Competing hybridization and consequences for magnetic ordering in ternary and quaternary correlated-electron systems

We present a method for calculating the hybridization induced f-f interionic interaction in systems where a d-electron species also hybridizes with the same Fermi sea. For the ternary and quaternary physical systems of interest, typically the f species is a light rare earth (e.g., Ce or Pr) or a light actinide (U) involving a partially filled f shell, and there may be experimental evidence of competition between magnetic ordering of the f- and d-electron systems (e.g., when f is U and d is Mn in ${\mathrm{UMn}}_2$ ${\mathrm{Si}}_2$ or ${\mathrm{UMn}}_2$ ${\mathrm{Ge}}_2$) or between magnetic ordering for the f-ionic system and superconductivity (e.g., when f is Pr and d is Cu in ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Pr}}_{\mathit{x}}$ ${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{y}}$). The method treats first the strong hybridization between the d and the conduction electrons to obtain a new ground state with delocalized d electrons. Then it calculates the f-f interionic interaction by perturbation theory. We find that the d electrons affect the f-f ion interaction by modifying the conduction electron spectral function. This process is quite sensitive to the degree of correlations among the d electrons.