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Frustrated Magnetism in FeGe$_3$O$_4$ with a Chiral Trillium Network

The discovery of new magnetic ground states in geometrically frustrated lattices remains a central challenge in materials science. Here, we report the synthesis, structural characterization, and frustrated magnetic properties of FeGe$_3$O$_4$, a newly identified compound that crystallizes in the noncentrosymmetric cubic space group $P2_13$. In this structure, Fe atoms form an intricate double-trillium lattice with nearest-neighbor Fe--Fe distances of $\sim$4.2~Å, while Ge$^{2+}$ ions mediate magnetic interactions through Fe-Ge-Fe pathways. Field-dependent magnetization at 2~K shows a pronounced nonlinearity, reaching a maximum moment of 2.55(3)~$μ_\mathrm{B}$/Fe$^{2+}$ at 70~kOe without evidence of saturation. Magnetic susceptibility, heat capacity, and neutron scattering collectively reveal the onset of short-range magnetic interactions near 5~K, with no long-range ordering detected down to 0.06~K. Specific heat measurements demonstrate strong frustration: only $\sim$34\% of the expected magnetic entropy is recovered at 2.4~K. Taken together, these results establish FeGe$_3$O$_4$ as a rare example of a geometrically frustrated trillium-lattice magnet, offering a promising platform for exploring exotic quantum magnetic phenomena.