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

Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

A Cost-Effective Semi-Ab Initio Approach to Model Relaxation in Rare-Earth Single-Molecule Magnets

We discuss a cost-effective approach to understand magnetic relaxation in the new generation of rare-earth single-molecule magnets. It combines ab initio calculations of the crystal field parameters, of the magneto-elastic coupling with local modes, and of the phonon density of states with fitting of only three microscopic parameters. Although much less demanding than a fully ab initio approach, the method gives important physical insights into the origin of the observed relaxation. By applying it to high-anisotropy compounds with very different relaxation, we demonstrate the power of the approach and pinpoint ingredients for improving the performance of single-molecule magnets.

Unveiling phonons in a molecular qubit with four-dimensional inelastic neutron scattering and density functional theory

Phonons are the main source of relaxation in molecular nanomagnets, and different mechanisms have been proposed in order to explain the wealth of experimental findings. However, very limited experimental investigations on phonons in these systems have been performed so far, yielding no information about their dispersions. Here we exploit state-of-the-art single-crystal inelastic neutron scattering to directly measure for the first time phonon dispersions in a prototypical molecular qubit. Both acoustic and optical branches are detected in crystals of [VO(acac)[Formula: see text]] along different directions in the reciprocal space. Using energies and polarisation vectors calculated with state-of-the-art Density Functional Theory, we reproduce important qualitative features of [VO(acac)[Formula: see text]] phonon modes, such as the presence of low-lying optical branches. Moreover, we evidence phonon anti-crossings involving acoustic and optical branches, yielding significant transfers of the spin-phonon coupling strength between the different modes.

Comparison of spin dynamics and magnetic properties in antiferromagnetic closed and open molecular Cr-based rings

We present magnetization and (1)H nuclear magnetic resonance (NMR) measurements performed in both closed Cr8 and open Cr8Zn antiferromagnetic molecular rings in the temperature range 1.65  <  T  <  300 K at different external magnetic fields. The magnetization measurements on Cr8Zn are consistent with a small decrease of the exchange constant J(Cr-Cr) and a much smaller gap between the singlet ground state and the first magnetic excited state when compared with the same properties of the closed ring Cr8, in agreement with previous inelastic neutron scattering results. The temperature dependence of the (1)H NMR nuclear spin lattice relaxation rate (NSLR), 1/T1(T), was found to be similar in both open and closed rings with a magnetic field dependent peak centered at a temperature of the order of the corresponding exchange constant J(Cr-Cr). Such main peak in the NSLR could be fitted with a single correlation frequency ω(c1) as in most molecular magnets. At low temperature T  <  4 K, a new feature not observed in previous NMR measurements on antiferromagnetic rings and consisting in a smaller peak of 1/T1(T) which is well resolved only in Cr8Zn, was singled out. This low-T peak indicates the presence of a second correlation frequency ω(c2) of the magnetization, found to be quite different between the two rings and thus possibly reflecting the different low temperature level structure associated with the different spin topology. The presence of ω(c2) is confirmed by the NMR spin-spin relaxation rate enhancement, which generates a two-steps wipe-out effect of the NMR signal intensity.

Coherent Spin Dynamics in Molecular Cr8Zn Wheels

Controlling and understanding transitions between molecular spin states allows selection of the most suitable ones for qubit encoding. Here we present a detailed investigation of single crystals of a polynuclear Cr8Zn molecular wheel using 241 GHz electron paramagnetic resonance (EPR) spectroscopy in high magnetic field. Continuous wave spectra are well reproduced by spin Hamiltonian calculations, which evidence that transitions in correspondence to a well-defined anticrossing involve mixed states with different total spin. We studied, by means of spin echo experiments, the temperature dependence of the dephasing time (T2) down to 1.35 K. These results are reproduced by considering both hyperfine and intermolecular dipolar interactions, evidencing that the dipolar contribution is completely suppressed at the lowest temperature. Overall, these results shed light on the effects of the decoherence mechanisms, whose understanding is crucial to exploit chemically engineered molecular states as a resource for quantum information processing.

Spin dynamics of the giant polyoxometalate molecule {Mn₄₀W₂₂₄} studied by NMR

(7)Li nuclear magnetic resonance (NMR) studies have been performed to investigate magnetic properties and spin dynamics of Mn(3+) (S = 2) spins in the giant polyoxometalate molecule {Mn₄₀W₂₂₄}. The (7)Li-NMR line width is proportional to the external magnetic field H as expected in a paramagnetic state above 3 K. Below this temperature the line width shows a sudden increase and is almost independent of H, which indicates freezing of the local Mn(3+) spins. The temperature dependence of T₁ for both (1)H and (7)Li reveals slow spin dynamics at low temperatures, consistent with spin freezing. The slow spin dynamics is also evidenced by the observation of a peak of 1/T₂ around 3 K, where the fluctuation frequency of spins is of the order of ∼200 kHz. An explicit form of the temperature dependence of the fluctuation frequency of Mn(3+) spins is derived from the nuclear relaxation data.

NMR chemical shift in an electronic state with arbitrary degeneracy

We present a theory of nuclear magnetic resonance shielding tensors for electronic states with arbitrary degeneracy. The shieldings are here expressed in terms of generalized Zeeman (g((k))) and hyperfine (A((k))) tensors, of all ranks k allowed by the size of degeneracy. Contrary to recent proposals [T. O. Pennanen and J. Vaara, Phys. Rev. Lett. 100, 133002 (2008)], our theory is valid in the strong spin-orbit coupling limit. Ab initio calculations for the fourfold degenerate Γ(8) ground state of lanthanide-doped fluorite crystals CaF(2):Ln (Ln=Pr(2+), Nd(3+), Sm(3+), and Dy(3+)) show that previously neglected contributions can account for more than 50% of the paramagnetic shift.

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.

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.

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.