Randomly Hopping Majorana Fermions in the Diluted Kitaev System α-Ru_{0.8}Ir_{0.2}Cl_{3}.

dc and ac magnetic susceptibility, magnetization, specific heat, and Raman scattering measurements are combined to probe low-lying spin excitations in α-Ru_{1-x}Ir_{x}Cl_{3} (x≈0.2), which realizes a disordered spin liquid. At intermediate energies (ℏω>3 meV), Raman spectroscopy evidences linearly ω-dependent Majorana-like excitations, obeying Fermi statistics. This points to robustness of a Kitaev paramagnetic state under spin vacancies. At low energies below 3 meV, we observe power-law dependences and quantum-critical-like scalings of the thermodynamic quantities, implying the presence of a weakly divergent low-energy density of states. This scaling phenomenology is interpreted in terms of the random hoppings of Majorana fermions. Our results demonstrate an emergent hierarchy of spin excitations in a diluted Kitaev honeycomb system subject to spin vacancies and bond randomness.

Emergence of the isotropic Kitaev honeycomb latticeα-RuCl3and its magnetic properties.

We present a comprehensive investigation of the crystal and magnetic structures of the van der Waals antiferromagnetα-RuCl3using single crystal x-ray and neutron diffraction. The crystal structure at room temperature is a monoclinic (C2/m). However, with decreasing temperature, a remarkable first-order structural phase transition is observed, leading to the emergence of a rhombohedral (R3-) structure characterized by three-fold rotational symmetry forming an isotropic honeycomb lattice. On further cooling, a zigzag-type antiferromagnetic order develops belowTN=6∼6.6K. The critical exponent of the magnetic order parameter was determined to beß=0.11(1), which is close to the two-dimensional Ising model. Additionally, the angular dependence of the magnetic critical field of the zigzag antiferromagnetic order for the polarized ferromagnetic phase reveals a six-fold rotational symmetry within theab-plane. These findingsreflect the symmetry associated with the Ising-like bond-dependent Kitaev spin interactions and underscore the universality of the Kitaev interaction-dominated antiferromagnetic system.

Structure and magnetism of the triangular lattice material YbBO3.

YbBO3is a member of the orthoborate family of materials which contains a triangular arrangement of Yb3+ions. Here we study the physical properties of YbBO3with neutron diffraction, inelastic neutron scattering, specific heat, and ac susceptibility measurements. The neutron diffraction measurements confirm that our samples of YbBO3crystallize in the monoclinic space groupC2/c(#15) which contains two crystallographically distinct Yb3+sites decorating a slightly distorted triangular lattice. Heat capacity and ac susceptibility measurements indicate a potential transition to magnetic order at 0.4 K. In agreement with these observations, neutron diffraction measurements at 0.044 K observe magnetic Bragg peaks which can be indexed by a propagation vector of (0 0 1). Although determining a unique spin configuration corresponding to the observed magnetic Bragg peaks is not possible, model refinements indicate that the ordered moments are likely in the range of 0.4-0.9 µBand, notably, require moments on both Yb sites. In addition to the magnetic Bragg peaks, diffuse scattering at lowQis observed indicating that the transition does not correspond to complete long range magnetic order. The two-site picture for YbBO3is further evidenced by the number of crystal field excitations observed by inelastic neutron scattering measurements. Together these results show that YbBO3is a two-site triangular lattice material with signatures of long-range order as well as shorter ranged spin correlations.

Decay and renormalization of a longitudinal mode in a quasi-two-dimensional antiferromagnet.

An ongoing challenge in the study of quantum materials, is to reveal and explain collective quantum effects in spin systems where interactions between different modes types are important. Here we approach this problem through a combined experimental and theoretical study of interacting transverse and longitudinal modes in an easy-plane quantum magnet near a continuous quantum phase transition. Our inelastic neutron scattering measurements of Ba2FeSi2O7 reveal the emergence, decay, and renormalization of a longitudinal mode throughout the Brillouin zone. The decay of the longitudinal mode is particularly pronounced at the zone center. To account for the many-body effects of the interacting low-energy modes in anisotropic magnets, we generalize the standard spin-wave theory. The measured mode decay and renormalization is reproduced by including all one-loop corrections. The theoretical framework developed here is broadly applicable to quantum magnets with more than one type of low energy mode.

Magnon bound states versus anyonic Majorana excitations in the Kitaev honeycomb magnet α-RuCl3.

The pure Kitaev honeycomb model harbors a quantum spin liquid in zero magnetic fields, while applying finite magnetic fields induces a topological spin liquid with non-Abelian anyonic excitations. This latter phase has been much sought after in Kitaev candidate materials, such as α-RuCl3. Currently, two competing scenarios exist for the intermediate field phase of this compound (B = 7 - 10 T), based on experimental as well as theoretical results: (i) conventional multiparticle magnetic excitations of integer quantum number vs. (ii) Majorana fermionic excitations of possibly non-Abelian nature with a fractional quantum number. To discriminate between these scenarios a detailed investigation of excitations over a wide field-temperature phase diagram is essential. Here, we present Raman spectroscopic data revealing low-energy quasiparticles emerging out of a continuum of fractionalized excitations at intermediate fields, which are contrasted by conventional spin-wave excitations. The temperature evolution of these quasiparticles suggests the formation of bound states out of fractionalized excitations.

Sub-gap optical response in the Kitaev spin-liquid candidate α-RuCl3.

We report detailed optical experiments on the layered compound α-RuCl3 focusing on the THz and sub-gap optical response across the structural phase transition from the monoclinic high-temperature to the rhombohedral low-temperature structure, where the stacking sequence of the molecular layers is changed. This type of phase transition is characteristic for a variety of tri-halides crystallizing in a layered honeycomb-type structure and so far is unique, as the low-temperature phase exhibits the higher symmetry. One motivation is to unravel the microscopic nature of THz and spin-orbital excitations via a study of temperature and symmetry-induced changes. The optical studies are complemented by thermal expansion experiments. We document a number of highly unusual findings: A characteristic two-step hysteresis of the structural phase transition, accompanied by a dramatic change of the reflectivity. A complex dielectric loss spectrum in the THz regime, which could indicate remnants of Kitaev physics. Orbital excitations, which cannot be explained based on recent models, and an electronic excitation, which appears in a narrow temperature range just across the structural phase transition. Despite significant symmetry changes across the monoclinic to rhombohedral phase transition and a change of the stacking sequence, phonon eigenfrequencies and the majority of spin-orbital excitations are not strongly influenced. Obviously, the symmetry of a single molecular layer determines the eigenfrequencies of most of these excitations. Only one mode at THz frequencies, which becomes suppressed in the high-temperature monoclinic phase and one phonon mode experience changes in symmetry and stacking. Finally, from this combined terahertz, far- and mid-infrared study we try to shed some light on the so far unsolved low energy (<1 eV) electronic structure of the ruthenium 4d 5 electrons in α-RuCl3.