Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits.

The use of d-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Magnetic molecules are ideal spin systems to realize these large-dimensional qudits. Indeed, their Hamiltonian can be engineered to an unparalleled extent and can yield a spectrum with many low-energy states. In particular, in the past decade, intense theoretical, experimental, and synthesis efforts have been devoted to develop quantum simulators based on molecular qubits and qudits. However, this remarkable potential is practically unexpressed, because no quantum simulation has ever been experimentally demonstrated with these systems. Here, we show the first prototype quantum simulator based on an ensemble of molecular qudits and a radiofrequency broadband spectrometer. To demonstrate the operativity of the device, we have simulated quantum tunneling of the magnetization and the transverse-field Ising model, representative of two different classes of problems. These results represent an important step toward the actual use of molecular spin qudits in quantum technologies.

Dinuclear Dysprosium Compounds: The Importance of Rigid Bridges.

We report the synthesis, structures and magnetic behaviour of two isostructural dinuclear Dy3+ complexes where the metal ions of a previously reported monomeric building block are connected by a peroxide (O22-) or a pair of fluoride (2 x F-) bridges. The nature of the bridge determines the distance between the metal ion dipoles leading to a dipolar coupling in the peroxido bridged compound of only ca. 70% of that in the bis-fluorido bridged dimer. The sign of the overall coupling between the metals is antiferromagnetic for the peroxido bridged compound and ferromagnetic for the bis-fluorido bridged complex. This in turn influences the magnetisation dynamics. We compare the relaxation characteristics of the dimers with those of the previously reported monomeric building block. The relaxation dynamics for the bis-fluorido system are very fast. On the other hand, comparing the properties of the monomer, the peroxido bridged sample and the corresponding Y-doped sample show that the relaxation properties via a Raman process have very similar parameters. We show that a second dysprosium is important for either tuning or detuning the Single Molecule Magnet (SMM) properties of a system.

Dipolar-Coupled Entangled Molecular 4f Qubits.

We demonstrate by use of continuous wave- and pulse-electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute YbIII ions in Yb0.01Lu0.99(trensal) that molecular entangled two-qubit systems can be constructed by exploiting dipolar interactions between neighboring YbIII centers. Furthermore, we show that the phase memory time and Rabi frequencies of these dipolar-interaction-coupled entangled two-qubit systems are comparable to the ones of the corresponding single qubits.

Spin-Lattice Relaxation Decoherence Suppression in Vanishing Orbital Angular Momentum Qubits.

Multifrequency electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute Gd(III) ions in Gd0.004Y0.996(trensal) is used to determine the Hamiltonian parameters of the ground 8S7/2 term and its phase memory time, Tm, characterizing its coherent spin dynamics. The vanishing orbital angular momentum of the 8S7/2 term makes it relatively insensitive to spin-lattice relaxation mediated by magnetoelastic coupling and leads to a Tm of 12 µs at 3 K, which is not limited by spin-lattice relaxation.

Magnetic Archimedean Tessellations in Metal-Organic Frameworks.

The self-assembly of lanthanide ions with ditopic organic spacers results in the formation of complex tiling patterns that mimic the structural motifs of quasi-periodic 2D materials. The linking of trans-{LnI2}+ nodes (Ln = Gd, Dy) by both closed-shell and anion radicals of 4,4'-bipyridine affords rare examples of Archimedean tessellations in a metal-organic framework. We furthermore demonstrate the occurrence of sizable magnetic exchange interactions and slow relaxation of magnetization behavior in a complex tessellation pattern. The implementation of Archimedean tessellations in lanthanide(III) coordination solids couriers a strategy to design elusive quasi-periodic metal-organic frameworks with inimitable magnetic properties.

[CrIII8NiII6]n+ Heterometallic Coordination Cubes.

