We elaborate the first theoretical realization of two dimensional itinerant topological magnons, based on the quarter filled Haldane-Hubbard model with a nearly-flat electron band. By using the exact diagonalization method with a projection onto this band, we obtain the spin wave excitations over the itinerant ferromagnetic ground state. In the flatband limit, the excitation exhibits similar dispersion to the free electron band with Dirac magnons. The nonflatness of the electron band opens a topological gap at Dirac points and leads to an acoustic magnon band with a nonzero Chern number. We further show that tuning the sublattice Hubbard interactions or the next-nearest-neighbor hopping can induce a topological transition characterized by the gap closing and reopening, and the existence of the in-gap magnons on magnetic domain walls. We find an exact set of bases for magnons in the flatband limit constructed from sublattice particle-hole vectors and derive an effective model to explore the origin of the topological magnon which is attributed to the ``mass inversion mechanism''.
Different from previous scenarios that topological magnons emerge in local spin models, we propose an alternative that itinerant electron magnets can host topological magnons. A one-dimensional Tasaki model with a flat band is considered as the prototype. This model can be viewed as a quarter filled periodic Anderson model with impurities located in between and hybridizing with the nearest-neighbor conducting electrons, together with a Hubbard repulsion for these electrons. By increasing the Hubbard interaction, the gap between the acoustic and optical magnons closes and reopens while the Berr…
SrRuO3 (SRO) is an itinerant ferromagnet with strong coupling between the charge, spin, and lattice degrees of freedom. This strong coupling suggests that the electronic and magnetic behaviors of SRO are highly susceptible to changes in the lattice distortion. Here we show how the spin interaction and resultant magnon formation change with the modification in the crystallographic orientation. We fabricated SRO epitaxial thin films with (100), (110), and (111) surface orientations, to systematically modulate the spin interaction and spin dimensionality. The reduced spin dimensionality and enhan…
Low-lying magnon dispersion in a S=1 Heisenberg antiferromagnetic (AF) chain is analyzed using the non-Abelian DMRG method. The scattering length $a_{\rm b}$ of the boundary coupling and the inter-magnon scattering length $a$ are determined. The scattering length $a_{\rm b}$ is found to exhibit a characteristic diverging behavior at the crossover point. In contrast, the Haldane gap $Δ$, the magnon velocity $v$, and $a$ remain constant at the crossover. Our method allowed estimation of the gap of the S=2 AF chain to be $Δ= 0.0891623(9)$ using a chain length longer than the correlation length $ξ…
The antiferromagnetic spin-one chain is considerably one of the most fundamental quantum many-body systems, with symmetry protected topological order in the ground state. Here, we present results for its dynamical spin structure factor at finite temperatures, based on a combination of exact numerical diagonalization, matrix-product-state calculations and quantum Monte Carlo simulations. Open finite chains exhibit a sub-gap band in the thermal spectral functions, indicative of localized edge-states. Moreover, we observe the thermal activation of a distinct low-energy continuum contribution to t…
We consider spin-1 Haldane chains with single-ion anisotropy, which exists in known Haldane chain materials. We develop a perturbation theory in terms of anisotropy, where magnon-magnon interaction is important even in the low temperature limit. The exact two-particle form factor in the O(3) nonlinear sigma model leads to quantitative predictions on several dynamical properties including dynamical structure factor and electron spin resonance frequency shift. These agree very well with numerical results, and with experimental data on the Haldane chain material Ni(C$_5$H$_{14}$N$_2$)$_2$N$_3$(PF…
We discuss electron spin resonance (ESR) shifts in spin-1 Heisenberg antiferromagnetic chains with a weak single-ion anisotropy based on several effective field theories, the O(3) nonlinear sigma model (NLSM) in the Haldane phase, free fermion theories around the lower and the upper critical fields. In the O(3) NLSM, the single-ion anisotropy corresponds to a composite operator which creates two magnons at the same time and position. Therefore, even inside a parameter range where free magnon approximation is valid, we have to take interactions among magnons into account. Though the O(3) NLSM i…
There was a slight error in calculating the nonlinear sigma-model prediction for the 2-magnon scattering continuum shown in Fig. 2 of cond-mat/0010049, and Phys. Rev. Lett. {\bf 87}, 017202 (2001). Present erratum explains what was incorrect, and shows a corrected version of the figure. The correction is minor and does not affect main conclusions drawn in the original paper.
