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 ${\mathrm{GdInO}}₃$. Rietveld refinements of the x-ray diffraction patterns reveal that the negative thermal expansion in the temperature range of 50--100 K stems from the triangular lattice of ${\mathrm{Gd}}³⁺$ ions. The downward deviation of the low-temperature inverse susceptibility $({\ensuremath{\chi}}^{\ensuremath{-}1})$ versus $T$ plot from the Curie-Weiss law and the large value of the ratio, $|{\ensuremath{\theta}}_{\text{CW}}|/{T}_N>28$, where ${\ensuremath{\theta}}_{\text{CW}}$ and ${T}_N$ are respectively Curie-Weiss and Neel temperature, indicate a strong spin frustration, which inhibits long-range magnetic ordering down to 1.8 K. Magnetostriction measurements clearly demonstrate a spin-lattice coupling in the system. 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 in ${\mathrm{GdInO}}₃$. The calculations suggest that the ${\mathrm{GdInO}}₃$ lattice is highly frustrated at low temperature. Further, the calculated normal mode frequencies of the Gd-related $\mathrm{\ensuremath{\Gamma}}$ point phonon modes reveal significant magnetoelastic coupling in this system. The competitive role of magnetic interaction energy and thermal stabilization energy in determining the change in interatomic distances is the possible origin for the negative thermal expansion in ${\mathrm{GdInO}}₃$ over a limited range of temperature.