Three new heterometallic [CrIII8NiII6] coordination cubes of formulae [CrIII8NiII6L24(H2O)12](NO3)12 (1), [CrIII8NiII6L24(MeCN)7(H2O)5](ClO4)12 (2), and [CrIII8NiII6L24Cl12] (3) (where HL = 1-(4-pyridyl)butane-1,3-dione), were synthesised using the paramagnetic metalloligand [CrIIIL3] and the corresponding NiII salt. The magnetic skeleton of each capsule describes a face-centred cube in which the eight CrIII and six NiII ions occupy the eight vertices and six faces of the structure, respectively. Direct current magnetic susceptibility measurements on (1) reveal weak ferromagnetic interactions between the CrIII and NiII ions, with JCr-Ni = + 0.045 cm-1. EPR spectra are consistent with weak exchange, being dominated by the zero-field splitting of the CrIII ions. Excluding wheel-like structures, examples of large heterometallic clusters containing both CrIII and NiII ions are rather rare, and we demonstrate that the use of metalloligands with predictable bonding modes allows for a modular approach to building families of related polymetallic complexes. Compounds (1)-(3) join the previously published, structurally related family of [MIII8MII6] cubes, where MIII = Cr, Fe and MII = Cu, Co, Mn, Pd.

Functionalized Trigonal Lanthanide Complexes: A New Family of 4f Single-Ion Magnets.

We report the synthesis, characterization, and magnetic properties of eight neutral functionalized trigonal lanthanide coordination complexes LnL with Ln = Gd (1), Tb (2), Dy (3), Ho (4), Er (5), Tm (6), Yb (7), Lu (8). These were prepared through a one-pot synthesis where, first, the ligand H3L was synthesized in situ through a Schiff base reaction of tris(2-aminoethyl)amine with 2,6-diformyl-p-cresol. Following addition of Ln(OTf)3·xH2O and base, LnL was obtained. Powder X-ray diffraction confirms that all complexes are isostructural. LnL contain pendant, noncoordinating carbonyl functions that are reactive and represent direct anchoring points to appropriately functionalized surfaces. Furthermore, these reactive carbonyl functions can be used to postfunctionalize LnL: for example, with aromatic π systems. We present herein the Schiff base condensation of 7 with benzylamine to yield 9 as well as the characterization and magnetic properties of 9. Our study establishes LnL as a truly versatile module for the surface deposition of Ln-based single-ion magnets.

Coherent Manipulation of a Molecular Ln-Based Nuclear Qudit Coupled to an Electron Qubit.

We demonstrate that the [Yb(trensal)] molecule is a prototypical coupled electronic qubit-nuclear qudit system. The combination of noise-resilient nuclear degrees of freedom and large reduction of nutation time induced by electron-nuclear mixing enables coherent manipulation of this qudit by radio frequency pulses. Moreover, the multilevel structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.

Modular [FeIII8MII6] n+ (MII = Pd, Co, Ni, Cu) Coordination Cages.

The reaction of the simple metalloligand [FeIIIL3] [HL = 1-(4-pyridyl)butane-1,3-dione] with a variety of different MII salts results in the formation of a family of heterometallic cages of formulae [FeIII8PdII6L24]Cl12 (1), [FeIII8CuII6L24(H2O)4Br4]Br8 (2), [FeIII8CuII6L24(H2O)10](NO3)12 (3), [FeIII8NiII6L24(SCN)11Cl] (4), and [FeIII8CoII6L24(SCN)10(H2O)2]Cl2 (5). The metallic skeleton of each cage describes a cube in which the FeIII ions occupy the eight vertices and the MII ions lie at the center of the six faces. Direct-current magnetic susceptibility and magnetization measurements on 3-5 reveal the presence of weak antiferromagnetic exchange between the metal ions in all three cases. Computational techniques known in theoretical nuclear physics as statistical spectroscopy, which exploit the moments of the Hamiltonian to calculate relevant thermodynamic properties, determine JFe-Cu = 0.10 cm-1 for 3 and JFe-Ni = 0.025 cm-1 for 4. Q-band electron paramagnetic resonance spectra of 1 reveal a significantly wider spectral width in comparison to [FeL3], indicating that the magnitude of the FeIII zero-field splitting is larger in the heterometallic cage than in the monomer.

Toward Molecular 4f Single-Ion Magnet Qubits.

Quantum coherence is detected in the 4f single-ion magnet (SIM) Yb(trensal), by isotope selective pulsed EPR spectroscopy on an oriented single crystal. At X-band, the spin-lattice relaxation (T1) and phase memory (Tm) times are found to be independent of the nuclei bearing, or not, a nuclear spin. The observation of Rabi oscillations of the spin echo demonstrates the possibility to coherently manipulate the system for more than 70 rotations. This renders Yb(trensal), a sublimable and chemically modifiable SIM, an excellent candidate for quantum information processing.

