Broad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit.

We explore how to encode more than a qubit in vanadyl porphyrin molecules hosting a S = 1/2 electronic spin coupled to a I = 7/2 nuclear spin. The spin Hamiltonian and its parameters, as well as the spin dynamics, have been determined via a combination of electron paramagnetic resonance, heat capacity, magnetization and on-chip magnetic spectroscopy experiments performed on single crystals. We find low temperature spin coherence times of micro-seconds and spin relaxation times longer than a second. For sufficiently strong magnetic fields (B > 0.1 T, corresponding to resonance frequencies of 9-10 GHz) these properties make vanadyl porphyrin molecules suitable qubit realizations. The presence of multiple equispaced nuclear spin levels then merely provides 8 alternatives to define the '1' and '0' basis states. For lower magnetic fields (B < 0.1 T), and lower frequencies (<2 GHz), we find spectroscopic signatures of a sizeable electronuclear entanglement. This effect generates a larger set of allowed transitions between different electronuclear spin states and removes their degeneracies. Under these conditions, we show that each molecule fulfills the conditions to act as a universal 4-qubit processor or, equivalently, as a d = 16 qudit. These findings widen the catalogue of chemically designed systems able to implement non-trivial quantum functionalities, such as quantum simulations and, especially, quantum error correction at the molecular level.

Magnetism of Dendrimer-Coated Gold Nanoparticles: A Size and Functionalization Study.

Highly sensitive magnetometry reveals paramagnetism in dendrimer-coated gold nanoparticles. Different types of such nanoparticles, as a result of (i) functionalizing with two distinct Percec-type dendrons, linked to gold via dodecanethiol groups, and (ii) postsynthesis annealing in a solvent-free environment that further promotes their growth have been prepared. Ultimately, for each of the two functionalization configurations, we obtain highly monodisperse and stable nanoparticles of two different sizes, with spherical shape. These characteristics allow singling out the source of the measured paramagnetic signals as exclusively arising from the undercoordinated gold atoms on the surfaces of the nanoparticles. Bulk gold and the functional groups of the ligands contribute only diamagnetically.

Charge Delocalization, Oxidation States, and Silver Mobility in the Mixed Silver-Copper Oxide AgCuO2 ¤.

The electronic structure of AgCuO2, and more specifically the possible charge delocalization and its implications for the transport properties, has been the object of debate. Here the problem is faced by means of first-principles density functional theory calculations of the electron and phonon band structures as well as molecular dynamics simulations for different temperatures. It is found that both Cu and Ag exhibit noninteger oxidation states, in agreement with previous spectroscopic studies. The robust CuO2 chains impose a relatively short contact distance to the silver atoms, which are forced to partially use their d z2 orbitals to build a band. This band is partially emptied through overlap with a band of the CuO2 chain, which should be empty if copper were in a Cu3+ oxidation state. In that way, although structural correlations could roughly be consistent with an Ag+Cu3+O2 formulation, the appropriate oxidation states for the silver and copper atoms become Ag(1+δ)+ and Cu(3-δ)+, and as a consequence, the stoichiometric material should be metallic. The study of the electronic structure suggests that Ag atoms form relatively stable chains that can easily slide despite the linear coordination with oxygen atoms of the CuO2 chains. Phonon dispersion calculations and molecular dynamics simulations confirm the stability of the structure although pointing out that sliding of the silver chains is an easy motion that does not lead to substantial modifications of the electronic structure around the Fermi level and, thus, should not alter the good conductivity of the system. However, this sliding of the silver atoms from the equilibrium position explains the observed large thermal factors.

Quantum Monte Carlo simulations of a giant {Ni21Gd20} cage with a S = 91 spin ground state.

