Magnetic Exchange Interactions in the Molecular Nanomagnet Mn_{12}.

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.

Magnetic properties and hyperfine interactions in Cr8, Cr7Cd, and Cr7Ni molecular rings from ¹9F-NMR.

A detailed experimental investigation of the (19)F nuclear magnetic resonance is made on single crystals of the homometallic Cr8 antiferromagnetic molecular ring and heterometallic Cr7Cd and Cr7Ni rings in the low temperature ground state. Since the F(-) ion is located midway between neighboring magnetic metal ions in the ring, the (19)F-NMR spectra yield information about the local electronic spin density and (19)F hyperfine interactions. In Cr8, where the ground state is a singlet with total spin S(T) = 0, the (19)F-NMR spectra at 1.7 K and low external magnetic field display a single narrow line, while when the magnetic field is increased towards the first level crossing field, satellite lines appear in the (19)F-NMR spectrum, indicating a progressive increase in the Boltzmann population of the first excited state S(T) = 1. In the heterometallic rings, Cr7Cd and Cr7Ni, whose ground state is magnetic with S(T) = 3/2 and S(T) = 1/2, respectively, the (19)F-NMR spectrum has a complicated structure which depends on the strength and orientation of the magnetic field, due to both isotropic and anisotropic transferred hyperfine interactions and classical dipolar interactions. From the (19)F-NMR spectra in single crystals we estimated the transferred hyperfine constants for both the F(-)-Ni(2+) and the F(-)-Cd(2+) bonds. The values of the hyperfine constants compare well to the ones known for F(-)-Ni(2+) in KNiF3 and NiF2 and for F(-)-Cr(3+) in K2NaCrF6. The results are discussed in terms of hybridization of the 2s, 2p orbitals of the F(-) ion and the d orbitals of the magnetic ion. Finally, we discuss the implications of our results for the electron-spin decoherence.

Chemical engineering of molecular qubits.

We show that the electron spin phase memory time, the most important property of a molecular nanomagnet from the perspective of quantum information processing, can be improved dramatically by chemically engineering the molecular structure to optimize the environment of the spin. We vary systematically each structural component of the class of antiferromagnetic Cr(7)Ni rings to identify the sources of decoherence. The optimal structure exhibits a phase memory time exceeding 15 µs.

Propagation of spin information at the supramolecular scale through heteroaromatic linkers.

We report an in-depth study on how spin information propagates at supramolecular scale through a family of heteroaromatic linkers. By density-functional theory calculations, we rationalize the behavior of a series of Cr7Ni dimers for which we are able to systematically change the aromatic linker thus tuning the strength of the magnetic interaction, as experimentally shown by low temperature micro-SQUID and specific heat measurements. We also predict a cos2 dependence of the magnetic coupling on the twisting angle between the aromatic cycles in bicyclic linkers, a mechanism parallel to charge transport on similar systems [L. Venkataraman et al., Nature (London) 442, 904 (2006)].

Entanglement in supramolecular spin systems of two weakly coupled antiferromagnetic rings (purple-Cr7Ni).

We characterize supramolecular magnetic structures, consisting of two weakly coupled antiferromagnetic rings, by low-temperature specific heat, susceptibility, magnetization and electron paramagnetic resonance measurements. Intra- and inter-ring interactions are modeled through a microscopic spin-Hamiltonian approach that reproduces all the experimental data quantitatively and legitimates the use of an effective two-qubit picture. Spin entanglement between the rings is experimentally demonstrated through magnetic susceptibility below 50 mK and theoretically quantified by the concurrence.

Breaking the ring: 53Cr-NMR on the Cr8Cd molecular nanomagnet.

An accurate experimental characterization of finite antiferromagnetic (AF) spin chains is crucial for controlling and manipulating their magnetic properties and quantum states for potential applications in spintronics or quantum computation. In particular, finite AF chains are expected to show a different magnetic behaviour depending on their length and topology. Molecular AF rings are able to combine the quantum-magnetic behaviour of AF chains with a very remarkable tunability of their topological and geometrical properties. In this work we measure the 53Cr-NMR spectra of the Cr8Cd ring to study the local spin densities on the Cr sites. Cr8Cd can in fact be considered a model system of a finite AF open chain with an even number of spins. The NMR resonant frequencies are in good agreement with the theoretical local spin densities, by assuming a core polarization field A C = -12.7 T µ B -1. Moreover, these NMR results confirm the theoretically predicted non-collinear spin arrangement along the Cr8Cd ring, which is typical of an even-open AF spin chain.

Portraying entanglement between molecular qubits with four-dimensional inelastic neutron scattering.

