This corrects the article DOI: 10.1103/PhysRevLett.110.157204.

Molecular Nanomagnets have attracted the attention of the scientific community since the rich physics behind their magnetic behaviour make them ideal test-beds for fundamental concepts in quantum mechanics. Sophisticated experiments and targeted research activities have also unveiled their potential for several technological applications. Inelastic neutron scattering is a powerful and widely used technique to investigate the properties of these systems. The new generation of spectrometers, equipped with arrays of position-sensitive detectors, enable to efficiently measure the neutron cross-sections as a function of energy and of the three component of the momentum transfer vector Q, in vast portions of the reciprocal space. Exploiting these capabilities together with the availability of sufficiently large singlecrystal samples of MNMs, it is now possible to obtain an unprecedented insight into the coherent spin dynamics of these molecular clusters. This is witnessed by several recent results, that we present in this review. By using the benchmark system Cr8, it has been demonstrated that the richness of the four-dimensional inelastic neutrons scattering technique enables to extract dynamical correlation functions directly from the data. This technique has been also applied to the archetypical single-molecule magnet Mn12 to unambiguously characterise its Spin Hamiltonian as well as to portray the entanglement between molecular qubits in (Cr7Ni)2.

In the Cr7Co model-system the anisotropy of CoII is effectively transferred to the whole cluster through strong and anisotropic exchange interactions.

The discovery of magnetic bistability in Mn-12 more than 20 years ago marked the birth of molecular magnetism, an extremely fertile interdisciplinary field and a powerful route to create tailored magnetic nanostructures. However, the difficulty to determine interactions in complex polycentric molecules often prevents their understanding. Mn-12 is an outstanding example of this difficulty: although it is the forefather and most studied of all molecular nanomagnets, an unambiguous determination of even the leading magnetic exchange interactions is still lacking. Here we exploit four-dimensional inelastic neutron scattering to portray how individual spins fluctuate around the magnetic ground state, thus fixing the exchange couplings of Mn-12 for the first time. Our results demonstrate the power of four-dimensional inelastic neutron scattering as an unrivaled tool to characterize magnetic clusters.

Entanglement is a crucial resource for quantum information processing and its detection and quantification is of paramount importance in many areas of current research. Weakly coupled molecular nanomagnets provide an ideal test bed for investigating entanglement between complex spin systems. However, entanglement in these systems has only been experimentally demonstrated rather indirectly by macroscopic techniques or by fitting trial model Hamiltonians to experimental data. Here we show that four-dimensional inelastic neutron scattering enables us to portray entanglement in weakly coupled molecular qubits and to quantify it. We exploit a prototype (Cr7Ni)(2) supramolecular dimer as a benchmark to demonstrate the potential of this approach, which allows one to extract the concurrence in eigenstates of a dimer of molecular qubits without diagonalizing its full Hamiltonian.

Abstract The spin dynamics of Cr8Mn, a nine‐membered antiferromagnetic (AF) molecular nanomagnet, are investigated. Cr8Mn is a rare example of a large odd‐membered AF ring, and has an odd‐number of 3d‐electrons present. Odd‐membered AF rings are unusual and of interest due to the presence of competing exchange interactions that result in frustrated‐spin ground states. The chemical synthesis and structures of two Cr8Mn variants that differ only in their crystal packing are reported. Evidence of spin frustration is investigated by inelastic neutron scattering (INS) and muon spin relaxation spectroscopy (μSR). From INS studies we accurately determine an appropriate microscopic spin Hamiltonian and we show that μSR is sensitive to the ground‐spin‐state crossing from S=1/2 to S=3/2 in Cr8Mn. The estimated width of the muon asymmetry resonance is consistent with the presence of an avoided crossing. The investigation of the internal spin structure of the ground state, through the analysis of spin‐pair correlations and scalar‐spin chirality, shows a non‐collinear spin structure that fluctuates between non‐planar states of opposite chiralities.

1. Materials and Synthesis Unless stated otherwise, all reagents and solvents were purchased from Sigma-Aldrich and used without further purification. Analytical data were obtained by the Microanalysis laboratory at the University of Manchester. Carbon, Hydrogen, Nitrogen analysis (CHN) by Flash 2000 elemental analyser. Metals analysis by Thermo iCap 6300 Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES).

We investigate the magnetic properties and the phonon-induced relaxation dynamics of the first regular Cr-9 antiferromagnetic (AF) ring, which represents a prototype frustrated AF ring. Geometrical frustration in Cr-9 yields an energy spectrum with twofold degenerate low-lying levels and a low-spin ground state. The electronic relaxation dynamics is probed by H-1-NMR through the temperature dependence of the spin-lattice relaxation rate 1/T-1. We develop a microscopic model that reproduces 1/T-1(T) curves, taking also into account the wipeout effect. By interpreting these measurements we determine the spin-phonon coupling strength and we investigate the decay of the cluster magnetization due to the spin-phonon interaction. We find that at very low temperatures, the relaxation is characterized by a single dominating Arrhenius-type relaxation process, whereas several relevant processes emerge at higher temperatures. In addition, we calculate the temperature andmagnetic field dependence of level lifetimes.

