Borrowing Intensity in Rare Earth Doped Materials; Magnetic Dipole Transitions

Abstract

This paper is dedicated to Professor Joe Paldus -a GIANT in both scientific and human scales -with the confidence that Brian Wybourne would have repeated these words.A theoretical model of magnetic dipole transitions in crystals doped by the lanthanide ions is based on the fourth-order perturbation theory applied for the Hamiltonian in which two perturbing mechanisms are taken into account. Namely, the impact due to the crystal field potential and also spin-orbit interaction operator is included in the transition amplitude. The analysis is performed in the language of Racah algebra applied for the formulation of the effective operators expressed in terms of unit double tensor operators. The radial integrals of the terms contributing at the fourth order are defined within the perturbed function approach, due to which their values are evaluated for the complete radial basis sets of one-electron states of given symmetry. The numerical analysis performed for the Eu 3+ ion provides the information on the relative importance of various effective operators and allows one to establish a hierarchy of important terms contributing to the transition amplitude. The results of the analysis lead also to the verification of possible importance of magnetic dipole transitions in the description of 0 ↔ 0 and 0 ↔ 1 electric dipole transitions via the so-called borrowing mechanism introduced by Wybourne.The so-called hypersensitive transitions in lanthanide ions are not the only ones for which a theoretical model of their description is not yet established. The second class of transitions that are at the center of attention are 0 ↔ 0 and 0 ↔ 1 that are observed for Eu 3+ and Sm 2+ in various hosts. Al-

Interpretation of europium(III) spectra

“…The occurrence of this transition is a well-known example of the breakdown of the selection rules of the Judd-Ofelt theory (a 0-0 transition is forbidden by the J selection rule of the Judd-Ofelt theory). Several authors have tried to theoretically explain why this transition is observed [132][133][134][135][136][137][138][139][140][141][142]. Theoretical models include the breakdown of the closure approximation in the Judd-Ofelt theory and third order perturbation theory.…”

Magnetic dipole transitions in crystals

“…Furthermore, the selection rules (19) and (20) indicate that magnetic dipole transitions occur between the states that belong to the same atomic term 2S+1 L. This means that requirements (19) and (20) are valid only for the LS-coupling scheme applied for the description of the energy states. The inclusion of the intra-shell spin-orbit interaction into the zeroth-order Hamiltonian H 0 (defined by Eq.…”

“…(48) and (49) are valid), then the inter-shell mechanism PV CF QV CF P expressed in terms of effective operators [19] contribute to the transition amplitude. Obviously, also the intra-shell mechanism contribute to these transitions.…”

“…However, if one considers the transition with | L| ≤ 6, then the transition amplitude can be determined by the contributions associated with the effective operator F 2 [6,19], which in an effective way reproduce the impact of the PV CF QV so P + PV so QV CF P inter-shell mechanism.…”

“…Terms associated with the crystal field included twice (λ 2 μ 0 ) were investigated in [19], where the discussion was focused on the possibility of the intensity borrowing from the magnetic dipole transitions in the case of a 0 ↔ 0 electric dipole transition. The selection rules for non-vanishing Γ 3 CF contributions to the transition amplitude for the pure LS-coupling scheme are the following | J| ≤ 7 + 2l 0 0 (47)…”