In-Depth Magnetic Characterization of a [2 × 2] Mn(III) Square Grid Using SQUID Magnetometry, Inelastic Neutron Scattering, and High-Field Electron Paramagnetic Resonance Spectroscopy.

A tetranuclear [2 × 2] grid-like manganese(III) Schiff base complex, Mn4, has been synthesized and characterized by single-crystal X-ray crystallography. Direct-current magnetization measurements were performed on the system and proved to be insufficient for an accurate magnetic model to be deduced. Combined inelastic neutron scattering (INS) and electron paramagnetic resonance (EPR) experiments provided the necessary information in order to successfully model the magnetic properties of Mn4. The resulting model takes into account both the magnitude and the relative orientations of the single-ion anisotropy tensors.

Structurally Flexible and Solution Stable [Ln4TM8(OH)8(L)8(O2CR)8(MeOH)y](ClO4)4: A Playground for Magnetic Refrigeration.

The family of compounds of general formula [LnIII4TMII8(OH)8(L)8(O2CR)8(MeOH)y](ClO4)4 {[Gd4Zn8(OH)8(hmp)8(O2CiPr)8](ClO4)4 (1a); [Y4Zn8(OH)8(hmp)8(O2CiPr)8](ClO4)4 (1b); [Gd4Cu8(OH)8(hmp)8(O2CiPr)8](ClO4)4 (2a); [Y4Cu8(OH)8(hmp)8(O2CiPr)8](ClO4)4 (2b); [Gd4Cu8(OH)8(hep)8(O2CiPr)8](ClO4)4 (3a); [Gd4Cu8(OH)8(Hpdm)8(O2CtBu)8](ClO4)4 (4a); [Gd4Cu8(OH)8(ea)8(O2CMe)8](ClO4)4 (5a); [Gd4Ni8(OH)8(hmp)8(O2CEt)8(MeOH)6](ClO4)4 (6a); [Y4Ni8(OH)8(hmp)8(O2CEt)8(MeOH)6](ClO4)4 (6b); [Gd4Co8(OH)8(hmp)8(O2CEt)8(MeOH)6](ClO4)4 (7a); [Y4Co8(OH)8(hmp)8(O2CEt)8(MeOH)6](ClO4)4 (7b)} can be formed very simply and in high yields from the reaction of Ln(NO3)3·6H2O and TM(ClO4)2·6H2O and the appropriate ligand blend in a mixture of CH2Cl2 and MeOH in the presence of a suitable base. Remarkably, almost all the constituent parts, namely the lanthanide (or rare earth) ions LnIII (here Ln = Gd or Y), the transition metal ions TMII (here TM = Zn, Cu, Ni, Co), the bridging ligand L (Hhmp = 2-(hydroxymethyl)pyridine; Hhep = 2-(hydroxyethyl)pyridine; H2pdm = pyridine-2,6-dimethanol; Hea = 2-ethanolamine), and the carboxylates can be exchanged while maintaining the structural integrity of the molecule. NMR spectroscopy of diamagnetic complex 1b reveals the complex to be fully intact in solution with all signals from the hydroxide, ligand L, and the carboxylates equivalent on the NMR time scale, suggesting the complex possesses greater symmetry in solution than in the solid state. High resolution nano-ESI mass spectrometry on dichloromethane solutions of 2a and 2b shows both complexes are present in two charge states with little fragmentation; with the most intense peak in each spectrum corresponding to [Ln4Cu8(OH)8(hmp)8(O2CiPr)8](ClO4)22+. This family of compounds offers an excellent playground for probing how the magnetocaloric effect evolves by introducing either antiferromagnetic or ferromagnetic interactions, or magnetic anisotropy, by substituting the nonmagnetic ZnII (1a) with CuII (2a), NiII (6a) or CoII (7a), respectively. The largest magnetocaloric effect is found for the ferromagnetically coupled complex 6a, while the predominant antiferromagnetic interactions in 2a yield an inverse magnetocaloric effect; that is, the temperature increases on lowering the applied field, under the proper experimental conditions. In spite of increasing the magnetic density by adding ions that bring in antiferromagnetic interactions (2a) or magnetic anisotropy (7a), the magnetocaloric effect is overall smaller in 2a and 7a than in 1a, where only four GdIII spins per molecule contribute to the magnetocaloric properties.

