Fig. 3: Internal fields and spin-flip probability.
From: Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets
a, b Distribution of internal field magnitudes Bint experienced by a Dy centre due to the dipolar fields produced by surrounding Dy centres, magnetised by a randomly oriented external field Bext. For \({[{{{{{{{\rm{Dy}}}}}}}}{({{{{{{{{\rm{Cp}}}}}}}}}^{{{{{{{{\rm{ttt}}}}}}}}})}_{2}]}^{+}\) (a), a uniform spatial distribution of 1000 randomly oriented single-molecule magnets (SMMs) around a central Dy(III) was assumed, corresponding to a 170 mM solution in dichloromethane. For the [Dy(bbpen)Br] molecular crystal (b), we considered the total dipolar field arising from all Dy centres within a 100 Å radius from a central Dy assuming 5% diamagnetic dilution. c, d Distribution of electronic (blue) and vibronic (orange) Landau–Zener spin–flip probabilities PLZ, calculated for a randomly oriented SMM subjected to the dipolar fields shown above, assuming an external field sweep rate of 10 Oe/s. Average values are shown as dashed lines: (c) 0.0104 (blue) and 0.0074 (orange); (d) 0.903 (blue) and 0.618 (orange). All histograms are obtained from an ensemble of 10,000 random external field orientations and dipole arrangements.
