Record Quantum Tunneling Time in an Air-Stable Exchange-Bias Dysprosium Macrocycle.

In recent years, dysprosium macrocycle single-molecule magnets (SMMs) have received increasing attention due to their excellent air/thermal stability, strong magnetic anisotropy, and rigid molecular skeleton. However, they usually display fast zero-field quantum tunneling of the magnetization (QTM) rate, severely hindering their data storage applications. Herein, we report the design, synthesis, and characterization of an air-stable monodecker didysprosium macrocycle integrating strong single-ion anisotropy, near-perfect local crystal field (CF) symmetry, and efficient exchange bias. These indispensable features enable clear-cut elucidation of the crucial role of very weak antiferromagnetic coupling on magnetization dynamics, creating a prominent SMM with a large effective energy barrier (Ueff) of 670 cm-1, open hysteresis loops at zero field up to 14.9 K, and a record relaxation time of QTM (τQTM), 24281 s, for all known nonradical-bridged lanthanide SMMs.

Magnetic behaviour of a spin-canted asymmetric lanthanide quinolate trimer.

An asymmetrical dysprosium trimer with a molecular formula of [Dy3(hq)7(hqH)(NO3)2(H2O)] was obtained through a reflux reaction employing as starting material Dy(NO3)3·nH2O and 8-quinolinoline as ligand. Magnetic susceptibility investigations show the system to be an SMM, which was corroborated by sub-Kelvin µSQUID studies. Upon cooling, the magnetic susceptibility also exhibits a decrease in the χMT product, which was confirmed to be due to intramolecular antiferromagnetic interactions. µSQUID measurements, moreover, reveal a marked magnetic behaviour in the angular dependence of the hysteresis loops. The latter is a direct consequence of the non-colinear spin arrangement of the anisotropy axes of each Dy(III) ion in [Dy3(hq)7(hqH)(NO3)2(H2O)] and the interaction between the ions, as also evidenced by CASSCF calculations. Our results evidence the effect of spin canting along with the intramolecular interactions, which can induce non-trivial magnetic behaviour in SMMs.

Observation of Josephson harmonics in tunnel junctions.

Approaches to developing large-scale superconducting quantum processors must cope with the numerous microscopic degrees of freedom that are ubiquitous in solid-state devices. State-of-the-art superconducting qubits employ aluminium oxide (AlOx) tunnel Josephson junctions as the sources of nonlinearity necessary to perform quantum operations. Analyses of these junctions typically assume an idealized, purely sinusoidal current-phase relation. However, this relation is expected to hold only in the limit of vanishingly low-transparency channels in the AlOx barrier. Here we show that the standard current-phase relation fails to accurately describe the energy spectra of transmon artificial atoms across various samples and laboratories. Instead, a mesoscopic model of tunnelling through an inhomogeneous AlOx barrier predicts percent-level contributions from higher Josephson harmonics. By including these in the transmon Hamiltonian, we obtain orders of magnitude better agreement between the computed and measured energy spectra. The presence and impact of Josephson harmonics has important implications for developing AlOx-based quantum technologies including quantum computers and parametric amplifiers. As an example, we show that engineered Josephson harmonics can reduce the charge dispersion and associated errors in transmon qubits by an order of magnitude while preserving their anharmonicity.

Phase transitions associated with magnetic-field induced topological orbital momenta in a non-collinear antiferromagnet.

Resistivity measurements are widely exploited to uncover electronic excitations and phase transitions in metallic solids. While single crystals are preferably studied to explore crystalline anisotropies, these usually cancel out in polycrystalline materials. Here we show that in polycrystalline Mn3Zn0.5Ge0.5N with non-collinear antiferromagnetic order, changes in the diagonal and, rather unexpected, off-diagonal components of the resistivity tensor occur at low temperatures indicating subtle transitions between magnetic phases of different symmetry. This is supported by neutron scattering and explained within a phenomenological model which suggests that the phase transitions in magnetic field are associated with field induced topological orbital momenta. The fact that we observe transitions between spin phases in a polycrystal, where effects of crystalline anisotropy are cancelled suggests that they are only controlled by exchange interactions. The observation of an off-diagonal resistivity extends the possibilities for realising antiferromagnetic spintronics with polycrystalline materials.

Insight into ferromagnetic interactions in CuII-LnIII dimers with a compartmental ligand.

