ABSTRACT

This paper gives for the first time a complete equation to analyze the temperature dependence (or thermal variation) of spin-Hamiltonian parameter from low to high temperatures for transition metal and rare-earth ions in crystals. This equation includes not only the dynamic effect (only considered in previous papers) caused by electron–phonon interaction but also the static effect owing to lattice thermal expansion. Based on the complete equation, the thermal variations of zero-field splitting b₄⁰ from low to high temperatures for cubic Eu²⁺ and Gd³⁺ centers in CdF₂ crystal are studied. The contributions due to static effect are estimated from the pressure dependence of zero-field splitting b₄⁰. The static parameters B (charactering the static effect) and the electron–phonon coupling parameters K (charactering the dynamic effect) for both systems are determined and the coefficients (B + K) in the complete equation are obtained. The results are discussed.

摘要

本文首次给出了一个完整的方程来分析晶体中过渡金属和稀土离子从低温到高温的自旋-哈密顿参数的温度依赖性（或热变化）。该方程不仅包括由电子 - 声子相互作用引起的动态效应（仅在以前的论文中考虑），还包括由晶格热膨胀引起的静态效应。基于完整方程，研究了CdF ₂晶体中立方Eu ²⁺和Gd ^{3+中心的零场分裂b} ₄ ⁰从低温到高温的热变化。静态效应的贡献是根据零场分裂的压力依赖性估计的 b ₄ ⁰. 确定了两个系统的静态参数B（表征静态效应）和电子 - 声子耦合参数K（表征动态效应），并获得了完整方程中的系数 ( B  +  K )。结果进行了讨论。