Magnetic clustering, half-moons, and shadow pinch points as signals of a proximate Coulomb phase in frustrated Heisenberg magnets

Abstract

We study the formation of magnetic clusters in frustrated magnets in their cooperative paramagnetic regime. For this purpose, we consider the J1-J2-J3 classical Heisenberg model on kagome and pyrochlore lattices with J2 = J3 = 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 S(q) and S(q, ω), 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, ω. 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, semi-classical 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 AB2O4 (A = Zn, Hg, Mg, B = Cr, Fe). PACS numbers: 75.10.Kt FIG. 6. The energy minima in the Brillouin zone for (a) J = 0.26 and (b) J = 1.1 in the kagome system. B. From pinch points to half-moons, near J1cThe flat bands form the ground-state manifold up to J = J 1c = 1/5 for kagome 36 and 1/6 for pyrochlore. This FIG. 7. The energy minima in the Brillouin zone on a hhlplane for (a) J = 0.22 and (b) J = 1 in the pyrochlore system.

Fragmentation in Frustrated Magnets: A Review

“…This has been proposed as an elegant mechanism for Nd 2 Zr 2 O 7 (see section 3.2.2) whose inelastic magnetic structure factor fragments into flat bands with divergenceless fluctuations and divergence-full fluctuations forming Bragg peaks and dispersive bands [64]. For a variety of frustrated systems [69,70], the divergence-full fluctuations also form pinch-point patterns but on the dispersive band of the energy spectrum. Measurements at iso-energy thus provide a cut of these dispersive pinch points in the characteristic form of half-moons [69,70].…”

Arc-shaped structure factor in the $J_1$-$J_2$-$J_3$ classical Heisenberg model on the triangular lattice

“…Furthermore, the static half-moons are a consequence of having several atoms in the unit cell as the half-moon is the complement of the flat band combined with another dispersive band with a continuous minimum. 26 Thus, except for their appearance, it is not clear if or how the arc nematic is related to the halfmoons.…”

Hedgehog-lattice spin texture in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice

“…The pyrochlore lattice is a three-dimensional network of corner-sharing tetrahedra. In the presence of not only the nearest-neighbor(NN) antiferromagnetic exchange interaction J 1 but also the third NN one along the bond directions J 3 , it turns out that classical Heisenberg spins are ordered into a quadruple-q state with the four ordering vectors q = ( 1 2 , 1 2 , 1 2 ), (− 1 2 , 1 2 , 1 2 ), ( 1 2 , − 1 2 , 1 2 ), and ( 12 , 1 2 , − 1 2 ) in units of 2π a in the cubic basis [50][51][52] and that the spins are collinearly aligned due to the effect of thermal fluctuations. Since the above J 1 -J 3 pyrochlore antiferromagnet can potentially host the hedgehog lattice in the sense that the ordered phase is the multiple-q state, we try to suppress the spin collinearity.…”