We present a family of spin ladder models which admit exact solution for the ground state and exhibit non-Haldane spin liquid properties as predicted recently by Nersesyan and Tsvelik [Phys. Rev. Lett. v.78, 3939 (1997)], and study their excitation spectrum using a simple variational ansatz. The elementary excitation is neither a magnon nor a spinon, but a pair of propagating triplet or singlet solitons connecting two spontaneously dimerized ground states. Second-order phase transitions separate this phase from the Haldane phase and the rung-dimer phase.
We consider quasi one dimensional spin-1 Heisenberg chains with crystal field anisotropy in a uniform magnetic field. We determine the dynamical structure factor in various limits and obtain a fairly complete qualitative picture of how it changes with the applied field. In particular, we discuss how the width of the higher energy single magnon modes depends on the field. We consider the effects of a weak interchain coupling. We discuss the relevance of our results for recent neutron scattering experiments on the quasi-1D Haldane-gap compound NDMAP.
The spin wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin-waves to be a nonanalytic function of the magnetization m. For low frequencies Ω, small wavevectors k, and small m, the dispersion relation is found to be of the form Ω~ m^{1-α} k^2, with α= (4-d)/2 (2<d<4) for disordered systems, and α= (3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3 (clean), Ω~ m ln(1/m) k^2. Experiments to test these predictions are proposed.
Controlling spin wave excitations in magnetic materials underpins the burgeoning field of magnonics. Yet, little is known about how magnons interact with the conduction electrons of itinerant magnets, or how this interplay can be controlled. Via a surface-sensitive spectroscopic approach, we demonstrate a strong and highly-tuneable electron-magnon coupling at the Pd-terminated surface of the delafossite oxide PdCoO$_2$, where a polar surface charge mediates a Stoner transition to itinerant surface ferromagnetism. We show how the coupling can be enhanced 7-fold with increasing surface disorder,…
Quantum confinement leads to the emergence of several magnon modes in ultrathin layered magnetic structures. We probe the lifetime of these quantum confined modes in a model system composed of three atomic layers of Co grown on different surfaces. We demonstrate that the quantum confined magnons exhibit nonlinear decay rates, which strongly depend on the mode number, in sharp contrast to what is assumed in the classical dynamics. Combining the experimental results with those of linear-response density functional calculations we provide a quantitative explanation for this nonlinear damping effe…
We present first principles calculations of the dynamic susceptibility in strained and doped ferromagnetic MnBi using time-dependent density functional theory. In spite of being a metal, MnBi exhibits signatures of strong correlation and a proper description in the framework of density functional theory requires Hubbard corrections to the Mn $d$-orbitals. To permit calculations of the dynamic susceptibility with Hubbard corrections applied to the ground state electronic structure, we use a consistent rescaling of the exchange-correlation kernel maintaining the delicate balance between the magn…
We study the photoinduced magnetic transition in an itinerant magnet described by the double-exchange model, in which conduction electrons couple with localized spins through the ferromagnetic (FM) Hund coupling. It is shown that intense light applied to the FM ground state induces an antiferromagnetic (AFM) order, in contrast to the AFM-to-FM transition due to the photocarrier injection. In particular, we focus on the mechanism for instability of the FM structure by the light irradiation. The magnon spectrum in the Floquet state is formulated on the basis of the pertrubative expansion of the …
Fe3GeTe2 is a 2-dimensional van der Waals material exhibiting itinerant ferromagnetism upto 230 K. Here, we study aspects of scattering mechanism in Fe3Ge2Te2 single crystals via resistivity, magneto-transport and Hall effect measurements. The quadratic temperature dependence of electrical resistivity below the Curie temperature hints towards the dominance of electron-magnon scattering. A non-saturating positive magnetoresistance (MR) is observed at low temperatures when the magnetic field is applied parallel to the sample plane. The linear negative MR at high fields for T < TC corroborates to…
