We investigate the doping-induced changes in the electronic structure of CeB$_6$ on a series of substituted Ce$_{1-x}R_x$B$_6$ samples ($R$ = La, Nd) using diffuse neutron scattering. We observe a redistribution of magnetic spectral weight across the Brillouin zone, which we associate with the changes in the Fermi-surface nesting properties related to the modified charge carrier concentration. In particular, a strong diffuse peak at the corner of the Brillouin zone ($R$ point), which coincides with the propagation vector of the elusive antiferroquadrupolar (AFQ) order in CeB$_6$, is rapidly suppressed by both La and Nd doping, like the AFQ order itself. The corresponding spectral weight is transferred to the $X(00frac{1}{2})$ point, ultimately stabilizing a long-range AFM order at this wave vector at the Nd-rich side of the phase diagram. At an intermediate Nd concentration, a broad diffuse peak with multiple local maxima of intensity is observed around the $X$ point, evidencing itinerant frustration that gives rise to multiple ordered phases for which Ce$_{1-x}$Nd$_x$B$_6$ is known. On the La-rich side of the phase diagram, however, dilution of the magnetic moments prevents the formation of a similar $(00frac{1}{2})$-type order despite the presence of nesting. Our results demonstrate how diffuse neutron scattering can be used to probe the nesting vectors in complex f-electron systems directly, without reference to the single-particle band structure, and emphasize the role of Fermi surface geometry in stabilizing magnetic order in rare-earth hexaborides.
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