In the last two decades, efforts have been devoted to obtaining insight into the magnetic interactions between CuII and LnIII utilizing experimental and theoretical means. Experimentally, it has been observed that the exchange coupling (J) in CuII-LnIII systems is often found to be ferromagnetic for ≥4f7 metal ions. However, exchange interactions at sub-Kelvin temperatures between CuII and the anisotropic/isotropic LnIII ions are not often explored. In this report, we have synthesized a series of heterobimetallic [CuLn(HL)(µ-piv)(piv)2] complexes (LnIII = Gd (1), Tb (2), Dy (3) and Er (4)) from a new compartmental Schiff base ligand, N,N'-bis(3-methoxy-5-methylsalicylidene)-1,3-diamino-2-propanol (H3L). X-ray crystallographic analysis reveals that all four complexes are isostructural and isomorphous. Magnetic susceptibility measurements reveal a ferromagnetic coupling between the CuII ion and its respective LnIII ion for all the complexes, as often observed. Moreover, µ-SQUID studies, at sub-Kelvin temperatures, show S-shaped hysteresis loops indicating the presence of antiferromagnetic coupling in complexes 1-3. The antiferromagnetic interaction is explained by considering the shortest Cu⋯Cu distance in the crystal structure. The nearly closed loops for 1-3 highlight their fast relaxation characteristics, while the opened loops for 4 might arise from intermolecular ordering. CASSCF calculations allow the quantitative assessment of the interactions, which are further supported by BS-DFT calculations.

A nested spin structure and single molecule magnet behaviour in an Fe8Dy12 heterometallic cyclic coordination cluster.

The 20-nuclearity compound [Fe8Dy12(tea)8(teaH)12(NO3)12]·8MeCN (where teaH3 = triethanolamine) was synthesised and characterised through single crystal X-ray diffraction and magnetic measurements. The shape of the magnetic hysteresis in the microSQUID measurements was rationalised using the MAGELLAN program.

Hilbert Space in Isotopologue Dy(III) SMM Dimers: Dipole Interaction Limit in [163/164Dy2(tmhd)6(tape)]0 Complexes.

Single-molecule magnets are molecular complexes proposed to be useful for information storage and quantum information processing applications. In the quest for multilevel systems that can act as Qudits, two dysprosium-based isotopologues were synthesized and characterized. The isotopologues are [164Dy2(tmhd)6(tape)] (1(I=0)) and [163Dy2(tmhd)6(tape)] (2(I=5/2)), where tmhd = 2,2,6,6-tetramethylheptandionate and tape = 1,6,7,12-tetraazaperylene. Both complexes showed slow relaxation at a zero applied magnetic field with dominant Orbach and Raman relaxation mechanisms. µSQUID studies at milli-Kelvin temperatures reveal quasi-single ion loops, in contrast with the expected S-shape (near zero field) butterfly loops, characteristic of antiferromagnetically coupled dimeric complexes. Through analysis of the low-temperature data, we find that the interaction operating between Dy(III) is small, leading to a small exchange biasing from the zero-field transition. The resulting indirectly coupled nuclear states are degenerate or possess a small energy difference between them. We, therefore, conclude that for the creation of Qudits with enlarged Hilbert spaces, shorter Dy(III)···Dy(III) distances are deemed essential.

Direct determination of high-order transverse ligand field parameters via µSQUID-EPR in a Et4N[160GdPc2] SMM.

The development of quantum technologies requires a thorough understanding of systems possessing quantum effects that can ultimately be manipulated. In the field of molecular magnetism, one of the main challenges is to measure high-order ligand field parameters, which play an essential role in the relaxation properties of SMMs. The development of highly advanced theoretical calculations has allowed the ab-initio determination of such parameters; however, currently, there is a lack of quantitative assessment of how good the ab-initio parameters are. In our quest for technologies that can allow the extraction of such elusive parameters, we develop an experimental technique that combines the EPR spectroscopy and µSQUID magnetometry. We demonstrate the power of the technique by performing EPR-µSQUID measurement of a magnetically diluted single crystal of Et4N[GdPc2], by sweeping the magnetic field and applying a range of multifrequency microwave pulses. As a result, we were able to directly determine the high-order ligand field parameters of the system, enabling us to test theoretical predictions made by state-of-the-art ab-initio methods.

Thermalization of Nuclear Spins in Lanthanide Molecular Magnets.

