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The surface magnetization of Fe$_3$GeTe$_2$ was examined by low-energy electron microscopy (LEEM) using an off-normal incidence electron beam. We found that the 180$^o$ domain walls are of Bloch type. Temperature-dependent LEEM measurements yield a surface magnetization with a surface critical exponent $\beta$1 = 0.79 +/- 0.02. This result is consistent with surface magnetism in the 3D semi-infinite Heisenberg ($\beta$1 = 0.84 +/- 0.01) or Ising ($\beta$1 = 0.78 +/- 0.02) models, which is distinctly different from the bulk exponent ($\beta$ = 0.34 +/- 0.07). The measurements reveal the power of LEEM with a tilted beam to determine magnetic domain structure in quantum materials. Single crystal diffraction measurements reveal inversion symmetry-breaking weak peaks and yield space group P-6m2. This Fe site defect-derived loss of inversion symmetry enables the formation of skyrmions in this Fe$_3$GeTe$_2$ crystal.

In NiTe$_3$O$_6$ with a chiral crystal structure, we report on a giant natural optical rotation of the lowest-energy magnon. This polarization rotation, as large as 140 deg/mm, corresponds to a path difference between right and left circular polarizations that is comparable to the sample thickness. Natural optical rotation, being a measure of structural chirality, is highly unusual for long-wavelength magnons. The collinear antiferromagnetic order of NiTe$_3$O$_6$ makes this giant effect even more peculiar: Chirality of the crystal structure does not affect the magnetic ground state but is strongly manifested in the lowest excited state. We show that the dynamic magnetoelectric effect, turning this magnon to a magnetic- and electric-dipole active hybrid mode, generates the giant natural optical rotation. In finite magnetic fields, it also leads to a strong optical magnetochiral effect., Comment: 9 pages, 4 figures

Magnetic skyrmions offer promising prospects for constructing future energy-efficient and high-density information technology, leading to extensive explorations of new skyrmionic materials recently. The topological Hall effect has been widely adopted as a distinctive marker of skyrmion emergence. Alternately, here we propose a novel signature of skyrmion state by quantitatively investigating the magnetoresistance (MR) induced by skyrmionic bubbles in CeMn2Ge2. An intriguing finding was revealed: the anomalous MR measured at different temperatures can be normalized into a single curve, regardless of sample thickness. This behavior can be accurately reproduced by the recent chiral spin textures MR model. Further analysis of the MR anomaly allowed us to quantitatively examine the effective magnetic fields of various scattering channels. Remarkably, the analyses, combined with the Lorentz transmission electronic microscopy results, indicate that the in-plane scattering channel with triplet exchange interactions predominantly governs the magnetotransport in the Bloch-type skyrmionic bubble state. Our results not only provide insights into the quantum correction on MR induced by skyrmionic bubble phase, but also present an electrical probing method for studying chiral spin texture formation, evolution and their topological properties, which opens up exciting possibilities for identifying new skyrmionic materials and advancing the methodology for studying chiral spin textures., Comment: 17 pages,5 figures,submitted

We use polarization resolved Raman spectroscopy to demonstrate that for a 3D giant Rashba system the bulk plasmon collective mode can directly couple to the Raman response even in the long wavelength $\mathbf q \rightarrow 0$ limit. Although conventional theory predicts the plasmon spectral weight to be suppressed as the square of its quasi-momentum and thus negligibly weak in the Raman spectra, we observe a sharp in-gap plasmon mode in the Raman spectrum of BiTeI below the Rashba continuum. This coupling, in a polar system with spin-orbit coupling, occurs without assistance from phonons when the incoming photon excitation is resonant with Rashba-split intermediate states. We discuss the distinctive features of BiTeI's giant Rashba system band structure that enable the direct observation of plasmon in Raman scattering., Comment: Editors' Suggestion

We study surface states in the three-dimensional topological insulators Bi$_2$Te$_{3-x}$Se$_{x}$ (x = 0, 2, 3) by polarization resolved resonant Raman spectroscopy. By tracking the spectral intensity of the surface phonon modes with respect to the incident photon energy, we show that the surface phonons are qualitatively similar to their bulk counterparts. Using the resonant Raman excitation profile, we estimated the binding energy of the surface conduction bands relative to bulk conduction bands. In addition, we selectively excite the surface-to-bulk electronic continuum near the Fermi energy in Bi$_2$Se$_3$ to determine the strength of Fano interaction between the most prominent surface phonon and the surface-to-bulk continuum.

