Continuous Spin Excitations in the Three-Dimensional Frustrated Magnet K_{2}Ni_{2}(SO_{4})_{3}.

Continuous spin excitations are widely recognized as one of the hallmarks of novel spin states in quantum magnets, such as quantum spin liquids (QSLs). Here, we report the observation of such kind of excitations in K_{2}Ni_{2}(SO_{4})_{3}, which consists of two sets of intersected spin-1 (Ni^{2+}) trillium lattices. Our inelastic neutron scattering measurement on single crystals clearly shows a dominant excitation continuum, which exhibits a distinct temperature-dependent behavior from that of spin waves, and is rooted in strong quantum spin fluctuations. Further using the self-consistent-Gaussian-approximation method, we determine that the fourth- and fifth-nearest-neighbor exchange interactions are dominant. These two bonds together form a unique three-dimensional network of corner-sharing tetrahedra, which we name as a "hypertrillium" lattice. Our results provide direct evidence for the existence of QSL features in K_{2}Ni_{2}(SO_{4})_{3} and highlight the potential for the hypertrillium lattice to host frustrated quantum magnetism.

Erratum: Quantifying and Controlling Entanglement in the Quantum Magnet Cs_{2}CoCl_{4} [Phys. Rev. Lett. 127, 037201 (2021)].

This corrects the article DOI: 10.1103/PhysRevLett.127.037201.

Dynamical fractal and anomalous noise in a clean magnetic crystal.

Fractals-objects with noninteger dimensions-occur in manifold settings and length scales in nature. In this work, we identify an emergent dynamical fractal in a disorder-free, stoichiometric, and three-dimensional magnetic crystal in thermodynamic equilibrium. The phenomenon is born from constraints on the dynamics of the magnetic monopole excitations in spin ice, which restrict them to move on the fractal. This observation explains the anomalous exponent found in magnetic noise experiments in the spin ice compound Dy2Ti2O7, and it resolves a long-standing puzzle about its rapidly diverging relaxation time. The capacity of spin ice to exhibit such notable phenomena suggests that there will be further unexpected discoveries in the cooperative dynamics of even simple topological many-body systems.

Hidden Local Symmetry Breaking in a Kagome-Lattice Magnetic Weyl Semimetal.

Exploring the relationship between intriguing physical properties and structural complexity is a central topic in studying modern functional materials. Co3Sn2S2, a newly discovered kagome-lattice magnetic Weyl semimetal, has triggered intense interest owing to the intimate coupling between topological semimetallic states and peculiar magnetic properties. However, the origins of the magnetic phase separation and spin glass state below TC in this ordered compound are two unresolved yet important puzzles in understanding its magnetism. Here, we report the discovery of local symmetry breaking surprisingly co-emerges with the onset of ferromagnetic order in Co3Sn2S2, by a combined use of neutron total scattering and half-polarized neutron diffraction. An anisotropic distortion of the cobalt kagome lattice at the atomic/nano level is also found, with distinct distortion directions among the two Co1 and four Co2 atoms. The mismatch of local and average symmetries occurs below TC, indicating that Co3Sn2S2 evolves to an intrinsically lattice disordered system when the ferromagnetic order is established. The local symmetry breaking with intrinsic lattice disorder provides new understanding of the puzzling magnetic properties. Our density functional theory (DFT) calculation indicates that the local symmetry breaking is expected to reorient local ferromagnetic moments, unveiling the existence of the ferromagnetic instability associated with the lattice instability. Furthermore, DFT calculation unveils that the local symmetry breaking could affect the Weyl property by breaking the mirror plane. Our findings highlight the fundamentally important role that the local symmetry breaking plays in advancing our understanding on the magnetic and topological properties in Co3Sn2S2, which may draw attention to explore the overlooked local symmetry breaking in Co3Sn2S2, its derivatives and more broadly in other topological Dirac/Weyl semimetals and kagome-lattice magnets.

Anomalous magnetic noise in an imperfectly flat landscape in the topological magnet Dy2Ti2O7.

Noise generated by motion of charge and spin provides a unique window into materials at the atomic scale. From temperature of resistors to electrons breaking into fractional quasiparticles, "listening" to the noise spectrum is a powerful way to decode underlying dynamics. Here, we use ultrasensitive superconducting quantum interference device (SQUIDs) to probe the puzzling noise in a frustrated magnet, the spin-ice compound Dy2Ti2O7 (DTO), revealing cooperative and memory effects. DTO is a topological magnet in three dimensions-characterized by emergent magnetostatics and telltale fractionalized magnetic monopole quasiparticles-whose real-time dynamical properties have been an enigma from the very beginning. We show that DTO exhibits highly anomalous noise spectra, differing significantly from the expected Brownian noise of monopole random walks, in three qualitatively different regimes: equilibrium spin ice, a "frozen" regime extending to ultralow temperatures, and a high-temperature "anomalous" paramagnet. We present several distinct mechanisms that give rise to varied colored noise spectra. In addition, we identify the structure of the local spin-flip dynamics as a crucial ingredient for any modeling. Thus, the dynamics of spin ice reflects the interplay of local dynamics with emergent topological degrees of freedom and a frustration-generated imperfectly flat energy landscape, and as such, it points to intriguing cooperative and memory effects for a broad class of magnetic materials.

