We study the formation of magnetic clusters in frustrated magnets in their cooperative paramagnetic regime. For this purpose, we consider the $J_1\text{−}{J}_2\text{−}{J}_3$ classical Heisenberg model on kagome and pyrochlore lattices with $J_2=J_3=J$. In the absence of farther-neighbor couplings, $J=0$, the system is in the Coulomb phase with magnetic correlations well characterized by pinch-point singularities. Farther-neighbor couplings lead to the formation of magnetic clusters, which can be interpreted as a counterpart of topological-charge clusters in Ising frustrated magnets [T. Mizoguchi, L. D. C. Jaubert, and M. Udagawa, Phys. Rev. Lett. 119, 077207 (2017)]. The concomitant static and dynamical magnetic structure factors, respectively $\mathcal{S}\left(\mathit{q}\right)$ and $\mathcal{S}(\mathit{q},\omega )$, develop half-moon patterns. As $J$ increases, the continuous nature of the Heisenberg spins enables the half-moons to coalesce into connected “star” structures spreading across multiple Brillouin zones. These characteristic patterns are a dispersive complement of the pinch-point singularities, and signal the proximity to a Coulomb phase. Shadows of the pinch points remain visible at finite energy $\omega$. This opens the way to observe these clusters through (in)elastic neutron scattering experiments. The origin of these features are clarified by complementary methods: large-$N$ calculations, semiclassical dynamics of the Landau-Lifshitz equation, and Monte Carlo simulations. As promising candidates to observe the clustering states, we revisit the origin of “spin molecules” observed in a family of spinel oxides $A{B}_2{\mathrm{O}}_4(A=\text{Zn},\text{Hg},\text{Mg},B=\text{Cr},\text{Fe})$.

• Received 22 June 2018
• Revised 15 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.144446