Frustrated Magnetism of the $S=1$ Trillium-Lattice Oxide Li${}_2$NiGe${}_3$O${}_8$

Abstract

We report magnetization and heat-capacity measurements on the ordered-spinel oxide Li${}_2$NiGe${}_3$O${}_8$, where Ni${}^{2+}$ ions with $S=1$ form a single three-dimensional trillium lattice. Powder x-ray diffraction confirms a cubic ordered-spinel structure with space group $P{4}_{1}32$ or $P{4}_{3}32$. The inverse susceptibility $H/M$ follows Curie--Weiss behavior above 50 K with an effective magnetic moment ${\mu }_{\mathrm{eff}}=3.124(4){\mu }_{\mathrm{B}}$ per Ni and a Weiss temperature ${\theta }_{\mathrm{W}}=-0.21(1)$ K, but deviates smoothly below about 10 K. The magnetic heat capacity $C_{\mathrm{mag}}/T$ shows a broad maximum near 3 K with a wide tail to about 10 K, and the entropy recovered between 2 and 40 K is about 88% of $R\ln 3$. The broad heat-capacity maximum is compared with Monte Carlo results for the local ferromagnetic Ising model on the trillium lattice using a characteristic scale $J$ of order 7 K, while the inverse susceptibility shows only qualitative similarity to the theoretical curve. These results establish Li${}_2$NiGe${}_3$O${}_8$ as a rare $S=1$ single-trillium oxide with frustrated magnetic correlations. The present data provide an experimental platform for discussing the relation between Heisenberg-like and spin-ice-like regimes on the trillium lattice.

8pages, 3figures, accepted in Journal of the Physical Society of Japan