Crystal Growth and Physical Properties of Orthorhombic Kagome Lattice Magnets $R$Fe$_6$Ge$_6$ ($R$=Y, Tb, Dy)

Kagome magnets represent a promising class of materials that exhibit intriguing electronic and magnetic properties, and they have recently garnered significant attention. While most kagome-lattice compounds are hexagonal, we report here single-crystal growth and physical property measurements of $R$Fe$_6$Ge$_6$ ($R$ = Y, Dy, Tb) compounds, which crystallize in an orthorhombic structure. The structure can be derived from a hexagonal prototype $R$Fe$_3$Ge$_2$ by replacing every other $R$ atom with a covalent Ge$_2$ dimer. Ordering of these dimers renders the structure orthorhombic, slightly distorts the kagome net, and makes the three Fe sites formally inequivalent. The iron and rare-earth sublattices order independently. Fe moments order above 400 K, forming ferromagnetic kagome planes stacked antiferromagnetically, while rare-earth moments order below 9 K. TbFe$_6$Ge$_6$ exhibits a single magnetic ordering transition associated with the Tb atoms, whereas DyFe$_6$Ge$_6$ shows two distinct magnetic phase transitions, strongly influenced by crystal electric field effects on the Dy$^{3+}$ ions. Density functional theory (DFT) calculations indicate that the ferromagnetic ordering of the Fe planes is driven by a high density of states at the Fermi energy. They also reveal three dramatically different structural energy scales: $R$ and Ge$_2$ form alternating 1D chains perpendicular to the kagome planes, and violating this alternation incurs a large energy cost. Aligning these chains is less costly, and achieving a two-dimensional order of anti-aligned chains requires very little energy. These compounds represent a unique class of materials, offering new opportunities to investigate the interplay between the distinct crystal lattice geometry and the underlying electronic and magnetic properties.