Through soft X-ray absorption spectroscopy, hard X-ray Raman scattering, and theoretical simulations, we provide the most in-depth and systematic study of the phase transformation and (de)lithiation effect on electronic structure in Li(x)FePO(4) nanoparticles and single crystals. Soft X-ray reveals directly the valence states of Fe 3d electrons in the vicinity of Fermi level, which is sensitive to the local lattice distortion, but more importantly offers detailed information on the evolution of electronic states at different electrochemical stages. The soft X-ray spectra of Li(x)FePO(4) nanoparticles evolve vividly with the (de)lithiation level. The spectra fingerprint the (de)lithiation process with rich information on Li distribution, valency, spin states, and crystal field. The high-resolution spectra reveal a subtle but critical deviation from two-phase transformation in our electrochemically prepared samples. In addition, we performed both first-principles calculations and multiplet simulations of the spectra and quantitatively determined the 3d valence states that are completely redistributed through (de)lithiation. This electronic reconfiguration was further verified by the polarization-dependent spectra collected on LiFePO(4) single crystals, especially along the lithium diffusion direction. The evolution of the 3d states is overall consistent with the local lattice distortion and provides a fundamental picture of the (de)lithiation effects on electronic structure in the Li(x)FePO(4) system.

The discovery of massless Dirac electrons in graphene and topological Dirac-Weyl materials has prompted a broad search for bosonic analogues of such Dirac particles. Recent experiments have found evidence for Dirac magnons above an Ising-like ferromagnetic ground state in a twodimensional (2D) kagome lattice magnet and in the van der Waals layered honeycomb crystal CrI3, and in a 3D Heisenberg magnet Cu3TeO6. Here we report on our inelastic neutron scattering investigation on large single crystals of a stacked honeycomb lattice magnet CoTiO3, which is part of a broad family of ilmenite materials. The magnetically ordered ground state of CoTiO3 features ferromagnetic layers of Co 2+ , stacked antiferromagnetically along the c-axis. We discover that the magnon dispersion relation exhibits strong easy-plane exchange anisotropy and hosts a clear gapless Dirac cone along the edge of the 3D Brillouin zone. Our results establish CoTiO3 as a model pseudospin-1/2 material to study interacting Dirac bosons in a 3D quantum XY magnet.The discoveries of graphene and topological insulators have led to significant advances in our understanding of the properties of electron in solids described by a Dirac equation. In particular, the fruitful analogy between fundamental massless Weyl-Dirac fermions in Nature and electrons in graphene or topological semimetals has allowed physicists to simulate theories of particle physics using tabletop experiments [1][2][3][4][5][6]. Remarkably, the concept of Dirac particles is not limited to electrons or other fermionic quasiparticles, prompting a search for analogues in photonic crystals [7,8], acoustic metamaterials [9], and quantum magnets [10][11][12][13]. In particular, Dirac magnons, or more broadly defined topological magnons [14][15][16][17][18][19], have attracted much attention as platforms to investigate the effect of inter-particle interaction or external perturbations on Dirac bosons, and are proposed to be of potential interest in spintronic applications.In contrast to light and sound, the symmetry broken states and emergent bosonic excitations of quantum magnets depend crucially on dimensionality and spin symmetry, which provides a fertile playground for examining the physics of topological bosons. To date, gapped topological magnons in Ising-like ferromagnets have been reported in a kagome lattice material Cu(1,3bdc) [16] and in a layered honeycomb magnet CrI 3 [17]. On the other hand, magnons exhibiting symmetry protected band crossings have been found only in a single material, a three-dimensional (3D) Heisenberg antiferromagnet Cu 3 TeO 6 [18,20]. It is thus desirable to explore new test-beds with distinct spin symmetries to expand our understanding of the physics of Dirac magnons.In this paper, we present a new model 3D quantum XY magnet realizing gapless Dirac magnons, CoTiO 3 , which has a simple ilmenite crystal structure. The magnetic lattice of Co 2+ ions in CoTiO 3 is a stacked honeycomb lattice, exactly the same as in ABC stacked graphene. Below T N ≈ 38 K, this mate...

