Erratum: Many-Body Models for Molecular Nanomagnets [Phys. Rev. Lett. 110, 157204 (2013)].

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

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.

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.

Magnetic properties and chiral states of a trimetallic uranium complex.

The magnetic properties of the triangular molecular nanomagnet [UO2L]3 (L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate) have been investigated through electron paramagnetic resonance spectroscopy, high-field magnetization and susceptibility measurements. The experimental findings are well reproduced by a microscopic model including exchange interactions and local crystal fields. These results show that [UO2L]3 is characterized by a non-magnetic ground doublet corresponding to two oppositely twisted chiral arrangements of the uranium moments. The non-axial character of single-ion crystal fields leads to quantum tunneling of the noncollinear magnetization in the presence of a magnetic field applied perpendicularly to the triangle plane.

Quantum information processing with hybrid spin-photon qubit encoding.

We introduce a scheme to perform quantum information processing that is based on a hybrid spin-photon qubit encoding. The proposed qubits consist of spin ensembles coherently coupled to microwave photons in coplanar waveguide resonators. The quantum gates are performed solely by shifting the resonance frequencies of the resonators on a nanosecond time scale. An additional cavity containing a Cooper-pair box is exploited as an auxiliary degree of freedom to implement two-qubit gates. The generality of the scheme allows its potential implementation with a wide class of spin systems.

Many-body models for molecular nanomagnets.

We present a flexible and effective ab initio scheme to build many-body models for molecular nanomagnets, and to calculate magnetic exchange couplings and zero-field splittings. It is based on using localized Foster-Boys orbitals as a one-electron basis. We apply this scheme to three paradigmatic systems, the antiferromagnetic rings Cr8 and Cr7Ni, and the single-molecule magnet Fe4. In all cases we identify the essential magnetic interactions and find excellent agreement with experiments.

Magnetic properties and relaxation dynamics of a frustrated Ni7 molecular nanomagnet.

The Ni7 nanomagnet represents an ideal model system for investigating the effects of geometrical frustration in magnetic interactions. The Ni ions in the magnetic core are arranged on two corner-sharing tetrahedra and interact through antiferromagnetic exchange couplings. We show that the high degree of frustration leads to a magnetic energy spectrum with large degeneracies which result in unusual static and dynamical magnetic properties. In particular, the relaxation dynamics of the magnetization is characterized by several distinct characteristic times. We also discuss the possible interest of Ni7 for magnetocaloric refrigeration.

Molecular nanomagnets as quantum simulators.

Quantum simulators are controllable systems that can be used to simulate other quantum systems. Here we focus on the dynamics of a chain of molecular qubits with interposed antiferromagnetic dimers. We theoretically show that its dynamics can be controlled by means of uniform magnetic pulses and used to mimic the evolution of other quantum systems, including fermionic ones. We propose two proof-of-principle experiments based on the simulation of the Ising model in a transverse field and of the quantum tunneling of the magnetization in a spin-1 system.

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.

Relaxation dynamics of the Fe8 molecular nanomagnet as probed by nuclear magnetic resonance.

The relaxation dynamics in molecular nanomagnets can be probed by measurements of NMR 1/T(1). By modelling magnetoelastic interactions, we theoretically investigate the behaviour of the prototype Fe(8) nanomagnet. The results of our model are in agreement with AC susceptibility and recent NMR measurements.

Quadrupolar waves in uranium dioxide.

In presence of active orbital degrees of freedom, elementary excitations around a broken-symmetry state may include multipolar waves, but none of these exotic dispersive excitation branches has ever been identified. We show that quadrupolar waves constitute a major component of the dynamics of uranium dioxide in its magnetoquadrupolar ordered phase, and that many unexplained features in existing inelastic neutron scattering data, including a whole excitation branch, are associated with these propagating quadrupolar fluctuations. Our model permits us to separate the role of Jahn-Teller and superexchange mechanisms as sources of quadrupolar interactions.

Unconventional nonequilibrium dynamics in Ni10 magnetic molecules: evidence from NMR.

