Magnetic clustering in frustrated Heisenberg magnets

Fractionalization is one of the fundamental properties of magnets with nontrivial topological character. For example in spin ice, fractionalized degrees of freedom take the form of magnetic monopoles which serve as elementary excitations with a conserved quantum number, their magnetic charge. Recently, it has been pointed out that the clustering of such topological charges leads to characteristic patterns in static structure factors, which we named half moons, distinct form the pinch points that serve as indicators of a Coulomb phase.
In this presentation, we present a theory of clustering of spins in a more general framework. For this purpose, we employ J1-J2-J3 Heisenberg models on kagome and pyrochlore lattices. By investigating the magnetic structure factor with a large-N approximation, we find that the pinch points turn into different characteristic patterns, namely half moons and stars. Those are the sign of the clustering of spins in the real space whose structures are similar to that in the Ising models. We also reveal by solving the Landau-Lifshitz equation that the characteristic patterns are also found in the dynamical structure factor, indicating that those patterns serve as a clue to find clustering states through inelastic neutron scattering spectra.