MnSb$_{2}$O$_{6}$ is based on the noncentrosymmetric $P321$ space group with magnetic Mn$^{2+}$ ($S={5/2}$, $L\approx 0$) spins ordering below $T_{\mathrm{N}}=12$ K in a helicoidal structure. The ground state magnetic structure, expected to be built and originate from 7 Heisenberg exchange constants, has been shown to be coupled to the underlying crystallographic chirality with polar domain switching being reported. We apply neutron spectroscopy to extract these symmetric exchange constants. Given the high complexity of the magnetic exchange network, crystallographic structure and complications fitting linear spin-wave models, we take advantage of multiplexed neutron instrumentation to use the first moment sum rule of neutron scattering to estimate the 7 exchange constants. We then use these parameters to calculate the low-energy spin-waves in the N\'eel state to reproduce the neutron response without strong antisymmetric coupling. Using Green's response functions, the stability of long-wavelength excitations in the context of proposed magnetic structures is then discussed. The results show the presence of strong exchange constants for the chiral exchange pathways and illustrate an underlying coupling between crystallographic and magnetic ``chirality" through predominantely symmetric exchange.

In order to explore the consequences of spin-orbit coupling on spin-phonon interactions in a set of chemically-similar mixed metal oxides, we measured the infrared vibrational properties of Co$_4B_2$O$_9$ ($B$ = Nb, Ta) as a function of temperature and compared our findings with lattice dynamics calculations and several different models of spin-phonon coupling. Frequency vs. temperature trends for the Co$^{2+}$ shearing mode near 150 cm$^{-1}$ reveal significant shifts across the magnetic ordering temperature that are especially large in relative terms. Bringing these results together and accounting for noncollinearity, we obtain spin-phonon coupling constants of -3.4 and -4.3 cm$^{-1}$ for Co$_4$Nb$_2$O$_9$ and the Ta analog, respectively. Analysis reveals that these coupling constants derive from interlayer (rather than intralayer) exchange interactions and that the interlayer interactions contain competing antiferromagnetic and ferromagnetic contributions. At the same time, beyond-Heisenberg terms are minimized due to fortuitous symmetry considerations, different than most other 4$d$- and 5$d$-containing oxides. Comparison with other contemporary oxides shows that spin-phonon coupling in this family of materials is among the strongest ever reported, suggesting an origin for magnetoelectric coupling.

We find novel polar orders that yield electron (e-) and hole (h+) gas and depend on surface terminations, using density functional theory (DFT) that, unlike existing reports, relaxed all the ion positions of ATiO3 having spontaneous polarization Ps (A: alkali earth metal). By the experiments of atomic-oxygen cleaned surfaces of BaTiO3, we find both e- and h+ gas that are proven to originate from Ps and constrain electrostatic potential, which has been missing. These experiments that remarkably agree with the DFTs of defect free BaTiO3 reveal the properties of Ps-originated e-h+ and, for ferroelectric basics, an e-h+-posed intrinsic constraint on depolarization field arising from Ps in proper time ranges., Comment: Main: 16pages 4 figures Supplement 30 pages 15 figures

