We provide an exact study of dynamical correlations for the quantum spin-orbital liquid phases of an SU(2)-symmetric Kitaev honeycomb lattice model. We show that the spin dynamics in this Kugel-Khomskii type model is exactly the density-density correlation function of S=1 fermionic magnons, which could be probed in resonant inelastic x-ray scattering experiments. We predict the characteristic signatures of spin-orbital fractionalization in inelastic scattering experiments and compare them to the ones of the spin-anisotropic Kitaev honeycomb spin liquid. In particular, the resonant inelastic x-ray scattering response shows a characteristic momentum dependence directly related to the dispersion of fermionic excitations. The neutron scattering cross section displays a mixed response of fermionic magnons as well as spin-orbital excitations. The latter has a bandwidth of broad excitations and a vison gap that is three times larger than that of the spin-1/2 Kitaev model.
A purely fermionic representation is introduced for the ferromagnetic Kondo lattice model which allows conventional diagrammatic tools to be employed to study correlation effects. Quantum 1/S corrections to magnon excitations are investigated using a systematic inverse-degeneracy expansion scheme which incorporates correlation effects in the form of self-energy and vertex corrections, while explicitly preserving the continuous spin-rotation symmetry. Magnon self-energy is studied in the full range of interaction strength, and shown to result in strong magnon damping and anomalous softening for…
We introduce an exactly solvable SU(2) symmetric Kitaev model with exotic spin excitations. With time reversal symmetry (TRS), the ground state is a spin liquid with gapless or gapped spin-1 but fermionic excitations. When TRS is broken, the resulting spin liquid exhibits deconfined vortex excitations which carry spin-1/2 quantum number and obey non-Abelian statistics. We show that this SU(2) invariant non-Abelian spin liquid exhibits spin quantum Hall effect with quantized spin Hall conductivity σ^s_{xy}=\hbar/2π, and that the spin response is effectively described the SO(3) level-1 Chern-Sim…
Topological phases in magnetic materials offer novel tunability of topological properties via varying the underlying magnetism. We show that three dimensional Kitaev materials can provide a great opportunity for controlling symmetry-protected topological nodal magnons. These materials are originally considered as strong candidates for the Kitaev quantum spin liquid due to the bond-dependent frustrating spin exchange interactions. As a concrete example, we consider the symmetry and topology of the magnons in the canted zig-zag ordered state in the hyperhoneycomb $β\text{-}\mathrm{Li_2IrO_3}$, w…
Spin excitations in an ordered Heisenberg magnet are magnons--bosons with spin 1. That may change when frustration and quantum fluctuations suppress the order and restore the spin-rotation symmetry. We show that spin excitations in the $S=1/2$ Heisenberg antiferromagnet on kagome are spinons--fermions with spin 1/2. In the ground state the system can be described as a collection of small, heavy pairs of spinons with spin 0. A magnetic excitation of lowest energy amounts to breaking up a pair into two spinons at a cost of $0.06 J$.
The topological properties of massive and massless fermionic quasiparticles have been intensively investigated over the past decade in topological materials without magnetism. Recently, the bosonic analogs of such quasiparticles arising from spin waves have been reported in the two-dimensional (2D) honeycomb lattice ferromagnet/antiferromagnet and the 3D antiferromagnet. Here we use time-of-flight inelastic neutron scattering to study spin waves of the S = 1 honeycomb lattice antiferromagnet BaNi2(AsO4)2, which has a zig-zag antiferromagnetic (AF) ground state identical to that of the Kitaev q…
RbFe$^{2+}$Fe$^{3+}$F$_6$ is an example of a charge ordered antiferromagnet where iron sites, with differing valences, are structurally separated into two interpenetrating sublattices. The low temperature magnetically ordered Fe$^{2+}$ ($S$=2) and Fe$^{3+}$ ($S$=5/2) moments form a noncollinear orthogonal structure with the Fe$^{3+}$ site displaying a reduced static ordered moment. Neutron spectroscopy on single crystals finds two distinct spin wave branches with a dominant coupling along the Fe$^{3+}$ chain axis ($b$-axis). High resolution spectroscopic measurements find an intense energy and…
We present the detailed inelastic neutron scattering measurements of the noncollinear antiferromagnet Mn$_3$Ge. Time-of-flight and triple-axis spectroscopy experiments were conducted at the temperature of 6~K, well below the high magnetic ordering temperature of 370~K. The magnetic excitations have a 5-meV gap and display an anisotropic dispersive mode reaching $\simeq 90$~meV at the boundaries of the magnetic Brillouin zone. The spectrum at the zone center shows two additional excitations that demonstrate characteristics of both magnons and phonons. The \textit{ab initio} lattice-dynamics cal…
For topological magnon spectra, determining and explaining the presence of a gap at a magnon crossing point is a key to characterize the topological properties of the system. An inelastic neutron scattering study of a single crystal is a powerful experimental technique that is widely employed to probe the magnetic excitation spectra of topological materials. Here, we show that when the scattering intensity rapidly disperses in the vicinity of a crossing point, such as a Dirac point, the apparent topological gap size is extremely sensitive to experimental conditions including sample mosaic, res…
A high-resolution neutron spectroscopic technique is used to measure momentum-resolved magnon lifetimes in the prototypical two- and three-dimensional antiferromagnets Rb2MnF4 and MnF2, over the full Brillouin zone and a wide range of temperatures. We rederived theories of the lifetime resulting from magnon-magnon scattering, thereby broadening their applicability beyond asymptotically small regions of wavevector and temperature. Corresponding computations, combined with a small contribution reflecting collisions with domain boundaries, yield excellent quantitative agreement with the data.