Spin Crossover in Fe(II) Complexes with N4S2 Coordination.

Reactions of Fe(II) precursors with the tetradentate ligand S,S'-bis(2-pyridylmethyl)-1,2-thioethane (bpte) and monodentate NCE(-) coligands afforded mononuclear complexes [Fe(bpte)(NCE)2] (1, E = S; 2, E = Se; 3, E = BH3) that exhibit temperature-induced spin crossover (SCO). As the ligand field strength increases from NCS(-) to NCSe(-) to NCBH3(-), the SCO shifts to higher temperatures. Complex 1 exhibits only a partial (15%) conversion from the high-spin (HS) to the low-spin (LS) state, with an onset around 100 K. Complex 3 exhibits a complete SCO with T1/2 = 243 K. While the γ-2 polymorph also shows the complete SCO with T1/2 = 192 K, the α-2 polymorph exhibits a two-step SCO with the first step leading to a 50% HS → LS conversion with T1/2 = 120 K and the second step proceeding incompletely in the 80-50 K range. The amount of residual HS fraction of α-2 that remains below 60 K depends on the cooling rate. Fast flash-cooling allows trapping of as much as 45% of the HS fraction, while slow cooling leads to a 14% residual HS fraction. The slowly cooled sample of α-2 was subjected to irradiation in the magnetometer cavity resulting in a light-induced excited spin state trapping (LIESST) effect. As demonstrated by Mössbauer spectroscopy, an HS fraction of up to 85% could be achieved by irradiation at 4.2 K.

Linked supramolecular building blocks for enhanced cluster formation.

Methylene-bridged calix[4]arenes have emerged as extremely versatile ligand supports in the formation of new polymetallic clusters possessing fascinating magnetic properties. Metal ion binding rules established for this building block allow one to partially rationalise the complex assembly process. The ability to covalently link calix[4]arenes at the methylene bridge provides significantly improved control over the introduction of different metal centres to resulting cluster motifs. Clusters assembled from bis-calix[4]arenes and transition metal ions or 3d-4f combinations display characteristic features of the analogous calix[4]arene supported clusters, thereby demonstrating an enhanced and rational approach towards the targeted synthesis of complex and challenging structures.

Facile interchange of 3d and 4f ions in single-molecule magnets: stepwise assembly of [Mn4 ], [Mn3Ln] and [Mn2Ln2 ] cages within calix[4]arene scaffolds.

The central Mn(II) ions in a series of calix[4]arene-stabilised butterflies can be sequentially replaced with Ln(III) ions, maintaining the structural integrity of the molecule but transforming its magnetic properties. The replacement of Mn(II) for Gd(III) allows for the examination of the transferability of spin-Hamiltonian parameters within the family as well as permitting their reliable determination. The introduction of the 4f ions results in weaker intramolecular magnetic exchange, an increase in the number of low-lying excited states, and an increase in magnetisation relaxation, highlighting the importance of exchange over single-ion anisotropy for the observation of SMM behaviour in this family of complexes. The presence of the [TM(II/III) (TBC[4])(OH)(solvent)] metalloligand (TM=transition metal, TBC=p-tBu-calix[4]arene) suggests that magnetic calix[n]arene building blocks can be employed to encapsulate a range of different "guests" within structurally robust "hosts".

Reversible Guest Binding in a Non-Porous Fe(II) Coordination Polymer Host Toggles Spin Crossover.

Formation of either a dimetallic compound or a 1 D coordination polymer of adiponitrile adducts of [Fe(bpte)](2+) (bpte=[1,2-bis(pyridin-2-ylmethyl)thio]ethane) can be controlled by the choice of counteranion. The iron(II) atoms of the bis(adiponitrile)-bridged dimeric complex [Fe2 (bpte)2 (µ2 -(NC(CH2 )4 CN)2 ](SbF6 )4 (2) are low spin at room temperature, as are those in the polymeric adiponitrile-linked acetone solvate polymer {[Fe(bpte)(µ2 -NC(CH2 )4 CN)](BPh4 )2 ⋅Me2 CO} (3⋅Me2 CO). On heating 3⋅Me2 CO to 80 °C, the acetone is abruptly removed with an accompanying purple to dull lavender colour change corresponding to a conversion to a high-spin compound. Cooling reveals that the desolvate 3 shows hysteretic and abrupt spin crossover (SCO) S=0↔S=2 behaviour centred at 205 K. Non-porous 3 can reversibly absorb one equivalent of acetone per iron centre to regenerate the same crystalline phase of 3⋅Me2 CO concurrently reinstating a low-spin state.

