Molecular spin-orbit interaction for d5 ions in covalent crystals: Spin-lattice coupling coefficients of Mn2+ in II-VI compounds.

Abstract

A very detailed ligand-field (LF) model is developed to account for the increase of one or two orders of magnitude of the spin-lattice coupling coefficients (SLCC) of ${\mathrm{Mn}}^{2+}$ in the common cation series ZnS, ZnSe, ZnTe, and CdTe. First, an overall LF model shows that the SLCC's are correctly given for all studied compounds by a second-order perturbation scheme involving twice the molecular spin-orbit interaction acting between the fundamental state $^{6}$${\mathit{A}}_{1}$ and the three excited states $^{4}$${\mathit{T}}_{1}$ at lower energy. This model gives the contributions to the SLCC's of the strain-induced variations of the electrostatic field of the crystal, of the ligand-ligand and metal-ligand group overlaps, and of the molecular spin-orbit interaction. Second, a new analysis of the LF model gives the strain-induced variations of the splitting of the states $^{4}$${\mathit{T}}_{1}$, of the monoelectronic molecular wave functions, and of the orbital operator of the molecular spin-orbit interaction. Finally, by expressing the SLCC's as a linear combination of quadratic terms in the spin-orbit constants ${\mathrm{\ensuremath{\zeta}}}_{\mathit{M}}$ of the electrons d of the metal and ${\mathrm{\ensuremath{\zeta}}}_{\mathit{L}}$ of the electrons p of the ligands and bilinear terms in ${\mathrm{\ensuremath{\zeta}}}_{\mathit{M}}$${\mathrm{\ensuremath{\zeta}}}_{\mathit{L}}$, it is shown that the terms in ${\mathrm{\ensuremath{\zeta}}}_{\mathit{M}}^{2}$ are approximately identical for all compounds, while the terms in ${\mathrm{\ensuremath{\zeta}}}_{\mathit{M}}$${\mathrm{\ensuremath{\zeta}}}_{\mathit{L}}$ which are partly compensated by the terms in ${\mathrm{\ensuremath{\zeta}}}_{\mathit{L}}^{2}$ become preponderant when passing from ZnS to ZnSe, ZnTe, and CdTe. These results account for the observed roughly linear dependence of the SLCC's on ${\mathrm{\ensuremath{\zeta}}}_{\mathit{L}}$ for the common cation series ZnS, ZnSe, and ZnTe and show that molecular spin-orbit interaction is essential to analyze spin-orbit-dependent spectroscopic constants when the ratio ${\mathrm{\ensuremath{\zeta}}}_{\mathit{L}}$/${\mathrm{\ensuremath{\zeta}}}_{\mathit{M}}$ is greater than unity.