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 $α$-RuCl$_3$. 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 natu…
Topological magnons are emergent quantum spin excitations featured by magnon bands crossing linearly at the points dubbed nodes, analogous to fermions in topological electronic systems. Experimental realization of topological magnons in three dimensions has not been reported so far. Here, by measuring spin excitations (magnons) of a three-dimensional antiferromagnet Cu$_{3}$TeO$_{6}$ with inelastic neutron scattering, we provide direct spectroscopic evidence for the coexistence of symmetry-protected Dirac and triply degenerate nodes, the latter involving three-component magnons beyond the Dira…
We investigate the excitation spectrum of a two-dimensional resonating valence bond (RVB) state. Treating the $pi$-flux phase with antiferromagnetic correlations as a variational ground state, we recover the long wavelength magnon as an "RVB exciton". However, we find that this excitation does NOT exhaust the entire spectral weight and the high energy spectrum is dominated by fermionic excitations. The latter can be observed directly by inelastic neutron scattering and we predict their characteristic energy scales along different high symmetry directions in the magnetic Brillouin zone. We also…
Guangdong Ocean University（广东海洋大学）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；Spallation Neutron Source Science Center（中国散裂中子源科学中心）；Sun Yat-Sen University（中山大学）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices（广东省磁电物理与器件重点实验室）；Research Center for Magnetoelectric Physics of Guangdong Province（广东省磁电物理研究中心）
We investigate the temperature dependent optical properties of NaV2O5, in the energy range 4meV-4eV. The symmetry of the system is discussed on the basis of infrared phonon spectra. By analyzing the optically allowed phonons at temperatures below and above the phase transition, we conclude that a second-order change to a larger unit cell takes place below 34 K, with a fluctuation regime extending over a broad temperature range. In the high temperature undistorted phase, we find good agreement with the recently proposed centrosymmetric space group Pmmn. On the other hand, the detailed analysis …
The operators of localized spins within a magnetic material commute at different sites of its lattice and anticommute on the same site, so they are neither fermionic nor bosonic operators. Thus, to construct diagrammatic many-body perturbation theory, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. However, to make calculations tractable, the square root of operators in the HP transformation is expanded into a Taylor series truncated to some low order. This poses a question…
Conventionally ordered magnets possess bosonic elementary excitations, called magnons. By contrast, no magnetic insulators in more than one dimension are known whose excitations are not bosons but fermions. Theoretically, some quantum spin liquids (QSLs) -- new topological phases which can occur when quantum fluctuations preclude an ordered state -- are known to exhibit Majorana fermions as quasiparticles arising from fractionalization of spins. Alas, despite much searching, their experimental observation remains elusive. Here, we show that fermionic excitations are remarkably directly evident…
We describe scanning tunneling spectroscopic signatures of Majorana zero modes (MZMs) in Kitaev spin liquids. The tunnel conductance is determined by the dynamical spin correlations of the spin liquid, which we compute exactly, and by spin-anisotropic cotunneling form factors. Near a $\mathbb{Z}_2$ vortex, the tunnel conductance has a staircase voltage dependence, where conductance steps arise from MZMs and (at higher voltages) from additional vortex configurations. By scanning the probe tip position, one can detect the vortex locations. Our analysis suggests that topological magnon bound stat…
Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet ZnCr2Se4 with a cubic spinel structure, in which spin-3/2 magnetic Cr3+ ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional…
The fractionalization of elementary excitations in quantum spin systems is a central theme in current condensed matter physics. The Kitaev honeycomb spin model provides a prominent example of exotic fractionalized quasiparticles, composed of itinerant Majorana fermions and gapped gauge fluxes. However, identification of the Majorana fermions in a three-dimensional honeycomb lattice remains elusive. Here we report spectroscopic signatures of fractional excitations in the harmonic-honeycomb iridates $β$- and $γ$-Li$_2$IrO$_3$. Using polarization resolved Raman spectroscopy, we find that the dyna…
Physics is said to be universal when it emerges regardless of the underlying microscopic details. A prominent example is the Efimov effect, which predicts the emergence of an infinite tower of three-body bound states obeying discrete scale invariance when the particles interact resonantly. Because of its universality and peculiarity, the Efimov effect has been the subject of extensive research in chemical, atomic, nuclear and particle physics for decades. Here we employ an anisotropic Heisenberg model to show that collective excitations in quantum magnets (magnons) also exhibit the Efimov effe…
