Magnetism exists on a spectrum spanning the local moment to itinerant moment limits. In the local moment limit, magnetic moments arise from partially filled electronic shells and the magnetic moments are localized in real space. Moments in itinerant magnets come from strong electron-electron interactions of itinerant electrons. Consequently, moments in the itinerant limit are delocalized in real space. While no current theory can successfully interpolate between the regimes, both are areas of vibrant research. This dissertation is composed of two projects, one at each end of the magnetic spectrum.

The first project details the single crystal growth and discovery of a new itinerant antiferromagnet, Ti3Cu4, which magnetically orders below the Neel temperature TN = 11.3 K. TN can be continuously suppressed towards a quantum critical point (QCP) at T = 0 with a magnetic field Hc II c = 4.89 T. A Fermi liquid-non-Fermi liquid crossover is measured convergent at the QCP together with the divergence of the Gruneisen parameter. Density functional theory (DFT) calculations reveal that Fermi surface nesting cannot explain the experimentally determined magnetic ordering wavevector, making Ti3Cu4 unique among the itinerant antiferromagnets. From a quantum criticality perspective, Ti3Cu4 is the first field-induced QCP in a d-electron system, likely reflecting an anomalously small energy scale compared to other d-electron magnets.

The second project describes the search for topological spin textures in the centrosymmetric square-net Eu(Ga1-xAlx)4 system. In non-centrosymmetric topological spin-texture hosts, the Dzyaloshinskii-Moriya (DM) interaction has been deemed crucial in stabilizing the topological spin textures. By contrast, the mechanism for stabilizing topological spin-textures in centrosymmetric magnets is debated since the DM interaction is absent. Here, the magnetic field – temperature phase diagrams of Eu(Ga1-xAlx)4 (0.15<x<0.90) are determined by thermodynamic measurements. The existence of topological or non-coplanar spin textures is established via the topological Hall effect with H IIl c for select compositions. Furthermore, angle-resolved photoemission spectroscopy and Hall effect measurements, together with DFT calculations, provide evidence that the Eu(Ga1-xAlx)4 compounds are topological semimetals. These results establish Eu(Ga1-xAlx)4 as a promising materials platform to study topological spin textures in centrosymmetric materials, as well as the interplay between real- and reciprocal- space topology.