Impact of finite phonon lifetimes on the spin dynamics of single- molecule magnets Rizwan Nabi, Jon G.C. Kragskow, Jakob K. Staab, Daniel Reta, Jonathan M. Skeltona, Nicholas F. Chiltona Department of Chemistry, The University of Manchester, Manchester, M13 9PL, UK *email: nicholas.chilton@manchester.ac.uk, jonathan.skelton@manchester.ac.uk The design of nanoscale information storage devices based on molecular magnets requires preparation of materials with well-designed spin-phonon interactions such that magnetic memory persists at ambient temperatures. Understanding the fine details of spin-phonon coupling is thus crucial in designing new materials for this task. Of crucial importance for molecular spin dynamics is the phonon density of states, which directly impacts the timescale of magnetic memory, and a core part of this is the knowledge of phonon linewidths, which are inversely proportional to their lifetimes. In the past we have assumed a fixed empirical linewidth of ca. 10 cm -1 [1] , but others have suggested a strong temperature and energy-dependence to the phonon linewidth (Equation 1) [2] . However, the phonon linewidths are, in principle, accessible from first-principles calculations; albeit at extraordinary computational cost. By judiciously choosing a compact, high-symmetry molecular magnet viz [Dy(bbpen)Br] [3], we have directly obtained the ab initio line widths. At 300 K, the linewidths vary on the order of 0.1 to 40 cm -1 , as a function of both energy and wavevector (Figure 1a), and have a marked temperature dependence. Subsequent ab initio calculation of the spin-phonon coupling and magnetic relaxation rates using these calculated linewidths are in good agreement with experiment (Figures 1b and 1c), however, there is no major difference between rates obtained with fixed, mode-dependent (Equation 1), or ab initio-calculated linewidths. Rather, the most important factor is the density of the q-point mesh of reciprocal space. Γ j =2( ℏwj) 2 e ℏw j /k B T /( e ℏw j /k B T −1) 2 (Equation 1)
Figure 1: a) Phonon linewidths at 50 K for unique q points in the 5×5×5 mesh, as a function of mode energy. Dashed line is Equation 1 at 50 K. b) and c) Experimental (black circles) and calculated magnetic relaxation rates using a 5×5×5 q-point mesh, considering single-phonon (b) and two-phonon (c) transitions. Linewidths are given by: Equation 1 (red), mode-dependent calculated linewidths at 300 K (green), fixed = 10 cm-1 (blue), and calculated (mode- and temperature-dependent) linewidths (purple points and dashed lines). References 1. D. Reta, J. G. C. Kragskow and N. F. Chilton, J. Am. Chem. Soc., 2021, 143, 5943. 2. A. Lunghi, F. Totti, R. Sessoli and S. Sanvito, Nature Commun., 2017, 8, 14620. 3. J. Liu, Y.-C. Chen, J.-L. Liu, V. Vieru, L. Ungur, J.-H. Jia, L. F. Chibotaru, Y. Lan, W. Wernsdorfer, S. Gao, X.-M. Chen and M.-L. Tong, J. Am. Chem. Soc., 2016, 138, 5441.
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