关键词: Mn²⁺: ZnO crystal, spin Hamiltonian (SH) parameter, local structure distortion, magnetic interaction

Abstract: The local structure distortion, the spin Hamiltonian (SH) parameters, and the electric fine structure of the ground state for Mn$^{2+}$(3d$^{5})$ ion in ZnO crystals are systematically investigated, where spin--spin (SS),  spin--other--orbit (SOO) and orbit--orbit (OO) magnetic interactions, besides the well-known spin--orbit (SO) coupling, are taken into account for the first time, by using the complete diagonalization method. The theoretical results of the second-order zero-field splitting (ZFS) parameter $D$, the fourth-order ZFS parameter ($a$-$F$), the Zeeman $g$-factors: $g_{//}$ and $g_{\bot}$, and the energy differences of the ground state: $\delta_{1}$ and  $\delta_{2}$ for Mn$^{2+}$ in Mn$^{2+}$: ZnO are in good agreement with experimental measurements when the three O$^{2-}$ ions below the Mn$^{2+}$ ion rotate by 1.085$^\circ$ away from the [111]-axis. Hence, the local  structure distortion effect plays an important role in explaining the spectroscopic properties of Mn$^{2+}$ ions in Mn$^{2+}$: ZnO crystals. It is found for Mn$^{2+}$ ions in Mn$^{2+}$: ZnO crystals that although the SO  mechanism is the most important one, the contributions to the SH parameters, made by other four mechanisms, i.e. SS, SOO, OO, and SO$\sim$SS$\sim$SOO$\sim$OO mechanisms, are significant and should not be omitted, especially  for calculating ZFS parameter $D$. 

Key words: Mn²⁺: ZnO crystal, spin Hamiltonian (SH) parameter, local structure distortion, magnetic interaction