Magnetic compounds with exotic Archimedean lattices

Geometrically frustrated magnetic materials provide an important platform for studying emergent quantum magnetism. Materials that host a triangular or Kagome magnetic sublattice have been intensively studied within this realm of research. Here, we point out that more lattice types can be considered geometrically frustrated since a single triangular motif is sufficient to introduce geometrical frustration. Archimedean lattices present uniform tiling in space. In addition to triangular and Kagome lattices, Archimedean lattices include maple-leaf (ML), Shastry-Sutherland (SS), trellis, ruby, and star lattices that are all triangle containing. Through a systematic search of the literature and known inorganic crystal structure databases (ICSDs), we identify materials that realize these less-common lattice types, offering new opportunities to study frustrated magnetism in diverse settings.

Understanding magnetism in different crystalline and chemical environments has been one of the main drivers for condensed matter physics research. Recent decades' research has shown that many emergent phases are closely related to quantum magnetism, for instance, quantum criticality, superconductivity, and quantum spin liquids (QSLs). Magnetic exchange interactions, quantum magnetic fluctuations, and orbital hybridization are some of the factors that influence the magnetic ground state. Among these factors, magnetism is also strongly affected by the geometry of the magnetic sublattice in compounds. Using a so-called geometrically frustrated lattice is one of the most effective ways to access exotic magnetic ground states due to a lack of a solution to simultaneously satisfy all magnetic interactions. Such geometrical frustration is often achieved by incorporating a triangular magnetic substructure building motif. When considering a closed loop of spins that are connected via nearest-neighbor (NN) antiferromagnetic interactions, an odd number of antiferromagnetic pairs gives rise to a competing interaction and, thus, magnetic frustration. The use of the triangular building motif yields a triangular lattice and Kagome lattice in two dimensions (2D) and pyrochlores in three dimensions (3D). Although this frustration is induced by similar triangular motifs, different lattice types present different relative energies for competing magnetic interactions and, therefore, different theoretically proposed ground states. In a triangular lattice, edge-sharing triangles give 6 NNs, as compared to the corner-sharing Kagome lattice, where only 4 NNs need to be considered in theoretical modeling. There have been many experimental searches for QSLs in real materials based on these lattice types, exploring not only QSLs but also other emergent magnetic states in the hopes of deepening our understanding of many-body entanglement physics.