The detailed analysis of magnetic interactions in a giant molecule is difficult both because the synthesis of such compounds is challenging and the number of energy levels increases exponentially with the magnitude and number of spins. Here, we isolated a {Ni21Gd20} nanocage with a large number of energy levels (≈5 × 1030) and used quantum Monte Carlo (QMC) simulations to perform a detailed analysis of magnetic interactions. Based on magnetization measurements above 2 K, the QMC simulations predicted very weak ferromagnetic interactions that would give a record S = 91 spin ground state. Low-temperature measurements confirm the spin ground state but suggest a more complex picture due to the single ion anisotropy; this has also been modeled using the QMC approach. The high spin and large number of low-lying states lead to a large low-field magnetic entropy (14.1 J kg-1 K-1 for ΔH = 1 T at 1.1 K) for this material.

Rational electrostatic design of easy-axis magnetic anisotropy in a Zn(II) -Dy(III) -Zn(II) single-molecule magnet with a high energy barrier.

Two novel trinuclear complexes [ZnCl(µ-L)Ln(µ-L)ClZn][ZnCl3 (CH3 OH)]⋅3 CH3 OH (Ln(III) =Dy (1) and Er (2)) have been prepared from the compartmental ligand N,N'-dimethyl-N,N'-bis(2-hydroxy-3-formyl-5-bromo-benzyl)ethylenediamine (H2 L). X-ray studies reveal that Ln(III) ions are coordinated by two [ZnCl(L)](-) units through the phenoxo and aldehyde groups, giving rise to a LnO8 coordination sphere with square-antiprism geometry and strong easy-axis anisotropy of the ground state. Ab initio CASSCF+RASSI calculations carried out on 1 confirm that the ground state is an almost pure MJ =±15/2 Kramers doublet with a marked axial anisotropy, the magnetic moment is roughly collinear with the shortest DyO distances. This orientation of the local magnetic moment of the Dy(III) ion in 1 is adopted to reduce the electronic repulsion between the oblate electron shape of the MJ =±15/2 Kramers doublet and the phenoxo-oxygen donor atoms involved in the shortest DyO bonds. CASSCF+RASSI calculations also show that the ground and first excited states of the Dy(III) ion are separated by 129 cm(-1) . As expected for this large energy gap, compound 1 exhibits, in a zero direct-current field, thermally activated slow relaxation of the magnetization with a large Ueff =140 K. The isostructural Zn-Er-Zn species does not present significant SMM behavior as expected for the prolate electron-density distribution of the Er(III) ion leading to an easy-plane anisotropy of the ground doublet state.

Origin of slow magnetic relaxation in Kramers ions with non-uniaxial anisotropy.

Transition metal ions with long-lived spin states represent minimum size magnetic bits. Magnetic memory has often been associated with the combination of high spin and strong uniaxial magnetic anisotropy. Yet, slow magnetic relaxation has also been observed in some Kramers ions with dominant easy-plane magnetic anisotropy, albeit only under an external magnetic field. Here we study the spin dynamics of cobalt(II) ions in a model molecular complex. We show, by means of quantitative first-principles calculations, that the slow relaxation in this and other similar systems is a general consequence of time-reversal symmetry that hinders direct spin-phonon processes regardless of the sign of the magnetic anisotropy. Its magnetic field dependence is a subtle manifestation of electronuclear spin entanglement, which opens relaxation channels that would otherwise be forbidden but, at the same time, masks the relaxation phenomenon at zero field. These results provide a promising strategy to synthesize atom-size magnetic memories.

Two C3 -symmetric Dy3III complexes with triple di-µ-methoxo-µ-phenoxo bridges, magnetic ground state, and single-molecule magnetic behavior.

