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

TL;DR

This study reports the growth and comprehensive characterization of orthorhombic Cmcm $R$Fe$_6$Ge$_6$ ($R$=Y,Tb,Dy) kagome magnets, unveiling a distorted Fe kagome network coupled to ordered $R$–Ge$_2$ chains. Fe moments order antiferromagnetically above ~400 K with ferromagnetic kagome planes, while Tb and Dy moments order at low temperatures with Tb exhibiting a single transition and Dy two transitions influenced by crystal-field effects; Y remains nonmagnetic in the $f$-subsystem. DFT calculations reveal a large $N(E_F)$ that drives Fe magnetism and a three-scale lattice-energy landscape controlling 1D chain disorder and in-plane chain alignment, suggesting a triangular Ising model description for the intraplanar ordering. The combination of structural distortions, high DOS at the Fermi level, and complex low-temperature magnetism makes this family a fertile platform for exploring the interplay between lattice geometry and electronic/magnetic properties, including potential Fermi-surface instabilities through chemical substitution.

Abstract

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.

Figures (15)

• Figure 1: a) Sketch of HfFe$_6$Ge$_6$-type crystal structure. b) Crystal structure of $R$Fe$_6$Ge$_6$ in the Cmcm space group. There are five inequivalent Ge atoms. A different color (black) is used for Ge1 to highlight its dimerization along a-axis. Other Ge atoms (Ge2-5) are all represented by blue colored balls. c) Ge–Ge dimers forming linear chains with $R$ atoms along the $a$-axis penetrating the Ge honeycomb and Fe kagome planes. d) a-axis view of the TbFe$_6$Ge$_6$-Cmcm structure highlighting the kagome network of Fe atoms. The bond lengths of atoms forming the kagome network slightly distorted due to the orthorhombic symmetry. The letters p, q, and r denote equivalent bond lengths within each kagome unit, as indicated in the legend. e) Sketch of a $R$Fe$_3$Ge$_2$ unit cell, a building block for the hexagonal $R$Fe$_6$Ge$_6$ structure. f) Schematic illustration of the formation of $R$Fe$_6$Ge$_6$ structure from doubling of $R$Fe$_3$Ge$_2$ (details are provided in the introduction section). The solid black lines in panels (a) and (b) and the dashed lines in panel (d) represent the unit cell of the corresponding crystal structures.
• Figure 2: a) Optical microscope image of a representative TbFe$_6$Ge$_6$ single crystal mounted on the tip of tweezers. b) Reciprocal space map of the $(0kl)$ scattering plane obtained via single-crystal X-ray diffraction, confirming the in-plane crystallographic order and symmetry of the DyFe$_6$Ge$_6$ structure. c) Simulated single-crystal diffraction pattern of DyFe$_6$Ge$_6$ along the [100] direction, for comparison with the experimental data shown in panel (b). The dashed hexagons in panels (b) and (c) serve as visual guides.
• Figure 3: Temperature dependence magnetic susceptibility (FC) measured at 0.1 T magnetic field along $a$ (black line), $b$ (blue line), and $c$ (brown line) crystallographic axes for a) YFe$_6$Ge$_6$, b) TbFe$_6$Ge$_6$, and c) DyFe$_6$Ge$_6$. Insets in panels $b$ and $c$ show first derivative of corresponding FC magnetic susceptibility in all three crystallographic directions.
• Figure 4: Field-dependent isothermal magnetization $M$ vs. $B$ or simply ($MB$) measured along the crystallographic $a$, $b$, and $c$ axes for (a–c) YFe$_6$Ge$_6$, (d–f) TbFe$_6$Ge$_6$, and (g–i) DyFe$_6$Ge$_6$, respectively. Measurements were performed at various temperatures with an applied magnetic field sweeping from 9 T to $-$9 T and $-$9 T to 9 T.
• Figure 5: Temperature variation of longitudinal resistivity measured with current applied along $a$-axis for a) YFe$_6$Ge$_6$, b) TbFe$_6$Ge$_6$, and c) DyFe$_6$Ge$_6$. Insets in panels (b) shows the temperature derivative of the resistivity and in panels (c) shows enlarge view of low temperature data.