Antiferromagnetic molecular rings are widely studied both for fundamental quantum-mechanical issues and for technological applications, particularly in the field of quantum information processing. Here we present a detailed first-principles study of two families---purple and green---of ${{\mathrm{Cr}}_{7}M}$ antiferromagnetic rings, where $M$ is a divalent transition metal ion ($M={\mathrm{Ni}}^{2+}, {\mathrm{Mn}}^{2+}$, and ${\mathrm{Zn}}^{2+}$). We employ a recently developed flexible and efficient scheme to build ab initio system-specific Hubbard models. From such many-body models we systematically derive the low-energy effective spin Hamiltonian for the rings. Our approach allows us to calculate isotropic as well as anisotropic terms of the spin Hamiltonian, without any a priori assumption on its form. For each compound we calculate magnetic exchange couplings, zero-field splitting tensors, and gyromagnetic tensors, finding good agreement with experimental results.

Nine new complexes are reported involving linked heterometallic rings; one ring is designed as a ligand for the second, and the compounds produced can be regarded as molecular prototypes for implementing quantum gates featuring two subtly different qubits.

Compounds of general formula [Cr7MF3(Etglu)(O2C(t)Bu)15(Phpy)] [H5Etglu = N-ethyl-d-glucamine; Phpy = 4-phenylpyridine; M = Zn (1), Mn (2), Ni (3)] have been prepared. The structures contain an irregular octagon of metal sites formed around the penta-deprotonated Etglu(5-) ligand; the chirality of N-ethyl-d-glucamine is retained in the final product. The seven Cr(III) sites have a range of coordination environments, and the divalent metal site is crystallographically identified and has a Phpy ligand attached to it. By using complementary experimental techniques, including magnetization and specific heat measurements, inelastic neutron scattering, and electron paramagnetic resonance spectroscopy, we have investigated the magnetic features of this family of {Cr7M} rings. Microscopic parameters of the spin Hamiltonian have been determined as a result of best fits of the different experimental data, allowing a direct comparison with corresponding parameters found in the parent compounds. We examine whether these parameters can be transferred between compounds and compare them with those of an earlier family of heterometallic rings.

We discuss a scalable scheme for the implementation of quantum-information processing in qubits formed by superconducting resonators and spin ensembles. The scheme is based on a hybrid dual-rail encoding, which allows one to perform both single- and two-qubit gates by shifting the resonator frequency. We estimate the quantum-gate fidelity by simulating the driven dynamics through a master-equation approach. High values of the fidelity can be achieved also in the presence of the main decoherence sources, namely, cavity-photon loss, and pure dephasing of the superconductive elements that are involved in the two-qubit gates. This result allows envisioning the scalability of such elements to a quantum-computing architecture made of an array of hybrid spin-photon qubits. Analogous results are obtained for a simpler, nonscalable setup, which we propose here in order to simplify the realization of the first proof-of-principle experiments.

Molecular nanomagnets are attractive candidate qubits because of their wide inter-and intra-molecular tunability. Uniform magnetic pulses could be exploited to implement one-and two-qubit gates in presence of a properly engineered pattern of interactions, but the synthesis of suitable and potentially scalable supramolecular complexes has proven a very hard task. Indeed, no quantum algorithms have ever been implemented, not even a proof-of-principle two-qubit gate. Here we show that the magnetic couplings in two supramolecular {Cr7Ni}-Ni-{Cr7Ni} assemblies can be chemically engineered to fit the above requisites for conditional gates with no need of local control. Microscopic parameters are determined by a recently developed many-body ab-initio approach and used to simulate quantum gates. We find that these systems are optimal for proof-of-principle two-qubit experiments and can be exploited as building blocks of scalable architectures for quantum simulation.

Compounds of general formula [Cr7MF3(Etglu)(O2C(t)Bu)15(Phpy)] [H5Etglu = N-ethyl-d-glucamine; Phpy = 4-phenylpyridine; M = Zn (1), Mn (2), Ni (3)] have been prepared. The structures contain an irregular octagon of metal sites formed around the penta-deprotonated Etglu(5-) ligand; the chirality of N-ethyl-d-glucamine is retained in the final product. The seven Cr(III) sites have a range of coordination environments, and the divalent metal site is crystallographically identified and has a Phpy ligand attached to it. By using complementary experimental techniques, including magnetization and specific heat measurements, inelastic neutron scattering, and electron paramagnetic resonance spectroscopy, we have investigated the magnetic features of this family of {Cr7M} rings. Microscopic parameters of the spin Hamiltonian have been determined as a result of best fits of the different experimental data, allowing a direct comparison with corresponding parameters found in the parent compounds. We examine whether these parameters can be transferred between compounds and compare them with those of an earlier family of heterometallic rings.

Compounds of general formula [Cr7MF3(Etglu)(O2C(t)Bu)15(Phpy)] [H5Etglu = N-ethyl-d-glucamine; Phpy = 4-phenylpyridine; M = Zn (1), Mn (2), Ni (3)] have been prepared. The structures contain an irregular octagon of metal sites formed around the penta-deprotonated Etglu(5-) ligand; the chirality of N-ethyl-d-glucamine is retained in the final product. The seven Cr(III) sites have a range of coordination environments, and the divalent metal site is crystallographically identified and has a Phpy ligand attached to it. By using complementary experimental techniques, including magnetization and specific heat measurements, inelastic neutron scattering, and electron paramagnetic resonance spectroscopy, we have investigated the magnetic features of this family of {Cr7M} rings. Microscopic parameters of the spin Hamiltonian have been determined as a result of best fits of the different experimental data, allowing a direct comparison with corresponding parameters found in the parent compounds. We examine whether these parameters can be transferred between compounds and compare them with those of an earlier family of heterometallic rings.