The critical role of ultra-low-energy vibrations in the relaxation dynamics of molecular qubits.

Improving the performance of molecular qubits is a fundamental milestone towards unleashing the power of molecular magnetism in the second quantum revolution. Taming spin relaxation and decoherence due to vibrations is crucial to reach this milestone, but this is hindered by our lack of understanding on the nature of vibrations and their coupling to spins. Here we propose a synergistic approach to study a prototypical molecular qubit. It combines inelastic X-ray scattering to measure phonon dispersions along the main symmetry directions of the crystal and spin dynamics simulations based on DFT. We show that the canonical Debye picture of lattice dynamics breaks down and that intra-molecular vibrations with very-low energies of 1-2 meV are largely responsible for spin relaxation up to ambient temperature. We identify the origin of these modes, thus providing a rationale for improving spin coherence. The power and flexibility of our approach open new avenues for the investigation of magnetic molecules with the potential of removing roadblocks toward their use in quantum devices.

Resonant inelastic x-ray spectroscopy on UO2 as a test case for actinide materials.

Resonant inelastic x-ray spectroscopy at the uranium N4 absorption edge at 778 eV has been used to reveal the excitations in UO2 up to 1 eV. The earlier (1989) studies by neutron inelastic scattering of the crystal-field states within the 3H4 multiplet are confirmed. In addition, the first excited state of the 3F2 multiplet at ∼520 meV has been established, and there is a weak signal corresponding to the next excited state at ∼920 meV. This represents a successful application of soft x-ray spectroscopy to an actinide sample, and resolves an open question in UO2 that has been discussed for 50 years. The technique is described and important caveats are drawn about possible future applications.

The fifty years it has taken to understand the dynamics of UO2 in its ordered state.

In 1966 Roger Cowley (together with Gerald Dolling) reported the first neutron inelastic scattering from the magnetic excitations from UO2 below its antiferromagnetic ordering temperature of 30 K. They showed the strong magnon-phonon coupling in this material and that the excitations appeared to contain an additional mode that was not anticipated. Cowley never returned to UO2, but showed a keen interest in the developments. Forty years after this pioneering work, unambiguous evidence was found (using resonance x-ray techniques) for the ordering below T N of the electric quadrupoles involving the anisotropy of the 5f charge distribution around the uranium nuclei. A further 10 years later, now armed with a full theory for the excitation spectrum expected for phonons, magnons, and quadrupoles, we can identify the latter as the source of the 'extra' mode reported first in 1966. The story is a long winding one, with the expected serendipity and dead ends, but is now (almost) completed.

Direct observation of pure pentavalent uranium in U2O5 thin films by high resolution photoemission spectroscopy.

Thin films of the elusive intermediate uranium oxide U2O5 have been prepared by exposing UO3 precursor multilayers to atomic hydrogen. Electron photoemission spectra measured about the uranium 4f core-level doublet contain sharp satellites separated by 7.9(1) eV from the 4f main lines, whilst satellites characteristics of the U(IV) and U(VI) oxidation states, expected respectively at 6.9(1) and 9.7(1) eV from the main 4f lines, are absent. This shows that uranium ions in the films are in a pure pentavalent oxidation state, in contrast to previous investigations of binary oxides claiming that U(V) occurs only as a metastable intermediate state coexisting with U(IV) and U(VI) species. The ratio between the 5f valence band and 4f core-level uranium photoemission intensities decreases by about 50% from UO2 to U2O5, which is consistent with the 5f 2 (UO2) and 5f 1 (U2O5) electronic configurations of the initial state. Our studies conclusively establish the stability of uranium pentoxide.

Probing Magnetism in the Vortex Phase of PuCoGa_{5} by X-Ray Magnetic Circular Dichroism.