MnSb$_{2}$O$_{6}$ is based on the structural chiral $P$321 space group #150 where the magnetic Mn$^{2+}$ moments ($S=5/2$, $L\approx 0$) order antiferromagnetically at $T_\mathrm{N}=12$ K. Unlike the related iron based langasite (Ba$_3$NbFe$_3$Si$_2$O$_{14}$) where the low temperature magnetism is based on a proper helix characterized by a time-even pseudoscalar `magnetic' chirality, the Mn$^{2+}$ ions in MnSb$_{2}$O$_{6}$ order with a cycloidal structure at low temperatures, described instead by a time-even vector `magnetic' polarity. A tilted cycloidal structure has been found [M. Kinoshita et al. Phys. Rev. Lett. 117, 047201 (2016)] to facilitate ferroelectric switching under an applied magnetic field. In this work, we apply polarized and unpolarized neutron diffraction analyzing the magnetic and nuclear structures in MnSb$_{2}$O$_{6}$ with the aim of understanding this magnetoelectric coupling. We find no evidence for a helicoidal magnetic structure with one of the spin envelope axes tilted away from the cycloidal $c$-axis. However, on application of a magnetic field $\parallel$ $\vec{c}$ the spin rotation plane can be tilted, giving rise to a cycloid-helix admixture that evolves towards a distorted helix (zero cycloidal component) for fields great than $\approx$ 2 T. We propose a mechanism for the previously reported ferroelectric switching based on coupled structural and magnetic chiralities requiring only an imbalance of structural chiral domains.

Magnetoelectrics with ultra-low symmetry and spin-orbit coupling are well known to display a number of remarkable properties including nonreciprocal directional dichroism. As a polar and chiral magnet, Ni$_3$TeO$_6$ is predicted to host this effect in three fundamentally different configurations, although only two have been experimentally verified. Inspired by the opportunity to unravel the structure-property relations of such a unique light-matter interaction, we combined magneto-optical spectroscopy and first-principles calculations to reveal nonreciprocity in the toroidal geometry and compared our findings with the chiral configurations. We find that formation of Ni toroidal moments is responsible for the largest effects near 1.1 eV - a tendency that is captured by our microscopic model and computational implementation. At the same time, we demonstrate deterministic control of nonreciprocal directional dichroism in Ni$_3$TeO$_6$ across the entire telecom wavelength range. This discovery will accelerate the development of photonics applications that take advantage of unusual symmetry characteristics., Comment: accepted in npj. Quantum Materials

We combined optical spectroscopy and first principles electronic structure calculations to reveal the charge gap in the polar magnet Fe$_2$Mo$_3$O$_8$. Iron occupation on the octahedral site draws the gap strongly downward compared to the Zn parent compound, and subsequent occupation of the tetrahedral site creates a narrow resonance near the Fermi energy that draws the gap downward even further. This resonance is a many-body effect that emanates from a flat valence band in a Mott-like state due to screening of the local moment - similar to expectations for a Zhang-Rice singlet, except that here, it appears in a semi-conductor. We discuss the unusual hybridization in terms of orbital occupation and character as well as the structure-property relationships that can be unveiled in various metal-substituted systems (Ni, Mn, Co, Zn).

The optical transitions between spin-polarized bands of the quasi-two dimensional Rashba system BiTeI are investigated using polarization resolved resonant Raman spectroscopy. We detect chiral excitations between states with opposite helicity and compare spectra to calculations within a three-band model. Using the resonant Raman excitation profile, we deduce the Rashba parameters and band gaps of the higher conduction bands near the Fermi level, and compare the parameters to values obtained by ab initio density function theory (DFT).

Hafnia (HfO2) is a promising material for emerging chip applications due to its high-k dielectric behaviour, suitability for negative capacitance heterostructures, scalable ferroelectricity, and silicon compatibility. The lattice dynamics along with phononic properties such as thermal conductivity, contraction, and heat capacity are under-explored, primarily due to the absence of high quality single crystals. Herein, we report the vibrational properties of a series of HfO2 crystals stabilized with yttrium (chemical formula HfO2:xY, where x = 20, 12, 11, 8, and 0%) and compare our findings with a symmetry analysis and lattice dynamics calculations. We untangle the effects of Y by testing our calculations against the measured Raman and infrared spectra of the cubic, antipolar orthorhombic, and monoclinic phases and then proceed to reveal the signature modes of polar orthorhombic hafnia. This work provides a spectroscopic fingerprint for several different phases of HfO2 and paves the way for an analysis of mode contributions to high-k dielectric and ferroelectric properties for chip technologies.