*When the energy eigenvalues of two coupled quantum states approach each other in a certain parameter space, their energy levels repel each other and level crossing is avoided 1 . Such level repulsion, or avoided level crossing, is commonly used to describe the dispersion relation of quasiparticles in solids 2 . However, little is known about the level repulsion when more than two quasiparticles are present; for example, in a strongly interacting quantum system where a quasiparticle can spontaneously decay into a many-particle continuum [3][4][5] . Here we show that even in this case level repulsion exists between a long-lived quasiparticle state and a continuum. In our fine-resolution neutron spectroscopy study of magnetic quasiparticles in the frustrated quantum magnet BiCu 2 PO 6 , we observe a renormalization of the quasiparticle dispersion relation due to the presence of the continuum of multi-quasiparticle states.A fundamental concept in condensed matter physics is the idea that strongly interacting atomic systems can be treated as a collection of weakly interacting and long-lived quasiparticles. Within a quasiparticle picture, complex collective excited states in a many-body system are described in terms of effective elementary excitations. The quanta of these excitations carry a definite momentum and energy, and are termed quasiparticles. Magnetic insulators containing localized S = 1/2 magnetic moments and having valence-bond solid ground states are ideal systems in which to study bosonic quasiparticles in an interacting quantum many-body system 6 . The elementary magnetic excitations in these materials are triply degenerate S = 1 quasiparticles called triplons, and their momentum-and energy-resolved dynamics can be probed directly though inelastic neutron scattering (INS) measurements.In particular, when the system's Hamiltonian has an interaction term coupling single-particle and multi-particle states, the single quasiparticles may decay into the continuum of multi-particle states 3,4 . In such a system, the Hamiltonian for the single quasiparticles is non-Hermitian and the energy eigenvalues are in general complex. The single-particle decay typically occurs in two ways. Often the single-particle mode stays as a resonance inside the continuum, but the lifetime becomes short and the mode is highly damped 3 . Sometimes the single quasiparticle simply ceases to exist, and the dispersion abruptly terminates when it crosses the continuum boundary 5 . However, there is a third possibility, in which the single-quasiparticle dispersion is significantly renormalized to avoid the multi-particle continuum. This is analogous to the wellknown avoided level crossing behaviour of coupled modes, but in the complex plane of energy eigenvalues 7 . Despite broad interest in strongly interacting quantum systems, experimentally realizing an ideal condition to study the interaction between a quasiparticle and a multi-particle continuum turns out to be extremely difficult. One realization occurs in semiconducting quantum do...

The nature of Na ion distribution, diffusion path, and the spin structure of P 2-type Na2Ni2TeO6 with a Ni honeycomb network has been explored. The nuclear density distribution of Na ions reveals a 2D chiral pattern within Na layers without breaking the original 3D crystal symmetry, which has been achieved uniquely via an inverse Fourier transform (iFT)-assisted neutron diffraction technique. The Na diffusion pathway described by the calculated iso-surface of Na ion bond valence sum (BVS) map is found consistent to a chiral diffusion mechanism. The Na site occupancy and Ni 2+ spin ordering were examined in detail with the electron density mapping, neutron diffraction, magnetic susceptibility, specific heat, thermal conductivity and transport measurements. Signatures of both strong incommensurate (ICM) and weak commensurate (CM) antiferromagnetic (AFM) spin ordering were identified in the polycrystalline sample studied, and the CM-AFM spin ordering was confirmed by using a single crystal sample through the k-scan in the momentum space corresponding to the AFM peak of ( 1 2 , 0, 1).

We report a nuclear magnetic resonance (NMR) study of Bi2Se3 single crystals grown by three different methods. All the crystals show 9 well-resolved peaks in their 209 Bi NMR spectra of the nuclear quadrupolar splitting, albeit with an intensity anomaly. Spectra at different crystal orientations confirm that all the peaks are purely from the nuclear quadrupolar effect, with no other hidden peaks. We identify the short nuclear transverse relaxation time (T2) effect as the main cause of the intensity anomaly. We also show that the 209 Bi signal originates exclusively from bulk, while the contribution from the topological surface states is too weak to be detected by NMR. However, the bulk electronic structure in these single crystals is not the same, as identified by the NMR frequency shift and nuclear spin-lattice relaxation rate (1/T1). The difference is caused by the different structural defect levels. We find that the frequency shift and 1/T1 are smaller in samples with fewer defects and a lower carrier concentration. Also, the low temperature power law of the temperature-dependent 1/T1 (∝ T α ) changes from the Korringa behavior α = 1 in a highly degenerate semiconductor (where the electrons obey Fermi statistics) to α < 1 in a less degenerate semiconductor (where the electrons obey Boltzmann statistics).2