We measure x-ray magnetic circular dichroism (XMCD) spectra at the Pu M_{4,5} absorption edges from a newly prepared high-quality single crystal of the heavy-fermion superconductor ^{242}PuCoGa_{5}, exhibiting a critical temperature T_{c}=18.7 K. The experiment probes the vortex phase below T_{c} and shows that an external magnetic field induces a Pu 5f magnetic moment at 2 K equal to the temperature-independent moment measured in the normal phase up to 300 K by a superconducting quantum interference device. This observation is in agreement with theoretical models claiming that the Pu atoms in PuCoGa_{5} have a nonmagnetic singlet ground state resulting from the hybridization of the conduction electrons with the intermediate-valence 5f electronic shell. Unexpectedly, XMCD spectra show that the orbital component of the 5f magnetic moment increases significantly between 30 and 2 K; the antiparallel spin component increases as well, leaving the total moment practically constant. We suggest that this indicates a low-temperature breakdown of the complete Kondo-like screening of the local 5f moment.

Absence of superconductivity in fluorine-doped neptunium pnictide NpFeAsO.

X-ray diffraction, specific heat, magnetic susceptibility and inelastic x-ray scattering measurements on the transurarium oxypnictides NpFeAsO and NpFeAsO0.85F0.15 are presented. No superconductivity down to 2 K was observed upon fluorine doping, contrary to the structurally analogous rare-earth pnictides. No modification of the phonon density of states was observed upon doping with fluorine. We discuss our results in light of the latest experimental and theoretical studies on the role of phonons in the superconducting pnictide compounds.

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.

Magnetic polarization of the americium J=0 ground state in AmFe(2).

Trivalent americium has a nonmagnetic (J=0) ground state arising from the cancellation of the orbital and spin moments. However, magnetism can be induced by a large molecular field if Am^{3+} is embedded in a ferromagnetic matrix. Using the technique of x-ray magnetic circular dichroism, we show that this is the case in AmFe_{2}. Since ⟨J_{z}⟩=0, the spin component is exactly twice as large as the orbital one, the total Am moment is opposite to that of Fe, and the magnetic dipole operator ⟨T_{z}⟩ can be determined directly; we discuss the progression of the latter across the actinide series.

A plutonium-based single-molecule magnet.

The magnetic properties of the 5f(5) [tris-(tri-1-pyrazolylborato)-plutonium(III)] complex have been investigated by ac susceptibility measurements, showing it to be the first plutonium single-molecule magnet; its magnetic relaxation slows down with decreasing temperature through a thermally activated mechanism followed by a quantum tunnelling regime below 5 K.

(237)Np Mössbauer effect study on NpFeAsO.

We report (237)Np Mössbauer measurements on NpFeAsO. The Np atoms were found to occupy only one crystallographic site. The value of the isomer shift (δ âˆ¼ 9.1 mm s(-1) versus NpAl2) indicates a 5f(4) electronic configuration (Np(3+) ions). The magnetic ordering of the Np sublattice below 60 K is established and the saturated ordered magnetic moment is determined to be 1.73µB at 3.6 K. The unique set of hyperfine parameters exclude a modulated magnetic structure or spin waves on the Np site. The neptunium magnetic moments µNp are found to lie along the tetragonal c-axis.

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.

Strong-coupling d-wave superconductivity in PuCoGa5 probed by point-contact spectroscopy.

Superconductivity is due to an attractive interaction between electrons that, below a critical temperature, drives them to form Cooper pairs and to condense into a ground state separated by an energy gap from the unpaired states. In the simplest cases, the pairing is mediated by lattice vibrations and the wavefunction of the pairs is isotropic. Less conventional pairing mechanisms can favour more exotic symmetries of the Cooper pairs. Here, we report on point-contact spectroscopy measurements in PuCoGa(5), a moderate heavy-fermion superconductor with a record high critical temperature T(c)=18.5 K. The results prove that the wavefunction of the paired electrons has a d-wave symmetry, with four lobes and nodes, and show that the pairing is likely to be mediated by spin fluctuations. Electronic structure calculations, which take into account the full structure of the f-orbital multiplets of Pu, provide a hint of the possible origin of these fluctuations.

