Lattice relaxation times for spin qubits in MOFs with semi-empirical spectral densities

Understanding the mechanisms that determine relaxation times for molecular spin qubits in metal-organic framework (MOF) crystals is essential for applications in precision measurements and quantum information processing [1]. Recent spin-echo experiments on the spin relaxation of vanadyl-based qubits as a function of magnetic field and temperature has stimulated the development of phenomenological and ab-initio quantum mechanical modeling techniques [1-3]. We propose an alternative method with a semi-empirical approach for building Redfield quantum master equations based on a stochastic fluctuation model for the molecular gyromagnetic tensor due to the interaction of molecular spin impurities with crystal lattice vibrations. The spin relaxation rates are obtained from a semi-empirical bath autocorrelation function that captures the experimental temperature dependence through a fitting procedure. These model spectral densities are used for computing the spin population and decoherence dynamics of vanadyl-based spin qubits beyond cryogenic temperatures (>50 K) and high magnetic fields, where the Zeeman effect dominate the relaxation dynamics. Our results quantitatively agree with experiments [3] and represent a solid foundation for the theoretical characterization of other spin qubits in MOFs, for the rational design of novel quantum magnetometers based on this material class.

[1] T. Yamabayashi, M. Atzori, L. Tesi, G. Cosquer, F. Santanni, M.-E. Boulon, E. Morra, S. Benci, R. Torre, M. Chiesa, L. Sorace, R. Sessoli, M. Yamashita, J. Am. Chem. Soc. 140, 12090–12101 (2018).

[2] A. Lunghi, and S. Sanvito, Sci. Adv. 2019;5: eaax7163.

[3] L. Tesi, A. Lunghi, M. Atzori, E. Lucaccini, L. Sorace, F. Totti, R. Sessoli, Dalton Trans. 45, 16635–16643 (2016).