We theoretically study a spin Hamiltonian for spin-orbit-coupled ferromagnets on the honeycomb lattice. We find that the effective Hamiltonian for magnons, a quanta of spin-wave excitations from ordered states, is equivalent to the Haldane model for electrons in the honeycomb lattice, which indicates the nontrivial topology of the magnon bands and the existence of the associated edge state. We also take the Schwinger boson (or bosonic spinon) representations of spins that are applicable both to ordered and disordered phases. We show that the spinon bands within the mean-field treatment are top…
We introduce a novel approach for the investigation of spin-wave excitations in itinerant ferromagnets. Our theory is based on a variational treatment of general multi-band Hubbard models which describe elements and compounds of transition metals. The magnon dispersion is derived approximately as the energy of a variational spin-wave state in the limit of large spatial dimensions. A numerical evaluation of our results is feasible for general multi-band models. As a first application we consider a model with two degenerate orbitals per lattice site. From our results we can conclude that spin-wa…
We analyze the resonant x-ray scattering (RIXS) spectra from Sr$_2$IrO$_4$ in an itinerant electron approach. Employing a multi-orbital tight-binding model on the square lattice, we calculate the one-electron energy band within the Hartree-Fock approximation, which leads to an antiferromagnetic ground state. We then evaluate the two-particle Green's functions for the particle-hole pair excitations within the random phase approximation, which are connected to the RIXS spectra within the fast collision approximation. The calculated RIXS spectra exhibit two-peak structure with slightly different …
Inelastic neutron scattering experiments on the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C9D24N4)(NO2)ClO4 have been performed under magnetic fields below and above a critical field Hc at which the energy gap closes. Normal field dependece of Zeeman splitting of the excited triplet modes below Hc has been observed, but the highest mode is unusually small and smears out with increasing field. This can be explained by an interaction with a low-lying two magnon continuum at q=pi that is present in dimerized chains but absent in uniform ones. Above Hc, we find only one excited…
We study the dynamical magnetic susceptibility of a strongly correlated electronic system in the presence of a time-dependent hopping field, deriving a generalized Bethe-Salpeter equation which is valid also out of equilibrium. Focusing on the single-orbital Hubbard model within the time-dependent Hartree-Fock approximation, we solve the equation in the non-equilibrium adiabatic regime, obtaining a closed expression for the transverse magnetic susceptibility. From this, we provide a rigorous definition of non-equilibrium (time-dependent) magnon frequencies and exchange parameters, expressed in…
Magnon-Mediated Superconductivity in a 2D Itinerant Ferromagnet with Weak Easy-plane Magnetic Anisotropy
School of Physics and Astronomy and William I. Fine Theoretical Physics Institute, University of Minnesota（明尼苏达大学物理与天文学学院及威廉·I·法因理论物理研究所）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；Department of Physics, Princeton University（普林斯顿大学物理系）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯科，巴斯克科学基金会）
Different realizations of the Hubbard operators in different Hilbert spaces give rise to various microscopic lattice electron models driven by strong correlations. In terms of the Gutzwiller projected operators, the most familiar examples are the t-J and the BCS-Hubbard models at strong coupling. We focus on the spin-dopon representation of the Hubbard operators. In this case the no double occupancy constraint (NDO) can be reexpressed as a Kondo interaction. As an explicit example, the effective low energy action is derived in terms of itinerant spineless fermions (dopons) strongly interacting…
In this work, we study the topological properties and magnon Hall effect of a three-dimensional ferromagnet in the ABC stacking honeycomb lattice, motivated by the recent inelastic neutron scattering study of CrI$_3$. We show that the magnon band structure and Chern numbers of the magnon branches are significantly affected by the interlayer coupling $J_c$, which moreover has a qualitatively different effect in the ABC stacking compared to the AA stacking adopted by other authors. The nontrivial Chern number of the lowest magnon band is stabilized by the next-nearest-neighbour Dzyaloshinsky-Mor…
