M A T E R I A L S F O R T O M O R R O W ' S I N N O V A T I V E A N D S U S T A I N A B L E I N D U S T R Y

S C I E N T I F I C H I G H L I G H T S

7 6 H I G H L I G H T S 2 0 2 3 I

Phonon-induced relaxation of a molecular qubit unravelled by inelastic X-ray scattering and spin dynamics simulations

Inelastic X-ray scattering measurements and periodic density functional theory calculations reveal the relaxation dynamics of a molecular qubit by directly accessing its phonon dispersions and polarisation vectors.

Molecular nanomagnets (MNMs) are very promising for quantum information processing. The molecular spin of these systems can encode a qubit (the basic unit of a quantum computer), which can be coherently manipulated with electromagnetic fields. By taking advantage of the high degree of chemical control of their molecular structure, the energy levels of MNMs can be tailored to match the envisaged technological applications. For instance, the presence of a sizeable number of low- energy levels enables one to define self-correcting qubits [1]. However, the use of MNMs as qubits is undermined by molecular vibrations and spin-phonon interactions, playing an important role in magnetic relaxation and determining the coherence times of superposition of states. The key to construct a reliable model of phonon- induced relaxation in MNMs is to have experimental access to phonon dispersions and eigenvectors, which are necessary for a quantitative evaluation of spin-phonon coupling coefficients.

In this work, inelastic X-ray scattering (IXS) was used at beamline ID28 to measure phonon dispersions in a crystal of molecular qubits. The main advantage of IXS compared to neutron scattering is the possibility of using very small samples, of the order of 1 mm3 volume. This, combined with an energy-independent resolution of about 1.5 meV, a complete decoupling between energy and momentum transfer, and the background-free signal, makes IXS a very powerful tool to study phonons in MNMs.

The material studied was a molecular crystal of [VO(TPP)] (VO = vanadyl, TPP = tetraphenylporphyrinate), a very promising molecular qubit embedding both electronic and nuclear spins suitable for implementing quantum gates [2]. Acoustic and optical branches of [VO(TPP)] were measured along different directions in the reciprocal space, probing both their energies and polarisation vectors (Figure 57). In particular, ultra-low- lying optical modes were detected at about 1-2 meV (Figure 57b,c), fully breaking down the Debye picture (a model for estimating the phonon contribution to the specific heat capacity in a solid) and deeply affecting magnetic relaxation.

The role of these low-energy modes in the relaxation dynamics of [VO(TPP)] was then investigated by combining the experimental results obtained by IXS with spin dynamics simulations based on state-of-the-art periodic density functional theory (pDFT). These calculations

Fig. 57: Representative ID28 data on [VO(TPP)] (blue scatters), obtained at T = 300 K and measured with longitudinal scans along the symmetry direction Γ Kz (a) at the (0 0 6.6) point with a resolution

of δE = 3 meV, and (b) at the (0 0 6.2) point with δE = 1.5 meV. Solid lines are results of the fit obtained with FIT28, a customised data analysis software developed on ID28. c) IXS cross-section (colour map)

simulated with DFT phonon energies and polarisation vectors along the Γ Kz directions. Cyan/white dots/squares are experimental IXS excitation energies extracted from the complete set of data over the

whole explored Q range. Adapted with permission from E. Garlatti et al., Nat. Commun. 14, 1653 (2023), under a Creative Commons Attribution 4.0 International License.