Single-molecule magnets (SMMs) distinguish themselves in the field of quantum magnetism through the ability to combine fundamental research with promising applications. The evolution of quantum spintronics in the last decade exemplifies the potential held by molecular-based quantum devices. Notably, the readout and manipulation of the nuclear spin states embedded in a lanthanide-based SMM hybrid device were employed in proof of principle studies of quantum computation at the single-molecule level. In the quest for further understanding of the relaxation behavior in SMMs for their integration in novel applications, herein, we study the relaxation dynamics of the 159Tb nuclear spins in a diluted molecular crystal employing the recently acquired understanding of the nonadiabatic dynamics of TbPc2 molecules. Through numerical simulation, we find that phonon-modulated hyperfine interaction opens a direct relaxation channel between the nuclear spins and the phonon bath. The mechanism is of potential importance for the theory of spin bath and the relaxation dynamics of the molecular spins.

Fe-Gd Ferromagnetic Cyclic Coordination Cluster [FeIII4GdIII4(teaH)8(N3)8(H2O)] with Magnetic Anisotropy─Theory and Experiment.

The synthesis, structural, and magnetic characterization of [FeIII4LnIII4(teaH)8(N3)8(H2O)] (Ln = Gd and Y) and the previously reported isostructural Dy analogue are discussed. The commonly held belief that both FeIII and GdIII can be regarded as isotropic ions is shown to be an oversimplification. This conclusion is derived from the magnetic data for the YIII analogue in terms of the zero-field splitting seen for FeIII and from the fact that the magnetic data for the new GdIII analogue can only be fit employing an additional anisotropy term for the GdIII ions. Furthermore, the Fe4Gd4 ring shows slow relaxation of magnetization. Our analysis of the experimental magnetic data employs both density functional theory as well as the finite-temperature Lanczos method which finally enables us to provide an almost perfect fit of magnetocaloric properties.

Very Anisotropic 2D Molecular Magnetic Materials Based on Pentagonal Bipyramidal Heptacyanidorhenate(IV).

The first neutral 2D heterometallic assemblies based on orbitally degenerate heptacyanidorhenate(IV) were prepared and structurally characterized. An analysis of the magnetic data for the polycrystalline samples of Ph4P[{Mn(acacen)}2Re(CN)7]·Solv (1) and PPN[{Mn(acacen)}2Re(CN)7]·Solv (2) have shown that both materials display slow magnetic relaxation at temperatures below 10 and 21 K for 1 and 2, respectively. Despite the presence of the same molecular magnetic modules that make up the anionic layers, the studied 2D networks differ significantly in magnetic anisotropy, having a small coercive field (0.115 T) for 1 and a large one (~2.5 T) for 2 at 2 K. In addition, for both polymers a M(H) value does not saturate at the maximum available field of 7 T, and the material 2 is a metamagnet. This intriguing difference originates from the cooperative anisotropic spin interaction in ReIV-CN-MnIII pairs and the zero field splitting (ZFS) effect of MnIII ions with a noncollinear alignment of the local magnetic axes in crystals of the compounds.

Lanthanide Luminescence Thermometry and Slow Magnetic Relaxation in 3-D Polycyanidometallate-Based Materials.

Two three-dimensional (3-D) polycyanidometallate-based luminescent thermometers with the general formula {Ln4Co4(CN)24(4-benpyo)17(H2O)·7H2O}n Ln = (Dy(III)(1), Eu(III)(2)), based on the red-emissive diamagnetic linker [Co(CN)6]3- and the bulky pyridine derivative that possesses the N-oxide moiety, 4-benzyloxy-pyridine N-oxide (benpyo), were prepared for the first time. The structure of compound 1 has been determined by single-crystal X-ray crystallography while the purity and structure of 2 have been confirmed by CHN, Fourier transform infrared spectroscopy (FT-IR), and powder X-ray diffraction (PXRD) analysis. Magnetic AC susceptibility measurements at zero field show no single-molecule magnet (SMM) behavior indicating fast relaxation operating in 1. Upon application of an optimal field of 2 kOe, the SMM character of compound 1 is revealed while the τ(Τ) can be reproduced solely considering the Raman process τ-1 = CTn with C = 7.0901(3) s-1 K-n and n = 3.58(1), indicating that a high density of low-lying states and optical as well as acoustic phonons play a major role in the relaxation mechanism. Micron-sized superconducting quantum interference device (µ-SQUID) loops show a very narrow opening in agreement with the AC susceptibility studies and complete active space self-consistent field (CASSCF) calculations. The interaction operating between the Dy(III) ions was quantified from CASSCF calculations. Good agreement is found by fitting the experimental DC χMΤ(Τ) and M(H), employing the Lines model, with JLines = -0.087 cm-1 (-0.125 K). The excitation spectra of compound 2 are used for temperature sensing in the 25-325 nm range with a maximum relative thermal sensitivity, Sr = 0.6% K-1 at 325 K, whereas compound 1 operates as a luminescent thermometer based on its emission features in the temperature range of 16-350 K with Sr ≈ 2.3% K-1 at 240 K.