One-band Hubbard model with hopping parameter $t$ and Coulomb repulsion $U$ is considered at half filling. By means of the Schwinger bosons and slave Fermions representation of the electron operators and integrating out the spin-singlet Fermi fields an effective Heisenberg model with antiferromagnetic exchange constant is obtained for vectors which identifies the local orientation of the spin of the itinerant electrons. The amplitude of the spin vectors is an effective spin of the itinerant electrons accounting for the fact that some sites, in the ground state, are doubly occupied or empty. Ac…
It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon-magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion …
Some well-established examples of itinerant-electron ferromagnetism in one dimension occur in a Mott-insulating phase. We examine the consequences of doping a ferromagnetic insulator and cou- pling magnons to gapless charge fluctuations. Using a bosonization scheme for strongly interacting electrons, we derive an effective field theory for the magnon-holon interaction. When the magnon momentum matches the Fermi momentum of the holons, the backscattering of the magnon at low energies gives rise to a Kondo effect of a pseudospin defined from the chirality degree of freedom (right- or left-moving…
Magnon Damping as a Probe of Kondo Coupling in Magnetically Ordered Systems
National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University（南京大学固体微结构物理国家重点实验室和物理系）；Collaborative Innovation Center of Advanced Microstructures and Jiangsu Physical Science Research Center, Nanjing University（南京大学先进微结构协同创新中心与江苏省物理科学研究中心组）；School of Physics, Beihang University（北京航空航天大学物理学院）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；Center of Materials Science and Optoelectronics Engineering, College of Materials Science and Opto-electronic Technology, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术学院材料科学与工程研究中心）；National Synchrotron Radiation Research Center（台湾国家同步辐射研究中心）；Institute of High Energy Physics, Chinese Academy of Sciences (CAS)（中国科学院高能物理研究所）；Spallation Neutron Source Science Center（东莞散裂中子源科学中心）
The kagome lattice is a fertile platform to explore topological excitations with both Fermi-Dirac and Bose-Einstein statistics. While relativistic Dirac Fermions and flat-bands have been discovered in the electronic structure of kagome metals, the spin excitations have received less attention. Here we report inelastic neutron scattering studies of the prototypical kagome magnetic metal FeSn. The spectra display well-defined spin waves extending up to 120 meV. Above this energy, the spin waves become progressively broadened, reflecting interactions with the Stoner continuum. Using linear spin w…
Quite a few low-dimensional magnets are quantum-disordered ``spin liquids'' with a characteristic gap in the magnetic excitation spectrum. Among these are antiferromagnetic chains of integer quantum spins. Their generic feature are long-lived massive (gapped) excitations (magnons) that are subject to Zeeman splitting in external magnetic fields. The gap in one of the magnon branches decreases with field, driving a soft-mode quantum phase transition. The system then enters a qualitatively new high-field phase. The actual properties at high fields, particularly the spin dynamics, critically depe…
We study the electronic structure of the Pd-terminated surface of the non-magnetic delafossite oxide metal PdCoO$_2$. Combining angle-resolved photoemission spectroscopy and density-functional theory, we show how an electronic reconstruction driven by surface polarity mediates a Stoner-like magnetic instability towards itinerant surface ferromagnetism. Our results reveal how this leads to a rich multi-band surface electronic structure, and provide spectroscopic evidence for an intriguing sample-dependent coupling of the surface electrons to a bosonic mode which we attribute to electron-magnon …
This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-$1/2$ quantum XY model with a next-nearest-neighbour Dzyaloshinsky-Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, thermal and spin Nernst conductivities. Due to the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological pr…
Driving a two-dimensional Mott insulator with circularly polarized light breaks time-reversal and inversion symmetry, which induces an optically-tunable synthetic scalar spin chirality interaction in the effective low-energy spin Hamiltonian. Here, we show that this mechanism can stabilize topological magnon excitations in honeycomb ferromagnets and in optical lattices. We find that the irradiated quantum magnet is described by a Haldane model for magnons that hosts topologically-protected edge modes. We study the evolution of the magnon spectrum in the Floquet regime and via time propagation …
