Kagome Metals

There are several pathways to realizing a strongly correlated electron system, with one of the newest being band engineering. In particular, if a flat band appears in the electronic band structure, strong correlation effects can emerge when the Fermi surface is tuned to intersect the flat band. A well-known example is the magic angle twisted bilayer graphene, where calculations predict that at a specific "magic angle," a flat band forms near the Dirac cone, effectively creating a strongly correlated electron system.

A similar phenomenon occurs in the tight-binding model of a kagome lattice. The lattice consists of hexagons separated by triangles, where the electron wavefunctions from the triangle corners interfere and cancel each other out, forming localized states at the hexagons. This localization manifests as flat bands in reciprocal space, which are indicative of strong correlation effects if the Fermi surface is tuned to its energy. The kagome flat band system has been shown to give rise to several iconic phases typically associated with strongly correlated systems, including magnetism, charge density waves, and superconductivity. Furthermore, the kagome band structure also includes Dirac cones and Van Hove singularities, providing potential realizations of nontrivial topological properties and pair density waves from Fermi surface nesting.

Research on Kagome metals has garnered significant attention, particularly following the discovery of superconductivity in CsV₃Sb₅, a Z₂ topological Kagome metal that undergoes a charge density wave transition at 94K. Given that CsV₃Sb₅ lacks unpaired spins, an intriguing question arises: can similarly rich phase diagrams be realized in Kagome materials that exhibit magnetism?

Among magnetic Kagome metals, iron-tin alloys FexSny have attracted attention. ARPES studies have confirmed the presence of flat bands, and antiferromagnetism in these alloys is believed to arise from the Stoner mechanism. A breakthrough occurs when tin is replaced by germanium. In a comprehensive and collaborative study of FeGe, utilizing neutron scattering, magnetometry, ARPES, and transport measurements, we successfully mapped out a rich phase diagram. The ground state of FeGe consists of three distinct phases: an a-type antiferromagnetic phase, a 2x2x2 charge density wave (CDW) phase, and an incommensurate conical magnetic structure. This discovery underscores the potential for complex emergent phases in magnetic Kagome systems like FeGe, demonstrating that band engineering within the Kagome lattice can indeed give rise to these emergent phases—one of the hallmarks of strongly correlated systems.

Magnetism, as one of the most common consequences of electron correlation, has been a central focus of research because it provides critical insights into electron interactions. For instance, in localized spin systems where magnetism arises primarily from exchange interactions, magnetic excitations—such as spin waves or magnons—are well-defined across the entire energy and momentum spectrum, as observed in the neutron scattering spectra of CrI3. On the other hand, in metallic magnets where magnetism is driven by the Stoner mechanism, spin excitations include both spin precession (spin waves) and accompanying electron motion, which causes a blurring of the spin excitation spectrum. Additionally, in systems with incommensurate spin density wave order, a gapless "phason" excitation appears as the Goldstone mode, emerging from the spontaneous breaking of translational symmetry.

These distinct excitation characteristics reflect the underlying origins of magnetic order in different types of magnets. FeGe serves as an excellent platform for investigating these various magnetic behaviors, as it exhibits a coexistence of antiferromagnetism and an incommensurate conical magnetic structure. Initially, this coexistence was thought to result solely from competition between different exchange interactions in localized moments. However, our neutron scattering experiments suggest otherwise. The spin excitations in FeGe reveal both well-defined localized spin wave excitations and a broad continuum of itinerant excitations, along with a gapless phason-like excitation that corresponds to the incommensurate magnetic structure. This suggests a more complex interplay between localized and itinerant magnetism in FeGe than previously understood.