We analyze the formation of multi-particle bound states in ladders with frustrated kinetic energy in two component bosonic and two component fermionic systems. We focus on the regime of light doping relative to insulating states at half-filling, spin polarization close to 100 percent, and strong repulsive interactions. A special feature of these systems is that the binding energy scales with single particle tunneling $t$ rather than exchange interactions, since effective attraction arises from alleviating kinetic frustration. For two component Fermi systems on a zigzag ladder we find a bound s…
A recent inelastic neutron scattering experiment on $\mathrm{Yb}_2 \mathrm{Ti}_2 \mathrm{O}_7$ uncovers an unusual scattering continuum in the spin excitation spectrum despite the splayed ferromagnetic order in the ground state. While there exist well defined spin wave excitations at high magnetic fields, the one magnon modes and the two magnon continuum start to strongly overlap upon decreasing the field, and eventually they become the scattering continuum at zero field. Motivated by these observations, we investigate the possible emergence of a magnetically ordered ground state with fraction…
Band topology, or global wave-function structure that enforces novel properties in the bulk and on the surface of crystalline materials, is currently under intense investigations for both fundamental interest and its technological promises. While band crossing of non-trivial topological nature was first studied in three dimensions for electrons, the underlying physical idea is not restricted to fermionic excitations. In fact, experiments have confirmed the possibility to have topological band crossing of electromagnetic waves in artificial structures. Fundamental bosonic excitations in real cr…
Resonant inelastic x-ray scattering (RIXS) is a spectroscopic technique which has been widely used to study various elementary excitations in correlated and other condensed matter systems. For strongly correlated materials, besides boosting the overall signal the dependence of the resonant profile on incident photon energy is still not fully understood. Previous endeavors in connecting indirect RIXS, such as Cu K-edge for example where scattering takes place only via the core-hole created as an intermediate state, with the charge dynamical structure factor S(q,ω) neglected complicated dependen…
We revisit Stoner instability, an old problem but in a modern point of view. An idea is to extract out dynamics of directional fluctuations of spins explicitly, resorting to the CP$^{1}$ representation and integrating over their amplitude fluctuations. As a result, we derive an effective field theory for ferromagnetic quantum phase transitions in terms of bosonic spinons and fermionic holons. We show that this effective field theory reproduces overdamped spin dynamics in a paramagnetic Fermi liquid and magnon spectrum in a ferromagnetic Fermi liquid. An interesting observation is that the velo…
We determine the radio-frequency (RF) spectra for non-stationary states of a fermionic condensate produced by a rapid switch of the scattering length. The RF spectrum of the nonequilibrium state with constant BCS order parameter has two features in contrast to equilibrium where there is a single peak. The additional feature reflects the presence of excited pairs in the steady state. In the state characterized by periodically oscillating order parameter RF-absorption spectrum contains two sequences of peaks spaced by the frequency of oscillations. Satellite peaks appear due to a process where a…
We propose an RKKY-type interaction that is mediated by a spin liquid. If a spin liquid ground state exists such an interaction could leave a fingerprint by ordering underlying localized moments such as nuclear spins. This interaction has a unique phenomenology that is distinct from the RKKY interaction found in fermionic systems; most notably the lack of a Fermi surface and absence of the requirement for itinerant electrons, since most spin liquids are insulators. As a working example we investigate the two-dimensional spin-1/2 kagome antiferromagnet (KAFM), although the treatment remains gen…
A lithium dopant in a cuprate spin ladder acts as a vacant (non-magnetic) site accompanied by an extra hole bound by a Coulomb potential. We find that, although the undoped ladder spin gap is not essentially altered by Li doping, a dopant-magnon bound state appears within the gap. Contrary to the case of Zn-doped ladders, we predict that, in the Li-doped ladder, the spin liquid character is very robust against antiferromagnetism. We also predict the spatial dependence of the density of states in the vicinity of the dopant which could be measured by local spectroscopic probes.
