  A very strong magnetoelastic effect in the CeCo$_{1-x}$Fe$_{x}$Si alloys is
reported. The strength of the magnetostrictive effect can be tuned upon
changing $x$. The moderate low-temperature linear magnetostriction observed at
low Fe concentrations becomes very large ($\frac {\Delta L}{L} \left(16 T,2
K\right) =$ 3$\times$10$^{-3}$) around the critical concentration ($x_c
\approx$ 0.23) at which the long-range antiferromagnetic order vanishes. Upon
increasing doping through the non-magnetic region ($x > x_c$), the
magnetostriction strength gradually weakens again. Remarkably the
low-temperature magnetostriction at the critical concentration shows a
pronounced $S$-like shape (centered at $B_m \sim$ 6 T) resembling other
well-known Ce-based metamagnetic systems like CeRu$_2$Si$_2$ and CeTiGe. Unlike
what is observed in these compounds, however, the field dependence of the
magnetization shows only a minor upturn around $B_m$ vaguely resembling a
metamagnetic behavior. The subtle interplay between magnetic order and the
Kondo screening seems to originate an enhanced valence susceptibility slightly
changing the Ce ions valence, ultimately triggering the large magnetostriction
observed around the critical concentration.