Crystals containing Ni10 magnetic molecules display an unprecedented form of out-of-equilibrium behavior of the bulk magnetization M at temperatures as high as 17 K. We have performed 1H NMR measurements to probe the local Ni magnetic moments and their dynamics. It is apparent that no freezing of the Ni moments occurs, in striking contrast to what is observed in blocked superparamagnetic systems. The average local moments display the same behavior as M, thus unambiguously demonstrating the intrinsic character of the phenomenon. This result supports the hypothesis that the slowing down of M is due to a resonant phonon trapping mechanism which prevents the thermalization of M but not the fast spin flippings of the individual molecular moments. Indeed, the measured nuclear spin-lattice relaxation rate points to fast single-molecule dynamics at low temperature.

Breakdown of the giant spin model in the magnetic relaxation of the Mn6 nanomagnets.

We study the spin dynamics in two variants of the high-anisotropy Mn6 nanomagnet by inelastic neutron scattering, magnetic resonance spectroscopy and magnetometry. We show that a giant-spin picture is completely inadequate for these systems and that excited S multiplets play a key role in determining the effective energy barrier for the magnetization reversal. Moreover, we demonstrate the occurrence of tunneling processes involving pair of states having different total spin.

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.

High-temperature slow relaxation of the magnetization in Ni10 magnetic molecules.

We investigate a family of molecular crystals containing noninteracting Ni10 magnetic molecules. We find slow relaxation of the magnetization below a temperature as high as 17 K and we show that this behavior is not associated with an anisotropy energy barrier. Ni10 has a characteristic magnetic energy spectrum structured in dense bands, the lowest of which makes the crystal opaque to phonons of energy below about 1 meV. We ascribe the nonequilibrium behavior to the resulting resonant trapping of these low-energy phonons. Trapping breaks up spin relaxation paths leading to a novel kind of slow magnetic dynamics which occurs in the lack of anisotropy, magnetic interactions and quenched disorder.

Hidden order and low-energy excitations in NpO2.

We investigate the nature of the hidden order parameter in the ordered phase of NpO2, which had been identified with a staggered arrangement of Gamma5 magnetic multipoles. By analyzing the existing experimental data, we show that the most likely driving order parameter is not provided by octupoles, as usually assumed, but rather by the rank-5 triakontadipoles. Calculations of the coupled dynamics of spins, Gamma5 quadrupoles, and Gamma5 triakontadipoles in the ordered phase enable us to analyze the resulting structure of low-energy excitations. We show that the powder inelastic neutron scattering cross section should contain, in addition to the already-observed peak at 6.5 meV, a second weaker peak at about 14 meV.

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.

NMR as a probe of the relaxation of the magnetization in magnetic molecules.

We investigate the time autocorrelation of the molecular magnetization M(t) for three classes of magnetic molecules (antiferromagnetic rings, grids, and nanomagnets), in contact with the phonon heat bath. For all three classes, we find that the exponential decay of the fluctuations of M(t) is characterized by a single characteristic time tau(T,B) for not too high temperature T and field B. This is reflected in a nearly single-Lorentzian shape of the spectral density of the fluctuations. We show that such fluctuations are effectively probed by NMR, and that our theory explains the recent phenomenological observation by Baek et al. [Phys. Rev. B 70, 134434 (2004)] that the Larmor-frequency dependence of 1/T(1) data in a large number of AFM rings fits to a single-Lorentzian form.

S mixing and quantum tunneling of the magnetization in molecular nanomagnets.

The role of S mixing in the quantum tunneling of the magnetization in nanomagnets has been investigated. We show that the effect on the tunneling frequency is huge and that the discrepancy (more than 3 orders of magnitude in the tunneling frequency) between spectroscopic and relaxation measurements in Fe(8) can be resolved if S mixing is taken into account.

Quantum magneto-oscillations in a supramolecular Mn(II)-[3 x 3] grid.

The magnetic grid molecule Mn(II)-[3 x 3] has been studied by high-field torque magnetometry at 3He temperatures. At fields above 5 T, the torque versus field curves exhibit an unprecedented oscillatory behavior. A model is proposed which describes these magneto-oscillations well.