A theoretical analysis of zero-field splitting parameters of Mn2+ in zinc lactate trihydrate
Abstract
The superposition model is used to investigate the crystal field parameters (CFP) of Mn2+ ion in single crystal of zinc lactate trihydrate, and then zero-field splitting (ZFS) parameters D and E are also evaluated by the perturbation formulae. These calculated values of ZFS parameters match well with the experimental values evaluated by electron paramagnetic resonance (EPR) at room temperature. With the help of CFA package and crystal field parameters evaluated by superposition model the energy band positions of optical absorption spectra of Mn2+ doped zinc lactate trihydrate are evaluated and compared with the experimental results.
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Introduction
Theoretical analysis predicts zero-field splitting (ZFS) parameters which would provide guidance for experiment. The crystal field theory is widely used in the theoretical study of the spin Hamiltonian parameters of d5 (6S) ions [1-5]. Using the formulae derived in these works, ZFS parameters are determined by the electrostatic, the spin-orbit coupling, and the crystalfield parameters of the d5 ion in a crystal. To obtain the crystal-field parameters, two models, namely the point-charge model and superposition model were used for some 3dn ions e.g. Cr3+; Al2O3 [6] and Fe2+ in garnets [7] and the results are satisfactory. These two models establish relations between the crystal field (CF) parameters and crystal-structure properties.
Host lattice provides valuable information about structural changes possible when small concentration of paramagnetic impurity is doped. Out of all transition metal of iron group, Mn2+ is important because its ground state is 6S5/2 [8-12]. The electron spin is affected by high order interaction of crystalline electric field, and in the presence of external magnetic field orientation of spins are free [13]. The spin–lattice relaxation time is large for S state ions, due to this property Mn2+ shows fine EPR spectra [12, 14-16] at room temperature.
Theoretical studies based on spin Hamiltonian of d5 (6S) ions are very interesting and useful for the studies of orbit lattice interaction [17-22]. Three perturbation procedures can be used for the study of effect of spin Hamiltonian mechanism. According to first and second procedures spin-orbit coupling, the low-symmetry components of the crystal field and the total crystal field, the spin-orbit interaction are used as perturbation terms. And for third procedure spin-orbit coupling, the lowsymmetry field, and the off-diagonal part of free-ion Hamiltonian are used as perturbation terms, cubic field and the diagonal part of the free-ion Hamiltonian are used as unperturbed Hamiltonian. This procedure shows good results described by Macfarlane for F-state ions [23].
In this paper, we present the evaluated ZFS parameters for the Mn2+ ion in zinc lactate trihydrate (ZLT) under the assumption that this ion occupies the interstitial site. For the calculation of ZFS parameters, Newman superposition model [6, 24] and perturbation expressions are used [25].
Conclusion
Zero-field splitting parameters have been investigated with the help of superposition model and perturbation formulae. The calculated ZFS parameters for the Mn2+ ion at the interstitial site in ZLT single crystal fairly match with the experimental values. The calculated optical energy levels using CFA package are in reasonable agreement with the experimental values. This suggests that the Mn2+ ion occupies an interstitial site in ZLT, which is consistent with the experimental result obtained earlier.