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.

Direct observation of finite size effects in chains of antiferromagnetically coupled spins.

Finite spin chains made of few magnetic ions are the ultimate-size structures that can be engineered to perform spin manipulations for quantum information devices. Their spin structure is expected to show finite size effects and its knowledge is of great importance both for fundamental physics and applications. Until now a direct and quantitative measurement of the spatial distribution of the magnetization of such small structures has not been achieved even with the most advanced microscopic techniques. Here we present measurements of the spin density distribution of a finite chain of eight spin-3/2 ions using polarized neutron diffraction. The data reveal edge effects that are a consequence of the finite size and of the parity of the chain and indicate a noncollinear spin arrangement. This is in contrast with the uniform spin distribution observed in the parent closed chain and the collinear arrangement in odd-open chains.

Local spin density in the Cr7Ni antiferromagnetic molecular ring and 53Cr-NMR.

We present (53)Cr-NMR spectra collected at low temperature in a single crystal of the heterometallic antiferromagnetic (AF) ring Cr(7)Ni in the S = 1/2 ground state with the aim of establishing the distribution of the local electronic moment in the ring. Due to the poor S/N we observed only one signal which is ascribed to three almost equivalent (53)Cr nuclei in the ring. The calculated spin density in Cr(7)Ni in the ground state, with the applied magnetic field both parallel and perpendicular to the plane of the ring, turns out to be AF staggered with the greatest component of the local spin for the Cr(3+) ions next to the Ni(2+) ion. The (53)Cr-NMR frequency was found to be in good agreement with the local spin density calculated theoretically by assuming a core polarization field of H(cp) = - 11 T/µ(B) for both orientations, close to the value found previously in Cr(7)Cd. The observed orientation dependence of the local spin moments is well reproduced by the theoretical calculation and evidences the importance of single-ion and dipolar anisotropies.

Observation of a level crossing in a molecular nanomagnet using implanted muons.

We have observed an electronic energy level crossing in a molecular nanomagnet (MNM) using muon spin relaxation. This effect, not observed previously despite several muon studies of MNM systems, provides further evidence that the spin relaxation of the implanted muon is sensitive to the dynamics of the electronic spin. Our measurements on a broken ring MNM [H(2)N(t)Bu(is)Pr][Cr(8)CdF(9)(O(2)CC(CH(3))(3))(18)], which contains eight Cr ions, show clear evidence for the S = 0 --> S = 1 transition that takes place at B(c) = 2.3 T. The crossing is observed as a resonance-like dip in the average positron asymmetry and also in the muon spin relaxation rate, which shows a sharp increase in magnitude at the transition and a peak centred within the S = 1 regime.

Quantum oscillations of the total spin in a heterometallic antiferromagnetic ring: evidence from neutron spectroscopy.

Using inelastic neutron scattering and applied fields up to 11.4 T, we have studied the spin dynamics of the Cr7Ni antiferromagnetic ring in the energy window 0.05-1.6 meV. We demonstrate that the external magnetic field induces an avoided crossing (anticrossing) between energy levels with different total-spin quantum numbers. This corresponds to quantum oscillations of the total spin of each molecule. The inelastic character of the observed excitation and the field dependence of its linewidth indicate that molecular spins oscillate coherently for a significant number of cycles. Precise signatures of the anticrossing are also found at higher energy, where measured and calculated spectra match very well.

Local spin moment distribution in antiferromagnetic molecular rings probed by NMR.

The NMR spectra of 19F and 53Cr have been obtained at low temperatures in a heterometallic substituted antiferromagnetic (AF) ring Cr7Cd with an S=3/2 ground state and compared with the spectra in a homometallic Cr8 AF ring with an S=0 ground state. From the analysis of the spectra one can derive directly model independent values of the staggered nonuniform distribution of the local moment in the heterometallic ring Cr7Cd. The experimental values are found to be in excellent agreement with the theoretical values calculated on the basis of an effective spin Hamiltonian which includes crystal field effects.

Molecular engineering of antiferromagnetic rings for quantum computation.

The substitution of one metal ion in a Cr-based molecular ring with dominant antiferromagnetic couplings allows the engineering of its level structure and ground-state degeneracy. Here we characterize a Cr7Ni molecular ring by means of low-temperature specific-heat and torque-magnetometry measurements, thus determining the microscopic parameters of the corresponding spin Hamiltonian. The energy spectrum and the suppression of the leakage-inducing S mixing render the Cr7Ni molecule a suitable candidate for the qubit implementation, as further substantiated by our quantum-gate simulations.