Method for determination of the fourth-rank zero field splitting parameters from the zero field energy levels for spin S̃ = 2 systems – Case studies: Fe2+ ions in [Fe(H2O)6](NH4)2(SO4)2 and forsterite (Fe2+:Mg2SiO4), and Cr2+ ions in (ND4)2Cr(D2O)6(SO4)2 and Rb2Cr(D2O)6(SO4)2

Recent developments in high-magnetic field/high-frequency electron magnetic resonance (HMF-EMR) techniques offer improved capabilities for determination of the spin Hamiltonian (SH) parameters, including the fourth-rank zero field splitting (ZFS) parameters (ZFSPs) for spin S = 2 systems. However, the density functional theory (DFT) and ab-initio methods provide predictions of the ZFS energies from which usually only the second-rank ZFSPs are obtained. Here we present an analytical method for determination of the fourth-rank ZFSPs from the ZFS energy levels for S = 2 ions at orthorhombic sites. This enables assessment of their significance and determination of the dominant parameters. Applications of this method for Fe2+ in [Fe(H2O)6](NH4)2(SO4)2, Fe2+ in forsterite (Fe2+:Mg2SiO4), and Cr2+ ions in (ND4)2Cr(D2O)6(SO4)2 and Rb2Cr(D2O)6(SO4)2 indicate an important role of the fourth-rank ZFSPs. The analytical formulas derived by us may be applied to other 3d6 and 3d4 (S = 2) ions at orthorhombic sites in various hosts for better modeling of spectroscopic and magnetic properties of these systems.