  High magnetic fields induce a pronounced in-plane electronic anisotropy in
the tetragonal antiferromagnetic metal CeRhIn$_{5}$ at $H^{*} \gtrsim 30$ T for
fields $\simeq 20^{\mathrm{o}}$ off the $c$-axis. Here we investigate the
response of the underlying crystal lattice in magnetic fields to $45$ T via
high-resolution dilatometry. Within the antiferromagnetic phase of
CeRhIn$_{5}$, a finite magnetic field component in the tetragonal $ab$-plane
explicitly breaks the tetragonal ($C_{4}$) symmetry of the lattice well below
$H^{*}$ revealing a finite nematic susceptibility at low fields. A modest
magnetostriction anomaly, $dL/L = -1.8 \times 10^{-6}$, at $H^{*} = 31$ T hence
presumably marks the crossover to a fluctuating nematic phase with large
electronic nematic susceptibility. Magnetostriction quantum oscillations
confirm a Fermi surface change at $H^*$ with the emergence of new orbits. By
analyzing the field-induced change in the crystal-field ground state, we
conclude that the in-plane Ce $4f$ hybridization is enhanced at $H^*$, carrying
the in-plane $f$-electron anisotropy to the Fermi surface. We argue that the
nematic behavior observed in this prototypical heavy-fermion material is of
electronic origin, and is driven by the hybridization between $4f$ and
conduction electrons.
