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Theoretical study on the variation of ordering vector in Ce(Pd$_{1-x}$M$_x$)$_2$Al$_3$ (M$=${Ag, Cu})

In heavy-fermion compounds, the crossover from the localized to itinerant heavy-fermion state is observed with lowering temperature, frequently accompanied by magnetism. Ordering vectors of magnetism often vary with applying pressure or with substituting atoms. In Ce(Pd$_{1-x}$M$_x$)$_2$Al$_3$ with $\mathrm{M}=\mathrm{Ag,Cu}$, the $(0,0,1/2)$-antiferromagnetic (AF), ferromagnetic (F), and another AF orders are observed for $x<0.05$, $0.1<x<0.4$, and $0.5<x$, respectively. This change in the ordering vector is considered to be caused by the change in the conduction-band structures. Using the anisotropic RKKY interaction model reflecting the spacial anisotropic distribution of the $f$ states and also the conduction-band structures, % obtained by the band calculation, we study the change in the ordering vector of Ce(Pd$_{1-x}$M$_x$)$_2$Al$_3$ with $x$ theoretically. As a result, the variation of the ordering vector is explained by treating the substitution of atoms as the conduction-electron doping, and the ordering vector of the AF state for $x>0.5$ is considered to be $(1/2,0,1/2)$.