Topological nematic spin liquid on the square kagome lattice

International audienceThe ground state of the spin-1/2 kagome antiferromagnet remains uncertain despite decades of active research. Here we step aside from this debated question to address the ground-state nature of a related, and potentially just as rich, system made of corner-sharing triangles: the square kagome lattice (SKL). Our work is motivated by the recent synthesis of a distorted SKL compound mentioned by Morita and Tohyama [J. Phys. Soc. Jpn. 87, 043704 (2018)]. We have studied its spin-1/2 J1−J2 phase diagram with an unrestricted Schwinger boson mean-field theory (SBMFT). Our results agree with previous observations of a plaquette phase (J2≪J1) and a ferrimagnet (J1≪J2). In addition, three original phases appear: two incommensurate orders and a topological quantum spin liquid with weak nematicity. The topological order is characterized by fluxes on specific gauge-invariant quantities and the phase is stable under anisotropic perturbations relevant for experiments. Finally, we provide dynamical structure factors of the reported phases that could be observed in inelastic neutron scattering

Fragmentation in Frustrated Magnets: A Review

International audienceSpin liquids are exotic phases of matter that often support emergent gauge fields and quasi-particle excitations. While spin liquids are commonly known for remaining disordered, their definition has been extended to include phases with broken symmetry corresponding to (partial) long-range order, such as chiral and nematic spin liquids for example. For Coulomb spin liquids, this ordering can be quantitatively understood via a Helmholtz decomposition between divergence-free and divergencefull terms. This phenomenon has been coined fragmentation, where spin degrees of freedom fragment into two components: the fluctuating disordered part and the ordered one. In this review, we will cover the theoretical and experimental aspects of this growing field, in particular its relation to magnetic monopoles in spin ice, its phase diagram and the possibility to observe it in solid-state crystal and artificial networks

Clustering of Topological Charges in a Kagome Classical Spin Liquid

Fractionalization is a ubiquitous phenomenon in topological states of matter. In this work, we study the collective behavior of fractionalized topological charges and their instabilities, through the J1-J2-J3 Ising model on a kagome lattice. This model can be mapped onto a Hamiltonian of interacting topological charges under the constraint of Gauss’ law. We find that the recombination of topological charges gives rise to a yet unexplored classical spin liquid. This spin liquid is characterized by an extensive residual entropy, as well as the formation of hexamers of same-sign topological charges. The emergence of hexamers is reflected by a half-moon signal in the magnetic structure factor, which provides a signature of this new spin liquid in elastic neutron-scattering experiments. To study this phase, a worm algorithm has been developed which does not require the usual divergence-free condition

Rank-2 U(1) spin liquid on the breathing pyrochlore lattice

Higher-rank generalizations of electrodynamics have recently attracted considerable attention because of their ability to host “fracton” excitations, with connections to both fracton topological order and gravity. However, the search for higher-rank gauge theories in experiment has been greatly hindered by the lack of materially relevant microscopic models. Here we show how a spin liquid described by rank-2 U(1) gauge theory can arise in a magnet on the breathing pyrochlore lattice. We identify Yb-based breathing pyrochlores as candidate systems, and make explicit predictions for how the rank-2 U(1) spin liquid would manifest itself in experiment.Design de la frustration: effets de surface et désordr

Schwinger boson theory of the J1,J2=J3 kagome antiferromagnet

We study the kagome antiferromagnet for quantum spin-1/2 with first J1, second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We use Schwinger-boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at J = 0 remains essentially stable over a large window, up to J = 1/3, because it is only weakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spin liquid condenses into a long-range chiral order because of the change of nature of local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus

Schwinger boson theory of the J1,J2=J3 kagome antiferromagnet

We study the kagome antiferromagnet for quantum spin-1/2 with first J1, second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We use Schwinger-boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at J = 0 remains essentially stable over a large window, up to J = 1/3, because it is only weakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spin liquid condenses into a long-range chiral order because of the change of nature of local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus

Schwinger boson theory of the J1,J2=J3 kagome antiferromagnet

We study the kagome antiferromagnet for quantum spin-1/2 with first J1, second J2 and third J3 neighbour exchanges, along the J2 = J3 = J line. We use Schwinger-boson mean-field theory for the precise determination of the phase diagram, and two different rewritings of the Hamiltonian to build an intuition about the origin of the transitions. The spin liquid obtained at J = 0 remains essentially stable over a large window, up to J = 1/3, because it is only weakly frustrated by the J term. Then at J = 1/2, the intermediate Z2 spin liquid condenses into a long-range chiral order because of the change of nature of local magnetic fluctuations. As a side benefit, our Hamiltonian rewriting offers an exact solution for the ground state of our model on a Husimi cactus.Design de la frustration: effets de surface et désordr

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

We study the formation of magnetic clusters in frustrated magnets in their cooperative param-agnetic region. 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)]. Reflecting the tendency of clustering, the 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 complementary of 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)