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.

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.

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.

Long aliphatic chain derivatives of trigonal lanthanide complexes.

The trigonal lanthanide complexes LnL (H3L = tris(((3-formyl-5-methylsalicylidene)amino)ethyl)amine) contain three pendant aldehyde groups and are known to react with primary amines. Reacting LnL (Ln = Yb, Lu) with 1-octadecylamine yields the novel aliphatic lanthanide complexes LnL18 (H3L18 = tris(((3-(1-octadecylimine)-5-methylsalicylidene)amino)ethyl)amine) where the three aldehyde groups are transformed to 1-octadecylimine groups. Herein the syntheses, structural characterisation and magnetic properties of LnL18 are presented. The crystal structure of YbL18 shows that the reaction of YbL with 1-octadecylamine leads to only very subtle perturbations in the first coordination sphere of Yb(III), with the Yb(III) ion retaining its heptacoordination and similar bond lengths and angles to the ligand. The three octadecyl chains in each complex were found to direct crystal packing into lipophilic arrays of van der Waals interaction-driven hydrocarbon stacking. The static magnetic properties of YbL18 were compared to those of the non-derivatised complex YbL. The energy level splitting of the 2F7/2 ground multiplet was found, by emission spectroscopy, to be very similar between the derivatised and non-derivatised complexes. A.c. magnetic susceptibility measurements on YbL18 and YbL diluted at 4.8% and 4.2% into the diamagnetic hosts LuL18 and LuL, respectively, revealed that the spin-lattice relaxation of both complexes is governed by a low temperature direct process and a high temperature Raman process. In the high temperature regime, the derivatised complex was also found to have faster spin-lattice relaxation, which is likely due to the increased number of phonons in the octadecyl chains.

Analysis of vibronic coupling in a 4f molecular magnet with FIRMS.

Vibronic coupling, the interaction between molecular vibrations and electronic states, is a fundamental effect that profoundly affects chemical processes. In the case of molecular magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in molecular magnets and qubits, respectively. The study of vibronic coupling is challenging, and most experimental evidence is indirect. Here we employ far-infrared magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H3trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an "envelope effect" in the vibronic coupling Hamiltonian, which we calculate fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C3 symmetry of the molecule. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in molecules.

Design of pure heterodinuclear lanthanoid cryptate complexes.

Heterolanthanide complexes are difficult to synthesize owing to the similar chemistry of the lanthanide ions. Consequently, very few purely heterolanthanide complexes have been synthesized. This is despite the fact that such complexes hold interesting optical and magnetic properties. To fine-tune these properties, it is important that one can choose complexes with any given combination of lanthanides. Herein we report a synthetic procedure which yields pure heterodinuclear lanthanide cryptates LnLn*LX3 (X = NO3 - or OTf-) based on the cryptand H3L = N[(CH2)2N[double bond, length as m-dash]CH-R-CH[double bond, length as m-dash]N-(CH2)2]3N (R = m-C6H2OH-2-Me-5). In the synthesis the choice of counter ion and solvent proves crucial in controlling the Ln-Ln* composition. Choosing the optimal solvent and counter ion afford pure heterodinuclear complexes with any given combination of Gd(iii)-Lu(iii) including Y(iii). To demonstrate the versatility of the synthesis all dinuclear combinations of Y(iii), Gd(iii), Yb(iii) and Lu(iii) were synthesized resulting in 10 novel complexes of the form LnLn*L(OTf)3 with LnLn* = YbGd 1, YbY 2, YbLu 3, YbYb 4, LuGd 5, LuY 6, LuLu 7, YGd 8, YY 9 and GdGd 10. Through the use of 1H, 13C NMR and mass spectrometry the heterodinuclear nature of YbGd, YbY, YbLu, LuGd, LuY and YGd was confirmed. Crystal structures of LnLn*L(NO3)3 reveal short Ln-Ln distances of ∼3.5 Å. Using SQUID magnetometry the exchange coupling between the lanthanide ions was found to be anti-ferromagnetic for GdGd and YbYb while ferromagnetic for YbGd.

Lanthanide cryptate monometallic coordination complexes.

We report the synthesis, characterisation and magnetic properties of six novel neutral lanthanide cryptate coordination complexes. Reaction of 2,6-diformyl-4-methylphenol, tris(2-aminoethyl)amine and Ln(OTf)3·9H2O in the ratio 3 : 2 : 1, respectively, and in the presence of base affords the isolation of the six complexes LnL·4H2O (Ln = Tb (1), Dy (2), Ho (3), Er (4), Tm (5) and Yb (6)), with H3L being the cryptand N[(CH2)2N[double bond, length as m-dash]CH-R-CH[double bond, length as m-dash]N-(CH2)2]3N (R = m-C6H2OH-2-Me-5). Powder X-ray diffraction confirms that the six complexes are isostructural. The crystal structure of 6 reveals that the Ln(iii) centre is heptacoordinated, in a geometry close to a monocapped distorted octahedron and lies on a pseudo (non-crystallographically imposed) C3 axis. This coordination sphere is similar to the one found in the previously studied Ln(trensal) complexes (H3trensal = 2,2',2''-tris(salicylideneimino)triethylamine). The static and dynamic magnetic properties of these complexes were investigated by SQUID magnetometry. Crystal field parameters were determined for all complexes by modelling of the direct current magnetic susceptibility and variable-temperature-variable-field magnetisation data. As for Ln(trensal), only complexes containing the Kramers ions Dy, Er and Yb displayed out-of-phase susceptibility signals in SQUID measurements in an applied magnetic field. Investigation of the dynamic susceptibility of the Yb complex revealed that the magnetic relaxation is governed by a direct process at low temperatures and a Raman process at higher temperatures, similar to Yb(trensal).

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.