Zero-field splitting of the ground state and local lattice distortions for Fe3+ ions at the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals

The relations between the zero-field splitting (ZFS) parameters and the structural parameters of the tetragonal FeF5O cluster center in Fe3+:KMgF3 crystals have been established by means of the microscopic spin Hamiltonian theory and the superposition model (SPM). On the basis of this, the local structure distortions, the second-order ZFS parameter D, the fourth-order one (a + 2F/3), and the energy level separations Δ1 and Δ2 of the ground spin state for Fe3+ ion doped in Fe3+:KMgF3 crystals are theoretically investigated. We use complete diagonalization method (CDM) and take into account the electronic magnetic interactions, i.e. the spin–spin (SS), the spin-other-orbit (SOO), and the orbit–orbit (OO) interactions, besides the well-known spin–orbit (SO) interaction. This investigation reveals that the replacement of O2− for F− and the induced lattice relaxation ΔR2(O), combined with an inward relaxation of the nearest five fluorine ions ΔR1(F) give rise to a strong tetragonal crystal field, which yields the large ZFS of the ground state. The theoretically calculated parameters D, (a + 2F/3), Δ1, and Δ2 for Fe3+:KMgF3 crystals are in good agreement with experimental ones when the five F− ions move toward Fe3+ by |ΔR1(F)| = 6.40 × 10−4 nm and the O2− ion toward Fe3+ by |ΔR2(O)| = 10.55 × 10−3 nm.

Graphical abstractThe theoretical ZFS parameter D, (a + 2F/3), and the energy level separations Δ1 and Δ2 of the ground state for Fe3+ ion in Fe3+:KMgF3 crystals yield a good agreement with experiment findings when the five F− ions moves toward the center ion Fe3+ by |ΔR1(F)| = 6.4 × 10−4 nm and the O2− ion toward the center ion Fe3+ by |ΔR2(O)| = 10.55 × 10−3 nm.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► A new complete diagonalization method for 3d5 ion at C4v crystal field is developed. ► Our method considers the contribution to the ZFS parameters from all 250 states. ► The local structure distortion for Fe3+:KMgF3 is studied by means of ZFS parameter. ► We obtain ΔR1(F) = −6.4 × 10−4 nm and ΔR2(O) = −10.55 × 10−3 nm.