Truncated forms of zero-field splitting (ZFS) Hamiltonians and implications for interpretation of ZFS parameters for Fe2+(S=2) ions in K2FeF4

► Truncated zero-field splitting (ZFS) terms for Fe2+ in K2FeF4 and A2MX4 analyzed. ► Relations between truncated ZFS parameters and proper ones derived. ► Truncation of 4th-rank operators significantly affects D values for S=2 systems. ► Origin of 2nd-rank rhombic ZFS E-term found controversial. ► Feedback for microscopic modeling for Fe2+(S=2) ions in A2MX4 provided.