Luminescence thermometry and field induced slow magnetic relaxation based on a near infrared emissive heterometallic complex.

The 1 : 1 : 1 reaction of YbCl3·6H2O, K3[Co(CN)6] and bpyO2 in H2O has provided access to a complex with formula [YbCo(CN)6(bpyO2)2(H2O)3]·4H2O (1) in a very good yield while its structure has been determined by single-crystal X-ray crystallography and characterised based on elemental analyses and IR spectra. Magnetic susceptibility studies showed the complex to be a field induced single molecule magnet, as confirmed by µ-SQUID measurements. CASSCF calculations confirm the existence of a mJ = 7/2 ground state, with rather large transverse components, responsible for the fast relaxation characteristic of compound 1 at zero DC field, which is reduced upon application of DC fields. Moreover, a combination of luminescence studies along with CASSCF calculation allows the identification of the band structure of the complex, which is ultimately related to its electronic properties. Compound 1 operates as a luminescent thermometer in the 125-300 K range with a maximum relative thermal sensitivity of ≈0.1% K-1 at 180 K.

Structural determinations and magnetic properties of a "chiral at metal" complex and its resulting [Cu-Ln]2 compounds.

A chiral trianionic ligand possessing one amide, one imine, two phenol functions and one asymmetric carbon atom into its diamino chain reacts with CuII ions to yield anionic [LCu]- units that crystallize in a non-centrosymmetric space group as infinite 1D zig-zag chains in which a transmission of chirality to the CuII ion is effective. The distorted square planar environment of the CuII ion is large enough to induce the presence of a stereogenic CuII centre. Further reaction with LnIII ions in presence of ancillary ligands does not preserve such an arrangement but yields a tetranuclear complex made of two [LCu-Ln] units in a head-to-tail position. The tetranuclear [LCu-Ln]2 complexes made with the racemic and chiral LCu units crystallize in different space groups, so that racemization does not occur. The structural determinations confirm that a symmetry centre is present in the two structures, except for the methyl groups linked to the chiral carbon atoms, which appear as disordered in the (S-S) tetranuclear entity. Such an arrangement implies a conformation change of the diamino chain linked to the CuII ion in one [LCu-Ln] unit of the (S-S) entity, and cancels any chirality contribution of the CuII ions, as in the meso compound. Ferromagnetic Cu-Ln interactions, resulting from an alternate distribution of the CuII and LnIII ions, are the only ones to be active. Eventually the micro-Squid studies confirm that the hysteresis loops of the corresponding racemate and chiral tetranuclear [LCu-Dy]2 entities are slightly different.

High-Performance Luminescence Thermometer with Field-Induced Slow Magnetic Relaxation Based on a Heterometallic Cyanido-Bridged 3d-4f Complex.

The 1:1:1 reaction of DyCl3·6H2O, K3[Co(CN)6] and bpyO2 in H2O has provided access to a complex with formula [DyCo(CN)6(bpyO2)2(H2O)3]·4H2O (1) in a very good yield, while [DyFe(CN)6(bpyO2)2 (H2O)3]·4H2O (2) was also precipitated (also in a high yield) using K3[Fe(CN)6] instead of K3[Co(CN)6]. Their structures have been determined by single-crystal X-ray crystallography and characterized based on elemental analyses and IR spectra. Combined direct current (dc) and alternating current (ac) magnetic susceptibility revealed slow magnetic relaxation upon application of a dc field. µ-SQUID measurements and CASSCF calculations revealed high-temperature relaxation dynamics for both compounds. Low-temperature magnetic studies show the relaxation characteristics for 1, while for compound 2 the dynamics corresponds to an antiferromagnetically coupled Dy···Fe pair. High-resolution optical studies have been carried out to investigate the performance of compounds 1 and 2 as luminescence thermometers. For 1, a maximum thermal sensitivity of 1.84% K-1 at 70 K has been calculated, which is higher than the acceptable sensitivity boundary of 1% K-1 for high-performance luminescence thermometers in a broad range of temperature between 40 and 140 K. Further optical studies focused on the chromaticity diagram of compound 1 revealed a temperature shift from warm white (3200 K) at 10 K toward a more natural white color near 4000 K at room temperature.

