applications require strong interaction between the constitutive properties, a criterion that is rarely met in classical inorganic ME materials at room temperature. We provide evidence of a strong ME coupling in a paramagnetic ferroelectric lanthanide coordination complex with magnetostrictive phenomenon. The properties of this molecular material suggest that it may be competitive with inorganic magnetoelectrics.

Electronic Communication as a Transferable Property of Molecular Bridges?

Electronic communication through molecular bridges is important for different types of experiments, such as single-molecule conductance, electron transfer, superexchange spin coupling, and intramolecular singlet fission. In many instances, the chemical structure of the bridge determines how the two parts it is connecting communicate, and does so in ways that are transferable between these different manifestations (for example, high conductance often correlates with strong antiferromagnetic spin coupling, and low conductance due to destructive quantum interference correlates with ferromagnetic coupling). Defining electronic communication as a transferable property of the bridge can help transfer knowledge between these different areas of research. Examples and limits of such transferability are discussed here, along with some possible directions for future research, such as employing spin-coupled and mixed-valence systems as structurally well-controlled proxies for understanding molecular conductance and for validating first-principles theoretical methodologies, building conceptual understanding for the growing experimental work on intramolecular singlet fission, and developing measures for the transferability of electronic communication as a bridge property.

Experimental determination of single molecule toroic behaviour in a Dy8 single molecule magnet

The enhancement of toroic motifs through coupling toroidal moments within molecular nanomagnets is a new, interesting and relevant approach for both fundamental research and potential quantum computation applications. We investigate a Dy8 molecular cluster and discover it has a antiferrotoroic ground state with slow magnetic relaxation. The experimental characterization of the magnetic anisotropy axes of each magnetic center and their exchange interactions represents a considerable challenge due to the non-magnetic nature of the toroidal motif. To overcome this and obtain access to the low energy states of Dy8 we establish a multi-orientation single-crystal micro Hall sensor magnetometry approach. Using an effective Hamiltonian model we then unpick the microscopic spin structure of Dy8, leading to a canted antiferrotoroidic tetramer molecular ground state. These findings are supported with electrostatic calculations that independently confirm the experimentally determined magnetic anisotropy axes for each DyIII ion within the molecule.

The Second Quantum Revolution: Role and Challenges of Molecular Chemistry

Implementation of modern Quantum Technologies might benefit from the remarkable quantum properties shown by molecular spin systems. In this Perspective, we highlight the role that molecular chemistry can have in the current second quantum revolution, i.e., the use of quantum physics principles to create new quantum technologies, in this specific case by means of molecular components. Herein, we briefly review the current status of the field by identifying the key advances recently made by the molecular chemistry community, such as for example the design of molecular spin qubits with long spin coherence and the realization of multiqubit architectures for quantum gates implementation. With a critical eye to the current state-of-the-art, we also highlight the main challenges needed for the further advancement of the field toward quantum technologies development.

Electric field modulation of magnetic exchange in molecular helices

The possibility to operate on magnetic materials through the application of electric rather than magnetic fields-promising faster, more compact and energy efficient circuits-continues to spur the investigation of magnetoelectric effects. Symmetry considerations, in particular the lack of an inversion centre, characterize the magnetoelectric effect. In addition, spin-orbit coupling is generally considered necessary to make a spin system sensitive to a charge distribution. However, a magnetoelectric effect not relying on spin-orbit coupling is appealing for spin-based quantum technologies. Here, we report the detection of a magnetoelectric effect that we attribute to an electric field modulation of the magnetic exchange interaction without atomic displacement. The effect is visible in electron paramagnetic resonance absorption of molecular helices under electric field modulation and confirmed by specific symmetry properties and spectral simulation.

Electric Field Control of Spins in Molecular Magnets

Coherent control of individual molecular spins in nanodevices is a pivotal prerequisite for fulfilling the potential promised by molecular spintronics. By applying electric field pulses during time-resolved electron spin resonance measurements, we measure the sensitivity of the spin in several antiferromagnetic molecular nanomagnets to external electric fields. We find a linear electric field dependence of the spin states in Cr_{7}Mn, an antiferromagnetic ring with a ground-state spin of S=1, and in a frustrated Cu_{3} triangle, both with coefficients of about 2  rad s^{-1}/V m^{-1}. Conversely, the antiferromagnetic ring Cr_{7}Ni, isomorphic with Cr_{7}Mn but with S=1/2, does not exhibit a detectable effect. We propose that the spin-electric field coupling may be used for selectively controlling individual molecules embedded in nanodevices.

Relevance of Dzyaloshinskii–Moriya spectral broadenings in promoting spin decoherence: a comparative pulsed-EPR study of two structurally related iron(iii) and chromium(iii) spin-triangle molecular qubits

Two related iron(iii) and chromium(iii) spin-triangle molecular qubits show coherent driving of their spins, and decoherence that is not significantly affected by Dzyaloshikskii–Moriya spectral broadenings.