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ECS Journal of Solid State Science and Technology

Perspectives of a Four Center Cooperative Process in Rare Earth Doped Crystals

K. C. Mishra, John Collins

Published Mar 1, 2026• 0 citations
Publisher

Abstract

We have investigated the possibility of realizing a 4-center energy transfer among trivalent rare Earth ions in suitable hosts. A 4-center energy transfer process was originally proposed in the context of photo-physics of dendrimer molecular systems using molecular quantum electrodynamics methods. Later, a similar theoretical construct was proposed for rare Earth ions in crystalline solids. Here, we search for rare Earth ions suitable for 4-center energy transfer based on observed energy levels of 4f n multiplet structures in suitable hosts. A search for this 4-center cooperative energy transfer process experimentally will open a novel area of research in luminescence.

DOI
10.1149/2162-8777/ae5341

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We have investigated the possibility of realizing a 4-center energy transfer among trivalent rare Earth ions in suitable hosts. A 4-center energy transfer process was originally proposed in the context of photo-physics of dendrimer molecular systems using molecular quantum electrodynamics methods. Later, a similar theoretical construct was proposed for rare Earth ions in crystalline solids. Here, we search for rare Earth ions suitable for 4-center energy transfer based on observed energy levels of 4f n multiplet structures in suitable hosts. A search for this 4-center cooperative energy transfer process experimentally will open a novel area of research in luminescence.
Three-center energy transfer affords the basic mechanism for a variety of multiphoton processes identified within materials doped with rare earths. Addressing the theory using quantum electrodynamics, general results are obtained for systems in which the fundamental photophysics engages three ions. Distinct cooperative and accretive mechanistic pathways are identified and the theory is formulated to elicit their role and features in energy transfer phenomena of pooling upconversion, sensitization, and downconversion or quantum cutting. It is shown that although the two mechanisms play significant roles in pooling and cutting, only the accretive mechanism is responsible for sensitization processes. Both mechanisms are shown to invoke Raman selection rules, which govern transitions of the mediator ions in the accretive mechanisms and transitions of the acceptor ions in the cooperative mechanisms. The local, microscopic level results are used to gauge the lattice response, encompassing concentration and structural effects. Attention is drawn to a general implication of implementing a multipolar description for the optical properties of doped solid-state ionic materials.
In CsCdBr3 the trivalent Rare-Earth (RE) ions substitute for the divalent Cd ions. For reasons of charge compensation and the specific crystal structure, RE centers of the form RE3+ - (Cd vacancy) - RE3+ are preferentially formed. These symmetric pair centers are very suitable for studying cooperative effects of RE ions. These include processes between the ions of the pair as well as processes between the coupled pair and the electronic excitations of the host lattice. Experiments will be shown and discussed on: (i) cross relaxation and up-conversion by direct ion-ion interaction; (ii) cooperative cross relaxation of the Pr3+ pairs with the host lattice; and (iii) cooperative vibronic emission of the Pr3+ pairs with high phonon progressions.
Rare-earth ions play an important role in modern technology as optically active elements in solid-state luminescent materials. In many of these materials, interactions between the electronic band states of the host crystal and the rare-earth ion's localized 4f N and 4f N−1 5d states influence the material's optical properties. The importance of these interactions is discussed for material applications in photon-gated hole burning, quantum information and phosphors. Material dependent trends in the relative binding energies of the 4f N states and the host bands have been observed and are summarized. An empirical model for the ion dependence of the 4f electron binding energies is formulated in terms of atomic number and compared with previous models. These models are extended to describe the 4f N−1 5d states with one additional parameter. Improved estimates for the free-ion ionization potentials used in the model are also presented and discussed.
Calculations made of the rates for several processes involving interactions between rare earth ions in crystals, such as resonance energy transfer, cooperative excitation transfer and cooperative optical transitions. These processes are assumed to originate from the electric multipole interactions between the ions concerned. A tensor operator method is employed in order to take account of the individual characters of the energy levels involved in the transition. Evaluation of the typical transition probability is also made on the lowest-order parity-allowed processes in nearest neighbour ions. The rates for the resonance transfer and cooperative transfer processes thus estimated are much smaller than those obtained by Miyakawa and Dexter.