Title: Theory of the Two-Impurity Kondo Effect in the Presence of an Impurity-Impurity Exchange Interaction
Abstract: We examine the two-impurity Kondo effect by deriving the equation of motion of a set of Green's functions using the two-impurity $s\ensuremath{-}d$ Hamiltonian with an added exchange term of the form $W({\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{0}\ifmmode\cdot\else\textperiodcentered\fi{}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{1})$, where ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{0}$ and ${\stackrel{\ensuremath{\rightarrow}}{\mathrm{S}}}_{1}$ are the spin operators of the two impurities. The resulting Green's functions are truncated and solved for self-consistency, keeping the most divergent terms. Our results show that all the $\mathrm{ln}T$ terms arising in the single-impurity Kondo effect are modified and replaced by $\mathrm{ln}{({T}^{2}+{{W}^{\ensuremath{'}}}^{2})}^{\frac{1}{2}}$, where ${W}^{\ensuremath{'}}$ is an energy approximately equal to $W$. This results in an effective Kondo temperature ${T}_{K}^{E}$, where ${T}_{K}^{E}={T}_{K}^{0}{[1\ensuremath{-}{(\frac{{W}^{\ensuremath{'}}}{{T}_{K}^{0}})}^{2}]}^{\frac{1}{2}}$, and ${T}_{K}^{0}$ is the single-impurity Kondo temperature. Thus the effective Kondo temperature decreases as the impurity-impurity interaction increases, and when ${W}^{\ensuremath{'}}$ is greater than ${T}_{K}^{0}$ the Kondo divergence is removed by the impurity-impurity interaction. Our results show that the interaction $W$ strongly modifies the spin-compensated state. We also derive expressions for the conduction-electron polarization as a function of ${W}^{\ensuremath{'}}$ for high values of ${W}^{\ensuremath{'}}$ or high temperatures.
Publication Year: 1973
Publication Date: 1973-01-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 22
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot