Evolution of magnetic Dirac bosons in a Kagome lattice*

We examine the magnetic properties and spin dynamics of Dirac nodes in a Heisenberg kagome lattice. Using linear spin theory, the phase diagrams and the evolution of exchange interactions in various magnetic configurations of the Kagome lattice are numerically calculated and produce spin waves that contain bosonic Dirac and Weyl points. Through the frustration of the magnetic geometry, we see a connection to the symmetry properties of the kagome lattice and the various antiferromagnetic configurations, where further study of external frustrations from a magnetic field, temperature, and anisotropy may reveal a controllability of the exchange interactions and nodal points.