Geometrically frustrated GdInO₃: An exotic system to study negative thermal expansion and spin-lattice coupling

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.