  In this article, we report negative thermal expansion and spin frustration in
hexagonal GdInO$_{3}$. Rietveld refinement of the XRD patterns reveal that the
negative thermal expansion in the temperature range of 50-100K stems from the
triangular lattice of Gd$^{3+}$ ions. At low temperature, the downward
deviation of the inverse susceptibility ($\chi^{-1}$) vs. $T$ plot from the
Curie-Weiss law indicates spin frustration which inhibits long-range magnetic
ordering down to 2K. Magnetostriction measurements clearly demonstrate a strong
spin-lattice coupling. Low temperature anomalous phonon softening, as obtained
from temperature dependent Raman measurements, also reveals the same. Our
experimental observations are supported by first principles density functional
theory calculations of the electronic and phonon dispersion of GdInO$_3$. The
calculations suggest that the GdInO$_3$ lattice is highly frustrated at low
temperature. Further, the calculated normal mode frequencies of the Gd related
$\Gamma$ point phonons are found to depend on the magnetic structure of the
lattice, suggesting significant magneto-elastic coupling.
