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

Abstract

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-ofthe-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) 2 ] 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) 2 ] 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.

Broad-band spectroscopy of a vanadyl porphyrin: a model electronuclear spin qudit

“…15,21 Combined experimental/theoretical studies of vibrational properties are nevertheless necessary to identify the origin of differences in T 1 , as done so far on few occasions. [22][23][24] Importantly, such long spin-lattice relaxation times ensure that T 1 will not be limiting the coherence time-scale. On the other hand, they can represent a drawback for an efficient qubit initialization.…”

Exploring the Organometallic Route to Molecular Spin Qubits: The [CpTi(cot)] Case

“…To generate a more comprehensive description, the vibrational spectrum was also computed for the crystalline phase of 1 at the Γ point ( 1 bulk ) within a periodic DFT approach (see the Supporting Information for details) [27b, 28, 29] . The spectrum compares well with the THz data, as shown in Figure 4 where the nature of the lowest vibration modes is also depicted.…”

Insights on the coupling between vibronically active molecular vibrations and lattice phonons in molecular nanomagnets

“…37 This is based on the generally accepted idea that it is often a convenient approximation to distinguish between "longitudinal" and "transverse" acoustic phonons, although in practice they are not pure. 24 Let us say we want to model the effect on a local excitation of a phonon field μ αβ , where α = x is the unit vector of the phonon amplitude and β = x is the unit vector of the phonon propagation direction. For simplicity we can take as an example the longitudinal phonon μ xx along x.…”

“…This could be experimentally characterized using 4D-INS as previously shown. 24 Application to [Ho(W 5 O 18 ) 2 ] 9− Fig. 3 shows the coupling of each molecular normal mode of vibration to our 9 model phonons (for full details, see ESI †).…”

“…This involves not only localized molecular vibrations, related to optical phonon, but also extended lattice vibrations, also known as acoustic phonons. 24 The participation of low-lying optical phonons, i.e. molecular vibrations, in spin relaxation is more obvious, since the distortions couple strongly with the spin Hamiltonian.…”