Unusual Exchange Couplings and Intermediate Temperature Weyl State in Co_{3}Sn_{2}S_{2}.

Understanding magnetism and its possible correlations to topological properties has emerged to the forefront as a difficult topic in studying magnetic Weyl semimetals. Co_{3}Sn_{2}S_{2} is a newly discovered magnetic Weyl semimetal with a kagome lattice of cobalt ions and has triggered intense interest for rich fantastic phenomena. Here, we report the magnetic exchange couplings of Co_{3}Sn_{2}S_{2} using inelastic neutron scattering and two density functional theory (DFT) based methods: constrained magnetism and multiple-scattering Green's function methods. Co_{3}Sn_{2}S_{2} exhibits highly anisotropic magnon dispersions and linewidths below T_{C}, and paramagnetic excitations above T_{C}. The spin-wave spectra in the ferromagnetic ground state is well described by the dominant third-neighbor "across-hexagon" J_{d} model. Our density functional theory calculations reveal that both the symmetry-allowed 120° antiferromagnetic orders support Weyl points in the intermediate temperature region, with distinct numbers and the locations of Weyl points. Our study highlights the important role Co_{3}Sn_{2}S_{2} can play in advancing our understanding of kagome physics and exploring the interplay between magnetism and band topology.

Quantifying and Controlling Entanglement in the Quantum Magnet Cs_{2}CoCl_{4}.

The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.

Machine-learning-assisted insight into spin ice Dy2Ti2O7.

Complex behavior poses challenges in extracting models from experiment. An example is spin liquid formation in frustrated magnets like Dy2Ti2O7. Understanding has been hindered by issues including disorder, glass formation, and interpretation of scattering data. Here, we use an automated capability to extract model Hamiltonians from data, and to identify different magnetic regimes. This involves training an autoencoder to learn a compressed representation of three-dimensional diffuse scattering, over a wide range of spin Hamiltonians. The autoencoder finds optimal matches according to scattering and heat capacity data and provides confidence intervals. Validation tests indicate that our optimal Hamiltonian accurately predicts temperature and field dependence of both magnetic structure and magnetization, as well as glass formation and irreversibility in Dy2Ti2O7. The autoencoder can also categorize different magnetic behaviors and eliminate background noise and artifacts in raw data. Our methodology is readily applicable to other materials and types of scattering problems.

Encoding Magnetic States in Monopole-Like Configurations Using Superconducting Dots.

A large manifold of nontrivial spin textures, including the stabilization of monopole-like fields, are generated by using a completely new and versatile approach based on the combination of superconductivity and magnetism. Robust, stable, and easily controllable complex spin structures are encoded, modified, and annihilated in a continuous magnetic thin film by defining a variety of magnetic states in superconducting dots.

Magnetic behaviour of layered Ag(II) fluorides.

Fluoride phases that contain the spin-1/2 4d9 Ag(II) ion have recently been predicted to have interesting or unusual magnetochemistry, owing to their structural similarity to the 3d9 Cu(II) cuprates and the covalence associated with this unusual oxidation state of silver. Here we present a comprehensive study of structure and magnetism in the layered Ag(II) fluoride Cs2AgF4, using magnetic susceptometry, inelastic neutron scattering techniques and both X-ray and neutron powder diffraction. We find that this material is well described as a two-dimensional ferromagnet, in sharp contrast to the high-T(C) cuprates and a previous report in the literature. Analyses of the structural data show that Cs2AgF4 is orbitally ordered at all temperatures of measurement. Therefore, we suggest that orbital ordering may be the origin of the ferromagnetism we observe in this material.

Quantum criticality and universal scaling of a quantum antiferromagnet.

Quantum effects dominate the behaviour of many diverse materials. Of particular current interest are those systems in the vicinity of a quantum critical point (QCP). Their physical properties are predicted to reflect those of the nearby QCP with universal features independent of the microscopic details. The prototypical QCP is the Luttinger liquid (LL), which is of relevance to many quasi-one-dimensional materials. The magnetic material KCuF3 realizes an array of weakly coupled spin chains (or LLs) and thus lies close to but not exactly at the LL quantum critical point. By using inelastic neutron scattering we have collected a complete data set of the magnetic correlations of KCuF3 as a function of momentum, energy and temperature. The LL description is found to be valid over an extensive range of these parameters, and departures from this behaviour at high and low energies and temperatures are identified and explained.