Raman relaxation in Yb(III) molecular qubits: non-trivial correlations between spin-phonon coupling and molecular structure

Abstract

The coordination complexes of Yb(III) exhibit some of the longest spin coherence times among 4f compounds, making them a promising platform for molecular quantum technologies. While spin-phonon relaxation remains a limiting factor for coherence times even at low temperature, its control through chemical design has the potential to push these spin qubits prototypes beyond current limits. With the aim of providing insights on how to chemically control spin-phonon relaxation, we here present a full ab initio study of spin-phonon dynamics for three Yb(III) molecules exhibiting minimal chemical differences, yet quantitatively different spin relaxation times. Results show that low-temperature relaxation is governed by Raman processes triggered by a small group of largely delocalized low-energy phonons. The analysis of these contributions highlights that the modulation of spin-phonon coupling by molecular structure modifications beyond the first coordination shell are highly non-trivial in nature and hard to rationalize in simple chemical terms. These findings call for a conceptual step change from the attempt to use simple magneto-structural correlations to interpret the effect of molecular structural modifications on spin-phonon relaxation, and present predictive first-principles frameworks as a potential driving force of future chemical design strategies

Figures (4)

• Figure 1: The molecular structure of Yb(trensal) (1), Yb(trenpvan) (2) and Yb(trenovan) (3). Color code: Yb = green, N = purple, O = red, C = grey, H = white. The red circles highlight the position of the methoxy groups that differentiate the three molecules.
• Figure 2: Energy spectra of the ground term $^2F_{7/2}$ for the three systems. The solid lines represent the energy levels retrieved from NEVPT2 calculations, whereas the dashed lines refer to the experimental spectroscopic valuesPedersen2015Kragskow2022Hansen2024a.
• Figure 3: Relaxation time as a function of temperature for Yb(trensal) (a), Yb(trenpvan) (b) and Yb(trenovan) (c). Simulated Raman (solid line) and Orbach (dashed) contributions are reported. Experimental data (hollow circles) are taken from Ref. Bode2023Hansen2024a. Panels d-f and g-i report the results of the energy cut-off analysis for each system, both in the case of Orbach relaxation (panels d-f, $T=100 \, K$) and Raman relaxation (panels g-i, $T= \, 10$ K), respectively. Colored curves report the relaxation time $T_1$ evaluated by considering phonons in the energy interval $[0,\omega_c]$, where $\omega_c$ is the cut-off frequency. The black curves report the same simulation for phonons in the interval $[\omega_\mathrm{c},\omega_\mathrm{max}]$, where $\omega_{max}$ is the fixed, maximum frequency of the phonons considered. The vertical, dashed lines mark the energy levels of the KD.
• Figure 4: Panels a-d: Normalized spin-phonon density of states for Yb(trensal) (a), Yb(trenpvan) (b) and Yb(trenovan) (c). In black: normalized phonon density of states for each system. Every spectrum is rescaled with respect to its maximum value (in modulus). The scale factor is about 0.91 for Yb(trensal), 0.55 for Yb(trenpvan) and 0.75 for Yb(trenovan). (d): zoom on the [0,70] cm$^{-1}$ interval. The adopted smearing is Gaussian and equal to 1 cm$^{-1}$. Panel e: Pictorial visualization of the low-energy oscillation modes, corresponding to the highest peaks of the spin-phonon DoS reported in (d), appearing at 53.3 cm$^{-1}$ (green), 56.6 cm$^{-1}$ (blue), and 57.6 cm$^{-1}$ (red), respectively. The geometry of the molecule at a certain instant (coloured molecule) is superimposed to the one at the beginning of the oscillation (shaded molecule). In this portrayal, the Yb atom colour is yellow to simplify its visualization.