In this work, we investigate the possible dramatic effects of Rashba or Dresselhaus spin-orbit coupling (SOC) on fermionic Hubbard model in a 2d square lattice. In the strong coupling limit, it leads to the Rotated Anti-ferromagnetic Heisenberg model which is a new class of quantum spin model. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground ( Y-y ) state subject to strong quantum fluctuations at $T=0$. We evaluate the quantum fluctuations by the spin wave expansion up to order $ 1/S^2 $. In some SOC parameter regime, the Y-y state supports a massive…
Magnetic Raman scattering in two-leg spin ladder materials and the relationship between the anisotropic exchange integrals are analyzed by P. J. Freitas and R. R. P. Singh in Phys. Rev. B, {\bf 62}, 14113 (2000). The angular dependence of the two-magnon scattering is shown to provide information for the magnetic anisotropy in the Sr_14Cu_24O_41 and La_6Ca_8Cu_24O_41 compounds. We point out that the experimental results of polarized Raman measurements at arbitrary angles with respect to the crystal axes have to be corrected for the light ellipticity induced inside the optically anisotropic crys…
Using Raman scattering, the quasi-two dimensional organic superconductor k-(BEDT-TTF)2Cu[N(CN)2]Br (T_c=11.8 K) and the related antiferromagnet k-(BEDT-TTF)2Cu[N(CN)2]Cl are studied. Raman scattering provides unique spectroscopic information about magnetic degrees of freedom that has been otherwise unavailable on such organic conductors. Below T=200 K a broad band at about 500 cm-1 develops in both compounds. We identify this band with two-magnon excitation. The position and the temperature dependence of the spectral weight are similar in the antiferromagnet and in the metallic Fermi-liquid. W…
Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $α$-RuCl$_3$, show magnetic order at low temperatures $T$, here we demonstrate numerically a dynamical crossover from magnon-like behavior at low $T$ and frequencies $ω$ to long-lived fractionalized fermionic quasiparticles at higher $T$ and $ω$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low…
Two-magnon Raman scattering provides important information about electronic correlations in the insulating parent compounds of high-$T_c$ materials. Recent experiments have shown a strong dependence of the Raman signal in $B_{1g}$ geometry on the frequency of the incoming photon. We present an analytical and numerical study of the Raman intensity in the resonant regime. It has been previously argued by one of us (A.Ch) and D. Frenkel that the most relevant contribution to the Raman vertex at resonance is given by the triple resonance diagram. We derive an expression for the Raman intensity in …
Optical properties of single-crystal monoclinic CuO in the range 70 - 6000 \cm were studied at temperatures from 7 to 300 K. Normal reflection spectra were obtained from the (001) and (010) crystal faces thus giving for the first time separate data for the $A_{u}$ and $B_{u}$ phonon modes excited in the purely transverse way (TO modes). Mode parameters, including polarizations of the $B_{u}$ modes not determined by the crystal symmetry, were extracted by the dispersion analysis of reflectivity curves as a function of temperature. Spectra of all the components of the optical conductivity tensor…
Spectroscopic evidences for the spontaneous symmetry breaking at the $SO(5)$ deconfined critical point of $J$-$Q_3$ model
Fudan University（复旦大学）；The University of Hong Kong（香港大学）；Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）；Guizhou Minzu University（贵州民族大学）
Magnetic Excitations of a Half-Filled Tl-based Cuprate
Universität Zürich（苏黎世大学）；The Chinese University of Hong Kong（香港中文大学）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；Chalmers University of Technology（查尔姆斯理工大学）
Analytical Structure and Spectroscopic Signatures of Quartic Nonlinear Electrodynamics in Holographic Fermion Systems
Institute of Geosciences and Exact Sciences, Physics Department, São Paulo State University (UNESP), Rio Claro, São Paulo, Brazil（圣保罗州立大学地球科学与精确科学学院物理系）
