Kagome-lattice magnets $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$ recently emerged as a new platform to exploit the interplay between magnetism and topological electronic states. Some of the most exciting features of this family are the dramatic dependence of the easy magnetization direction on the rare-earth specie, despite other magnetic and electronic properties being essentially unchanged, and the kagome geometry of the Mn planes that in principle can generate flat bands and Dirac points; gapping of the Dirac points by spin-orbit coupling has been suggested recently to be responsible for the observed anomalous Hall response in the member ${\mathrm{TbMn}}_6{\mathrm{Sn}}_6$. In this paper, we address both issues with ab initio calculations. We have discovered the significant role played by higher-order crystal-field parameters and rare-earth magnetic anisotropy constants in these systems. We demonstrate that the microscopic origin of rare-earth magnetic anisotropy can also be quantified and understood at various levels: ab initio, phenomenological, and analytical. In particular, using a simple and physically transparent analytical model based on perturbation theory, we are able to explain, with full quantitative agreement, the evolution of rare-earth magnetic anisotropy across the series. We analyze in detail the topological properties of Mn-dominated bands and demonstrate how they emerge from the multiorbital planar kagome model. We further show that, despite this fact, most of the topological features at the Brillouin zone corner K are strongly 3D and therefore cannot explain the observed quasi-2D anomalous Hall effect, while the most pronounced quasi-2D dispersion are too far removed from the Fermi level. By employing self-consistent calculations with ab initio many-body approaches, we demonstrate that the exchange-correlation effects beyond the density functional theory for itinerant Mn-$d$ electrons do not significantly alter the obtained electronic and magnetic structure. Therefore, we conclude that, contrary to previous claims, the most pronounced 2D kagome-derived topological band features bear little relevance to transport in $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$, albeit they may possibly be brought to focus by electron or hole doping.

Recently, kagome materials have become an engrossing platform to study the interplay among symmetry, magnetism, topology, and electron correlation. The latest works on $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$ ($R$ = rare-earth metal) compounds have illustrated that this family could be intriguing to investigate various physical phenomena due to large spin-orbit coupling and strong magnetic ordering. However, combined transport and spectroscopic studies in $R{\mathrm{Mn}}_6{\mathrm{Sn}}_6$ materials are still limited. Here, we report magnetic, magnetotransport, and angle-resolved photoemission spectroscopy measurements of a kagome magnet ${\mathrm{ErMn}}_6{\mathrm{Sn}}_6$ that undergoes antiferromagnetic ($T_N=345\mathrm{K}$) to ferrimagnetic ($T_C=68\mathrm{K}$) phase transitions in the presence of a field. We observe large anomalous and topological Hall effects serving as transport signatures of the nontrivial Berry curvature. The isothermal magnetization exhibits strong anisotropic nature and the topological Hall effect of the compound depends on the critical field of metamagnetic transition. Our spectroscopic results complemented by theoretical calculations show the multiorbital kagome fermiology. This Letter provides new insight into the tunability and interplay of topology and magnetism in a kagome magnet.

Magnetic first-order phase transitions are key for the emergence of functionalities of fundamental and applied significance, including magnetic shape memory as well as magnetostrictive and magnetocaloric effects. Such transitions are usually associated with thermomagnetic hysteresis. We report the observation of a first-order transition in $\mathrm{P}{\mathrm{r}}_2\mathrm{In}$ from a paramagnetic to a ferromagnetic state at $T_C=57\mathrm{K}$ without a detectable thermomagnetic hysteresis, which is also accompanied by a large magnetocaloric effect. The peculiar electronic structure of $\mathrm{P}{\mathrm{r}}_2\mathrm{In}$ exhibiting a large density of states near the Fermi energy explains the highly responsive magnetic behavior of the material. The magnetic properties of $\mathrm{P}{\mathrm{r}}_2\mathrm{In}$ are reported, including observation of another (second-order) magnetic transition at 35 K.

With intricate lattice structures, kagome materials are an excellent platform to study various fascinating topological quantum states. In particular, kagome materials, revealing large responses to external stimuli such as pressure or magnetic field, are subject to special investigation. Here we study the kagome-net ${\mathrm{HoMn}}_6{\mathrm{Sn}}_6$ magnet that undergoes paramagnetic to ferrimagnetic transition (below 376 K) and reveals spin-reorientation transition below 200 K. In this compound, we observe the topological Hall effect and substantial contribution of anomalous Hall effect above 100 K. We unveil the pressure effects on magnetic ordering at a low magnetic field from the pressure tunable magnetization measurement. By utilizing high-resolution angle-resolved photoemission spectroscopy, Dirac-like dispersion at the high-symmetry point K is revealed in the vicinity of the Fermi level, which is well supported by the first-principles calculations. Our investigation will pave the way to understanding the magnetotransport and electronic properties of various rare-earth-based kagome magnets.