Two series of isostructural C(3)-symmetric Ln(3) complexes Ln(3)⋅[BPh(4)] and Ln(3)⋅0.33[Ln(NO(3))(6)] (in which Ln(III) =Gd and Dy) have been prepared from an amino-bis(phenol) ligand. X-ray studies reveal that Ln(III) ions are connected by one µ(2)-phenoxo and two µ(3)-methoxo bridges, thus leading to a hexagonal bipyramidal Ln(3)O(5) bridging core in which Ln(III) ions exhibit a biaugmented trigonal-prismatic geometry. Magnetic susceptibility studies and ab initio complete active space self-consistent field (CASSCF) calculations indicate that the magnetic coupling between the Dy(III) ions, which possess a high axial anisotropy in the ground state, is very weakly antiferromagnetic and mainly dipolar in nature. To reduce the electronic repulsion from the coordinating oxygen atom with the shortest Dy-O distance, the local magnetic moments are oriented almost perpendicular to the Dy(3) plane, thus leading to a paramagnetic ground state. CASSCF plus restricted active space state interaction (RASSI) calculations also show that the ground and first excited state of the Dy(III) ions are separated by approximately 150 and 177 cm(-1), for Dy(3)⋅[BPh(4)] and Dy(3)⋅0.33[Dy(NO(3))(6)], respectively. As expected for these large energy gaps, Dy(3)⋅[BPh(4)] and Dy(3)⋅0.33[Dy(NO(3)(6)] exhibit, under zero direct-current (dc) field, thermally activated slow relaxation of the magnetization, which overlap with a quantum tunneling relaxation process. Under an applied Hdc field of 1000 Oe, Dy(3)⋅[BPh(4)] exhibits two thermally activated processes with U(eff) values of 34.7 and 19.5 cm(-1), whereas Dy(3)⋅0.33[Dy(NO(3))(6)] shows only one activated process with Ueff =19.5 cm(-1).

Insertion of a single-molecule magnet inside a ferromagnetic lattice based on a 3D bimetallic oxalate network: towards molecular analogues of permanent magnets.

The insertion of the single-molecule magnet (SMM) [Mn(III)(salen)(H2O)]2(2+) (salen(2-) = N,N'-ethylenebis-(salicylideneiminate)) into a ferromagnetic bimetallic oxalate network affords the hybrid compound [Mn(III)(salen)(H2O)]2[Mn(II)Cr(III)(ox)3]2⋅(CH3OH)⋅(CH3CN)2 (1). This cationic Mn2 cluster templates the growth of crystals formed by an unusual achiral 3D oxalate network. The magnetic properties of this hybrid magnet are compared with those of the analogous compounds [Mn(III)(salen)(H2O)]2[Zn(II)Cr(III)(ox)3]2⋅(CH3OH)⋅(CH3CN)2 (2) and [In(III)(sal2-trien)][Mn(II)Cr(III)(ox)3]⋅(H2O)0.25⋅(CH3OH)0.25⋅(CH3CN)0.25 (3), which are used as reference compounds. In 2 it has been shown that the magnetic isolation of the Mn2 clusters provided by their insertion into a paramagnetic oxalate network of Cr(III) affords a SMM behavior, albeit with blocking temperatures well below 500 mK even for frequencies as high as 160 kHz. In 3 the onset of ferromagnetism in the bimetallic Mn(II) Cr(III) network is observed at Tc = 5 K. Finally, in the hybrid compound 1 the interaction between the two magnetic networks leads to the antiparallel arrangement of their respective magnetizations, that is, to a ferrimagnetic phase. This coupling induces also important changes on the magnetic properties of 1 with respect to those of the reference compounds 2 and 3. In particular, compound 1 shows a large magnetization hysteresis below 1 K, which is in sharp contrast with the near-reversible magnetizations that the SMMs and the oxalate ferromagnetic lattice show under the same conditions.

A molecular [Mn14] coordination cluster featuring two slowly relaxing nanomagnets.

An extended polypyrazolyl ligand has been used to assemble Mn ions into high spin entities, in the form of one stable molecule composed of two well defined clusters. The slow relaxation of the magnetisation observed is demonstrated to arise from each "half-SMM" composing this molecular cluster pair.

Single-molecule magnetic behavior in a neutral terbium(III) complex of a picolinate-based nitronyl nitroxide free radical.

The terdentate anionic picolinate-based nitronyl nitroxide (picNN) free radical forms neutral and robust homoleptic complexes with rare earth-metal ions. The nonacoordinated Tb(3+) complex Tb(picNN)(3)·6H(2)O is a single-molecule magnet with an activation energy barrier Δ = 22.8 ± 0.5 K and preexponential factor τ(0) = (5.5 ± 1.1) × 10(-9) s. It shows magnetic hysteresis below 1 K.