Semi-empirical spin-lattice relaxation models for molecular spin qubits in metal-organic frameworks

Katy Arauchan Universidad de Santiago de Chile

K. Aruachan (1), Y. Colón (2), D. Aravena (3), F. Herrera (1,4)

(1) Department of Physics, Universidad de Santiago de Chile, Santiago. Chile (2) Department of Chemical and Biomolecular Engineering, University of Notre Dame, IN, USA (3) Department of Chemistry and Biology, Universidad de Santiago de Chile, Santiago. Chile (4) Millennium Institute for Research in Optics (MIRO), Chile.

Understanding the mechanisms that determine spin-lattice T1 relaxation times for molecular spin qubits in metal-organic framework (MOF) crystals is critical for near-term 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 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 vibrational Raman fluctuations and 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.

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[2] A. Lunghi, and S. Sanvito, How do phonons relax molecular spins? Sci. Adv. 2019;5: eaax7163.

[3] L. Tesi, A. Lunghi, M. Atzori, E. Lucaccini, L. Sorace, F. Totti, R. Sessoli, Giant spin-phonon bottleneck effects in evaporable vanadyl-based molecules with long spin coherence, Dalton Trans. 45, 16635–16643 (2016).