Design of Single-Molecule Magnets: Insufficiency of the Anisotropy Barrier as the Sole Criterion.

Determination of the electronic energy spectrum of a trigonal-symmetry mononuclear Yb(3+) single-molecule magnet (SMM) by high-resolution absorption and luminescence spectroscopies reveals that the first excited electronic doublet is placed nearly 500 cm(-1) above the ground one. Fitting of the paramagnetic relaxation times of this SMM to a thermally activated (Orbach) model {τ = τ0 × exp[ΔOrbach/(kBT)]} affords an activation barrier, ΔOrbach, of only 38 cm(-1). This result is incompatible with the spectroscopic observations. Thus, we unambiguously demonstrate, solely on the basis of experimental data, that Orbach relaxation cannot a priori be considered as the main mechanism determining the spin dynamics of SMMs. This study highlights the fact that the general synthetic approach of optimizing SMM behavior by maximization of the anisotropy barrier, intimately linked to the ligand field, as the sole parameter to be tuned, is insufficient because of the complete neglect of the interaction of the magnetic moment of the molecule with its environment. The Orbach mechanism is expected dominant only in the cases in which the energy of the excited ligand field state is below the Debye temperature, which is typically low for molecular crystals and, thus, prevents the use of the anisotropy barrier as a design criterion for the realization of high-temperature SMMs. Therefore, consideration of additional design criteria that address the presence of alternative relaxation processes beyond the traditional double-well picture is required.

A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings.

The term "frustration" in the context of magnetism was originally used by P. W. Anderson and quickly adopted for application to the description of spin glasses and later to very special lattice types, such as the kagomé. The original use of the term was to describe systems with competing antiferromagnetic interactions and is important in current condensed matter physics in areas such as the description of emergent magnetic monopoles in spin ice. Within molecular magnetism, at least two very different definitions of frustration are used. Here we report the synthesis and characterization of unusual nine-metal rings, using magnetic measurements and inelastic neutron scattering, supported by density functional theory calculations. These compounds show different electronic/magnetic structures caused by frustration, and the findings lead us to propose a classification for frustration within molecular magnets that encompasses and clarifies all previous definitions.

[Cr(III)8M(II)6](12+) Coordination Cubes (M(II)=Cu, Co).

[Cr(III)8M(II)6](12+) (M(II) =Cu, Co) coordination cubes were constructed from a simple [Cr(III) L3 ] metalloligand and a "naked" M(II) salt. The flexibility in the design proffers the potential to tune the physical properties, as all the constituent parts of the cage can be changed without structural alteration. Computational techniques (known in theoretical nuclear physics as statistical spectroscopy) in tandem with EPR spectroscopy are used to interpret the magnetic behavior.

[ReF(6)](2-) : a robust module for the design of molecule-based magnetic materials.

A facile synthesis of the [ReF6 ](2-) ion and its use as a building block to synthesize magnetic systems are reported. Using dc and ac magnetic susceptibility measurements, INS and EPR spectroscopies, the magnetic properties of the isolated [ReF6 ](2-) unit in (PPh4 )2 [ReF6 ]⋅2 H2 O (1) have been fully studied including the slow relaxation of the magnetization observed below ca. 4 K. This slow dynamic is preserved for the one-dimensional coordination polymer [Zn(viz)4 (ReF6 )]∞ (2, viz=1-vinylimidazole), demonstrating the irrelevance of low symmetry for such magnetization dynamics in systems with easy-plane-type anisotropy. The ability of fluoride to mediate significant exchange interactions is exemplified by the isostructural [Ni(viz)4 (ReF6 )]∞ (3) analogue in which the ferromagnetic Ni(II) -Re(IV) interaction (+10.8 cm(-1) ) dwarfs the coupling present in related cyanide-bridged systems. These results reveal [ReF6 ](2-) to be an unique new module for the design of molecule-based magnetic materials.