Dynamic Orbit-Lattice Interactions for PbF₂:Gd³⁺Single Crystals

Abstract

Temperature dependence of the second-order spin-lattice coefficients for PbF2:Gd3+ is reported. It is shown that the thermal expansion of the crystal 1attice contributes only in about 14 % to the observed dependence and the rest should be ascribed to a dynamic coupling between the 4f 7 electrons and lattice vibrations. The results are parametrized in both the Einstein and the Debye models and it is shown that the phenomenological parameters obtained from such parametrization can be made to coincide in both models if a specific value of the Einstein frequency ω is properly chosen. Both models of parametrization show that the Γ39 vibrating mode couples to the 4f 7 electrons much weaker than the Γ55 one.

Gd3+Spin-Phonon Interactions in Rare-Earth Fluoride Crystals

“…On the other ha nd, i n G d 3 + -do p ed PbF 2 sing l e crysta l the val ue of K 2 = À 0 : 1 0 7 9 G Hz for tetra gona l deform ati ons and K 2 = 0 : 3 6 8 8 G Hz for tri gona l deform ati ons wa s obta i ned f rom EPR uni axi al stress exp eri ment i n the tem pera ture ra nge 130{ 600 K by Kuri ata et al . [29 ]. Thi s shows tha t di sto rti on of the crysta l Ùel d (tri gona l i s l ower sym m etry tha n tetra gona l ) i nÛuences signi Ùcantl y the 4 f 7 electro n{ pho no n coupl i ng consta nt K 2 .…”

Spin-Phonon Interactions for PbF2:Gd3+- Comparison between Theory and Experiment

“…The experimental data reported in [1] indicated that the temperature dependence of the second-order spin-lattice coefficients for PbF2:Gd 3+ can be parametrized in the Einstein as well' as the Debye models if the "averaged" frequency for the optical modes is chosen to be ωE = 2.5 x 10 13 8-1 . The Einstein model will be analyzed below due to its simplicity.…”

“…The Einstein model will be analyzed below due to its simplicity. In this model the temperature dependence of the second-order spin-lattice parameters is parametrized by the following function (see for example [1]):…”

“…In view of the above and also in view of the fact that the discussion concerning the comparison between the experimental and theoretical results published in [1] was, as it now seems, based on the calculations which rather greatly underestimated the role of one of the analyzed microscopic models, we intend to report here in detail the data on the effectiveness of the microscopic models based principally on the relativistic approach to the orbit-lattice interactions for the 8 S7/ 2 ground state ins.…”

“…In our previous paper [1] we reported the experimental data on the dynamic orbit-lattice interactions for PbF 2 :Gd3+ single crystals. We demonstrated that the data can be parametrized using the Einstein as well as the Debye schemes.…”