Complex Magnetic Ground States in the Layered Compounds LnTAl4Ge2 with Triangular Lanthanide Nets

Strongly correlated spin systems continue to draw significant interest due to the complex interplay between structural, charge, and spin degrees of freedom. This intricate relationship gives rise to a range of novel phenomena, such as topologically protected spin textures (like skyrmions), unconventional electronic band physics (e.g., flat bands), and other emergent states. In this dissertation, we present our results from investigations into three distinct compounds within the category of geometrically frustrated materials, specifically those of the LnTAl4Ge2 variety. We elucidate the process of design and synthesis for these compounds, followed by a thorough characterization of their physical properties, including magnetic, thermal, and electronic attributes. First, we outlined the design and synthesis of new materials, specifically LnTAl4Ge2 single crystals, utilizing the molten metal flux crystal growth method. By modulating the molar ratio of the reactive elements and the heating/cooling profile, we successfully produced phase-pure crystals. We then elucidated the crystalline structures of the synthesized LnTAl4Ge2 single crystals using Powder X-ray Diffraction (PXRD) and Energy Dispersive Spectroscopy (EDS), highlighting that the fabrication of large, phase-pure specimens poses significant challenges. We observed the presence of impurity phases such as AuAl2, LnAl2Ge2, and Ln2Al3Ge4 alongside with LnTAl4Ge2 phases. Furthermore, we found that compounds where the Ln = Ce, Sm, Gd, and Tb can be more easily obtained as phase-pure LnAuAl4Ge2 crystals; similarly, when Ln = Sm, Gd, Tb, Y, and Lu, the production of phase-pure LnNiAl4Ge2 crystals can be more easily achievable. Then, We focus on examples with novel magnetism and reported the comprehensive study of magnetic, thermal, and electrical properties in the antiferromagnetic phase of TbAuAl4Ge2. Following the discussion of TbAuAl4Ge2, GdAuAl4Ge2 compound is studied, together with the thermal results of YAuAl4Ge2. The temperature and magnetic field-dependent magnetization, heat capacity, and electrical resistivity measurements reveal that both Tb- and Gd-variant compounds exhibit several magnetically ordered states at low temperatures, with evidence for magnetic fluctuations extending into the paramagnetic temperature region. For magnetic fields applied in the ab-plane, there is particularly rich behavior, with several ordered state regions that are separated by metamagnetic phase transitions. Despite Gd being an isotropic S-state ion and Tb having an anisotropic J-state, there are similarities in the phase diagrams for the two compounds, suggesting that factors such as the symmetry of the crystalline lattice, which features well-separated triangular planes of lanthanide ions, or the Ruderman-Kittel-Kasuya-Yosida interaction control the magnetism. We also point out similarities to other centrosymmetric compounds that host skyrmion lattices, such as Gd2PdSi3, and propose that the LnAuAl4Ge2 family of compounds are of interest as reservoirs for complex magnetism and electronic behaviors. Next, we reported and bulk physical properties of SmAuAl4Ge2 single crystals, together with experimental results for LuAuAl4Ge2. Temperature-dependent magnetic susceptibility measurements reveal van Vleck paramagnetism due to trivalent samarium ions, with complex antiferromagnetic ordering at TN1 = 13.2 K and TN2 = 7.4 K. Heat capacity measurements show that the transitions at TN1 and TN1 are first and second order, respectively, while also revealing that the Sommerfeld coefficient is not enhanced compared to the nonmagnetic analog YAuAl4Ge2. Together with electrical resistivity measurements, these results show that SmAuAl4Ge2 is a weakly correlated metal, where the combination of van Vleck paramagnetism with the triangular net arrangement of the samarium ions, leads to complex magnetic ordering at low temperatures, resembling what is seen in other LnAuAl4Ge2 (Ln = Gd and Tb) analogues. In addition, positive linear magnetoresistance appears within the ordered states over a wide field range, further establishing SmAuAl4Ge2 and the broader family as hosts for novel magnetism and anomalous magnetotransport behaviors. Finally, we reported results for GdNiAl4Ge2, which crystallizes in a rhombohedral structure that features geometrically frustrated triangular nets of lanthanide ions. Magnetic, thermodynamic, and electrical transport measurements reveal metallic behavior with antiferromagnetic-like ordering in small magnetic fields, which strongly evolves to produce anomalous hysteresis for magnetic fields applied in the ab-plane. In particular, over a limited portion of the temperature-field phase space, the magnetic susceptibility of the field-cooled curves is smaller than that of the zero-field-cooled curves, and the ac magnetic response exhibits frequency and field-dependent peaks only in the zero- field-cooled curves. This suggests the formation of history-dependent spin structures or domains with complex spin relaxation dynamics, resembling what is seen on other materials with nontrivial spin textures. This establishes GdNiAl4Ge2 as a host for intriguing quantum spin states and further focuses attention on this family of materials. Taken together, the great sensitivity of these properties to changes in temperature and magnetic fields, as well as chemical tune, make the LnTAl4Ge2 family of materials as a reservoir for an environment to search for strongly correlated magnetism and connect them to broader classes of anomalous magnetic metals, including those with geometric frustration [83, 84, 85, 5, 86], topological protection [87, 88, 89, 90], unconventional Hall effects [91, 92], skyrmion states [71, 93, 7, 27, 94, 36], and possibly a metallic quantum spin liquid behavior [95]. This makes our work a great value in developing the present understanding of magnetism. In addition, our work has attracted solid researchers to further study these materials [81, 152]and will be of great value to the theorists for guiding the improvements in understanding magnetism.