Fig. 3
From: Spin–phonon couplings in transition metal complexes with slow magnetic relaxation
Schematic view of the spin–phonon coupling. a Zero-field splitting 2D' of the magnetic/spin quartet ground state (with eigenfunctions in Fig. 1c when no field is applied; off-axis field induces additional M S mixing). b Vibrational states of a selected phonon with eigenfunctions |0〉 and |1〉 and a small energy separation δ above the excited KD ϕ3,4. c Spin–phonon product states with product functions ϕ i |n〉 still without vibronic coupling. d Vibronic coupling with coupling constant Λ, leading to an energy shift and splitting: Δ± = (δ2 + Λ2)1/2. The ZFS transition (in gray color) is vanishingly weak in Raman spectra because it is only magnetic-dipole-allowed. e Zeeman splitting of vibronic states in a field B and avoided crossing from the coupling between the ϕ4|0〉 and ϕ1|1〉 states. Note the states ϕ1,2|0〉 and ϕ1,2|1〉 have pairwise identical slopes, whereas ϕ1,2|0〉 and ϕ3,4|0〉 have different slopes. The net transition from the lowest level ϕ1|0〉 to ϕ1|1〉 is in essence a phonon excitation and thus Raman-allowed (black arrow), and it is field-independent. When ϕ4|0〉, the upper magnetic level of the excited electronic KD, approaches ϕ1|1〉, additional coupling occurs, leading to a field-dependent transition. The ZFS transitions in (d) are vanishingly weak in Raman spectra, because they are only magnetic-dipole-allowed. The same holds for the ϕ1|0〉 → ϕ3|0〉, ϕ1|0〉 → ϕ4|0〉, and ϕ1|0〉 → ϕ2|1〉 transitions, which are not marked in (e). (Transitions from the first excited level, ϕ2|0〉, are neglected because of vanishing thermal population at 1.5–5 K.) f Avoided crossing in the Raman spectra based on Eq. (2). The red branches are weak in Raman intensity and only partially visible because they represent quasi-pure magnetic-dipole transitions
