Fig. 2: Zeeman splitting of the ground Kramers doublet in \({[{{{{{{{\rm{Dy}}}}}}}}{({{{{{{{{\rm{Cp}}}}}}}}}^{{{{{{{{\rm{ttt}}}}}}}}})}_{2}]}^{+}\).
From: Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets
a Electronic ground doublet splitting (Δ1, top) and vibronic correction (\({\Delta }_{1}^{{{{{{{{\rm{vib}}}}}}}}}-{\Delta }_{1}\), bottom) as a function of the orientation of the magnetic field, parametrised in terms of polar and azimuthal angles θ and ϕ. The polar angle θ is measured with respect to the axis joining the cyclopentadienyl centroids, corresponding approximately to the easy axis. The dashed (solid) line corresponds to the electronic (vibronic) hard plane. The magnitude of the magnetic field is fixed to 1 T. b, c Electronic (dashed) and vibronic (solid) Zeeman splitting of the ground doublet as a function of the external field magnitude Bext in the presence of a transverse internal field Bint = 1 mT calculated from Eq. (8). External and internal fields are perpendicular to each other and were both chosen to lie in the hard plane of either the electronic (b, purple) or vibronic (c, green) g-matrix. The orientation of the external (internal) field is shown for both cases as circles (crosses) in the inset in (a), with colours matching the ones in (b) and (c).