High nuclearity structurally - related Mn supertetrahedral T4 aggregates.

The simultaneous employment of 1,3-propanediol and di-2-pyridyl ketone in Mn carboxylate chemistry has provided access to three new, structurally-related [Mn24] and [Mn23] clusters. They are based on nanosized supertetrahedal T4 Mn/O structural cores and exhibit slow relaxation of magnetization below 3.5 K.

Exchange-Bias Quantum Tunneling of the Magnetization in a Dysprosium Dimer.

Single-molecule magnets (SMMs) have been shown to possess bewildering phenomena leading to their proposal in several futuristic applications ranging from data storage devices to the basic unit of quantum computers. The main characteristic for the proposal of SMMs in such schemes is their inherent and intriguing quantum mechanical properties, which in turn, could be exploited in novel devices with larger capacities, such as for data storage or enhanced properties, such as quantum computers. In the quest of SMMs displaying such intriguing quantum effects, herein, we explore the synthesis, structural, and magnetic characterization of a dimeric dysprosium-based SMM composed of a tetradentate Schiff-base ligand with formula [Dy2(HL)2(benz)2(NO3)2]. Magnetic studies show that the complex is an SMM, while sub-Kelvin µ-SQUID studies revealed the exchange-bias characteristics of the system attributed to the presence of exchange interaction between the Dy3+ pair.

Synthesis, characterization, magnetism and theoretical analysis of hetero-metallic [Ni2Ln2] partial di-cubane assemblies.

A family of four isostructural [Ln2Ni2(L)2(µ3-OCH3)2(µ1,3-PhCO2)2(PhCO2)2(CH3OH)4]·2CH3OH [where Ln = Gd (1), Tb (2), Dy (3) and Ho (4)] complexes has been synthesized using Schiff base ligand 2-[{(2-hydroxybenzyl)imino}methyl]-6-methoxyphenol (H2L). All the complexes possess a partial di-cubane core structure where the growth of the core is contingent upon the ligand anions and solvent generated µ3-OCH3 groups. DC magnetic analysis revealed dominating ferromagnetic interactions between the metal ions, however, we find no slow relaxation characteristics in the AC susceptibility. Further insight into the magnetic behavior of the reported complexes was achieved using DFT and CASSCF theoretical calculations, leading to the comprehension of the fast relaxation characteristics observed by magnetometry.

Ultrasensitive nano-optomechanical force sensor operated at dilution temperatures.

Cooling down nanomechanical force probes is a generic strategy to enhance their sensitivities through the concomitant reduction of their thermal noise and mechanical damping rates. However, heat conduction becomes less efficient at low temperatures, which renders difficult to ensure and verify their proper thermalization. Here we implement optomechanical readout techniques operating in the photon counting regime to probe the dynamics of suspended silicon carbide nanowires in a dilution refrigerator. Readout of their vibrations is realized with sub-picowatt optical powers, in a situation where less than one photon is collected per oscillation period. We demonstrate their thermalization down to 32 ± 2 mK, reaching very large sensitivities for scanning probe force sensors, 40 zN Hz-1/2, with a sensitivity to lateral force field gradients in the fN m-1 range. This opens the road toward explorations of the mechanical and thermal conduction properties of nanoresonators at minimal excitation level, and to nanomechanical vectorial imaging of faint forces at dilution temperatures.

Increasing the Hilbert space dimension using a single coupled molecular spin.

Quantum technologies are expected to introduce revolutionary changes in information processing in the near future. Nowadays, one of the main challenges is to be able to handle a large number of quantum bits (qubits), while preserving their quantum properties. Beyond the usual two-level encoding capacity of qubits, multi-level quantum systems are a promising way to extend and increase the amount of information that can be stored in the same number of quantum objects. Recent work (Kues et al. 2017), has shown the possibility to use devices based on photonic integrated circuits to entangle two qudits (with "d" being the number of available states). In the race to develop a mature quantum technology with real-world applications, many possible platforms are being investigated, including those that use photons, trapped ions, superconducting and silicon circuits and molecular magnets. In this work, we present the electronic read-out of a coupled molecular multi-level quantum systems, carried by a single Tb2Pc3 molecular magnet. Owning two magnetic centres, this molecular magnet architecture permits a 16 dimensions Hilbert space, opening the possibility of performing more complex quantum algorithms.