Raman selection rules for electronic and magnetic excitations in BaFe2As2 were theoretically investigated and applied them to the separate detection of the nodal and anti-nodal gap excitations at the spin density wave (SDW) transition and the separate detection of the nearest and the next nearest neighbor exchange interaction energies. The SDW gap has Dirac nodes, because many orbitals participate in the electronic states near the Fermi energy. Using a two-orbital band model the electronic excitations near the Dirac node and the anti-node are found to have different symmetries. Applying the sy…
$\mathbb{Z}_2$ Vortex Crystals in Tetrahedral Antiferromagnets: Fractional Charges and Topological Magnons
Aoyama Gakuin University（青山学院大学）；University of Münster（明斯特大学）；Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学）；University of Duisburg-Essen（杜伊斯堡-埃森大学）
Using the exact results of the O(3) nonlinear sigma model (NLSM) and a few quantitative numerical data for integer-spin antiferromagnetic (AF) chains, we systematically estimate all magnon excitation energies of N-leg integer-spin AF ladders and tubes in the weak-interchain-coupling regime. Our method is based on a first-order perturbation theory for the strength of the interchain coupling. It can deal with any kind of interchain interactions, in principle. We confirm that results of the perturbation theory are in good agreement with those of a quantum Monte Carlo simulation and with our recen…
An effective theory for the hole doped spin-1 antiferromagnetic chain is proposed in this paper. The two branches of low energy quasipaticle excitation is obtained by the diagrammic technique. In the large t limit(in which t is the hole hopping term), the lower band is essentially the bound state of one hole and one magnon and the other band is the sigle hole state. We find a critical value of t, $t_c=0.21Δ_H$(in which $Δ_H$ is the Haldane gap).For $t>t_c$, with the decrement of t, the mixing of these two bands become stronger and stronger, and at the same time the effective band mass becomes …
Within a minimal model for the iron-based superconductors in which itinerant electrons interact with a band of local moments, we derive a a general conclusion for multi-band superconductivity. In a multi-band superconductor, due to the Adler theorem, the inter-band scattering dominates the intra-band scattering at the long wave length limit as long as both interactions are induced by Goldstone boson (which is magnon in our case) and the transfered momentum is nonzero. Such kind of interaction leads to a well-known sigh-reversing superconductivity even if the inter-band and intra-band interacti…
One-band Hubbard model with transverse anisotropy is considered at density of electrons $n=0.4$. It is shown that when the anisotropy is appropriately chosen, the ground state is ferromagnetic with magnetic order perpendicular to the anisotropy. The increasing of the ratio $\frac tU$, where $t$ is the hopping parameter and $U$ is the Coulomb repulsion, decreases the Curie temperature, and the system arrives at the quantum critical point $(T_C=0)$. The result is obtained introducing Schwinger bosons and slave Fermions representation of the electron operators. Integrating out the spin-singlet Fe…
Topological Kondo insulators are strongly correlated materials, where itinerant electrons hybridize with localized spins giving rise to a topologically non-trivial band structure. Here we use non-perturbative bosonization and renormalization group techniques to study theoretically a one-dimensional topological Kondo insulator. It is described as a Kondo-Heisenberg model where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel - a strongly correlated version of the prototypical Tamm-Shockley model. We derive and solve renormali…
Symmetric Mode Ansatz: Theory of Magnon Collective Modes in Chern Insulators
Princeton Center for Theoretical Science, Princeton University（普林斯顿大学理论科学中心）；Department of Physics, Princeton University（普林斯顿大学物理系）；Institut für Theoretische Physik und Astrophysik and Würzburg-Dresden Cluster of Excellence ctd.qmat, Julius-Maximilians-Universität Würzburg（维尔茨堡大学理论与天体物理研究所及维尔茨堡-德累斯顿卓越集群ctd.qmat）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊卡巴斯科，巴斯克科学基金会）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究院计算量子物理中心）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎第七大学，索邦巴黎城）