Localized 5f electrons in superconducting PuCoIn5: consequences for superconductivity in PuCoGa5.

The physical properties of the first In analog of the PuMGa(5) (M = Co, Rh) family of superconductors, PuCoIn(5), are reported. With its unit cell volume being 28% larger than that of PuCoGa(5), the characteristic spin-fluctuation energy scale of PuCoIn(5) is three to four times smaller than that of PuCoGa(5), which suggests that the Pu 5f electrons are in a more localized state relative to PuCoGa(5). This raises the possibility that the high superconducting transition temperature T(c) = 18.5 K of PuCoGa(5) stems from the proximity to a valence instability, while the superconductivity at T(c) = 2.5 K of PuCoIn(5) is mediated by antiferromagnetic spin fluctuations associated with a quantum critical point.

Magnetic and electronic properties of NpFeGa5.

NpFeGa(5) single crystals prepared by the Ga-flux method have been investigated by magnetisation, specific heat and (237)Np Mössbauer spectroscopy measurements. An antiferromagnetic (AF) transition has been observed at T(N) ~114 K. The second AF transition which takes place at T* ~74 K has only been detected in the magnetisation data. A saturated ordered Np moment of 1.00(5) µ(B) and the occurrence of an Np(3 + ) charge state were inferred from the Mössbauer data. The angle between the Np ordered moment and the basal plane was shown to be ~17°, in good agreement with the value observed by neutron diffraction in the low temperature AF phase. The absence of change of the quadrupole interaction parameters at T* did not allow us to gain information on the Np moment reorientation at T*. The trend of the isomer shift along the NpTGa(5) series and the discrepancy between the Np moments determined by neutron diffraction and Mössbauer spectroscopy indicated a partial spatial delocalisation of the 5f electrons in NpFeGa(5).

Superexchange coupling and slow magnetic relaxation in a transuranium polymetallic complex.

{Np(VI)O2Cl2}{Np(V)O2Cl(thf)3}2 is the first studied example of a polymetallic transuranic complex displaying both slow relaxation of the magnetization and effective superexchange interactions between 5f centers. The coupling constant for Np(V)-Np(VI) pairs is 10.8 K, more than 1 order of magnitude larger than the common values found for rare-earth ions in similar environments. The dynamic magnetic behavior displays slow relaxation of magnetization of molecular origin with an energy barrier of 140 K, which is nearly twice the size of the highest barrier found in polymetallic clusters of the d block. Our observations also suggest that future actinide-based molecular magnets will have very different behavior to lanthanide-based clusters.

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.

Polarized-neutron-scattering study of the spin-wave excitations in the 3-k ordered phase of uranium antimonide.

The anisotropy of magnetic fluctuations propagating along the [1 1 0] direction in the ordered phase of uranium antimonide has been studied using polarized inelastic neutron scattering. The observed polarization behavior of the spin waves is a natural consequence of the longitudinal 3-k magnetic structure; together with recent results on the 3-k-transverse uranium dioxide, these findings establish this technique as an important tool to study complex magnetic arrangements. Selected details of the magnon excitation spectra of USb have also been reinvestigated, indicating the need to revise the currently accepted theoretical picture for this material.

Electronic state of PuCoGa5 and NpCoGa5 as probed by polarized neutrons.

By using single crystals and polarized neutrons, we have measured the orbital and spin components of the microscopic magnetization in the paramagnetic state of NpCoGa(5) and PuCoGa(5). The microscopic magnetization of NpCoGa(5) agrees with that observed in bulk susceptibility measurements and the magnetic moment has spin and orbital contributions as expected for intermediate coupling. In contrast, for PuCoGa(5), which is a superconductor with a high transition temperature, the microscopic magnetization in the paramagnetic state is small, temperature-independent, and significantly below the value found with bulk techniques at low temperatures. The orbital moment dominates the magnetization.

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.

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.