Investigations of the spin Hamiltonian parameters and local structures for Fe3+, Cr3+ and Mn4+ in rutile TiO2 single crystal

The spin Hamiltonian parameters (g factors, hyperfine structure constants and zero-field splittings (ZFSs)) and local structures for the rhombic substitutional Fe3+, Cr3+ and Mn4+ in rutile (TiO2) single crystal are theoretically investigated from the high order perturbation calculations based on the cluster approach including both the crystal-field (CF) and charge-transfer (CT) contributions to the g factors and hyperfine structure constants. The impurity centers are found to undergo the local axial distortions ΔZ (≈0.22, 0.14 and -0.18 Ǻ) and the planar bond angle variations Δφ (≈4.3, 5.9 and 0.2°) for Fe3+, Cr3+ and Mn4+, respectively. The signs for ZFSs D and E are analyzed in the light of those for ΔZ and rhombic distortion angle δφ (=φ′-π/4) related to an ideal octahedron. The magnitudes of ΔZ and Δφ are conveniently illustrated by the axial and perpendicular ZFS relative variations ΔF and ΔG for the deviations of D and E based on the local distortion parameters from those (DH and EH) based on the host structural data of Ti4+ site. The validity of the above local structures is discussed in view of size and charge mismatch of the various impurity centers. The CT contributions to g-shift are opposite in sign and about 13-56% in magnitude compared with the CF ones, indicating the increasing importance (Cr3+