Doped IrTe$_2$ is considered a platform for topological superconductivity and therefore receives currently a lot of interest. In addition, the superconductivity in these materials exists in close vicinity of electronic valence bond crystals, which we explore here by means of high-pressure single crystal x-ray diffraction in combination with density functional theory. Our crystallographic refinements provide unprecedented information about the structural evolution as a function of applied pressure up to 42 GPa. Using this structural information for density functional theory calculations, we show that the valence bond formation in IrTe$_2$ is driven by changes in the Ir-Te-Ir bond angle. When a valence bond is formed, this bond angle decreases drastically, leading to a stabilization of local valence bonds large enough to push them out of a broad band continuum. This unusual local mechanism of valence bond formation in an itinerant material provides a natural explanation for the different valence bond orders in IrTe$_2$, implies a very strong electron-phonon coupling and is most likely relevant for the superconductivity as well., Comment: 10 pages, 6 figures

The temperature-dependent phase transitions in Ruddlesden-Popper oxides with perovskite bilayers have been under increased scrutiny in recent years due to the so-called hybrid improper ferroelectricity that some chemical compositions exhibit. However, little is currently understood about the hydrostatic pressure dependence of these phase transitions. Herein we present the results of a high-pressure powder synchrotron X-ray diffraction experiment and $ab~initio$ calculations on the bilayered Ruddlesden-Popper phases Ca$_{3}$Mn$_{2}$O$_{7}$ and Ca$_{3}$Ti$_{2}$O$_{7}$. In both compounds we observe a first-order phase transition between polar $A2_{1}am$ and non-polar $Acaa$ structures. Interestingly, we show that while the application of pressure ultimately favours a non-polar phase -- as is commonly observed for proper ferroelectrics -- regions of response exist where pressure actually acts to increase the polar mode amplitudes. The reason for this can be untangled by considering the varied response of octahedral tilts and rotations to hydrostatic pressure and their trilinear coupling with the polar instability., Comment: 8 pages, 9 figures

The van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$ (CGT) has a two-dimensional crystal structure where each layer is stacked through van der Waals force. We have investigated the nature of the ferromagnetism and the weak perpendicular magnetic anisotropy (PMA) of CGT by means of X-ray absorption spectroscopy and X-ray magnetic circular dichroism (XMCD) studies of CGT single crystals. The XMCD spectra at the Cr $L_{2,3}$ edge for different magnetic field directions were analyzed on the basis of the cluster-model multiplet calculation. The Cr valence is confirmed to be 3+ and the orbital magnetic moment is found to be nearly quenched, as expected for the high-spin $t_{2g}$$^3$ configuration of the Cr$^{3+}$ ion. A large ($\sim 0.2$ eV) trigonal crystal-field splitting of the $t_{2g}$ level caused by the distortion of the CrTe$_6$ octahedron has been revealed, while the single-ion anisotropy (SIA) of the Cr atom is found to have a sign {\it opposite} to the observed PMA and too weak compared to the reported anisotropy energy. The present result suggests that anisotropic exchange coupling between the Cr atoms through the ligand Te $5p$ orbitals having strong spin-orbit coupling has to be invoked to explain the weak PMA of CGT, as in the case of the strong PMA of CrI$_3$., Comment: 17 pages, 5 figures

CaFe$_{2}$O$_{4}$ is an $S=5/2$ antiferromagnet exhibiting two magnetic orders which shows regions of coexistence at some temperatures. Using a Green's function formalism, we model neutron scattering data of the spin wave excitations in this material, ellucidating the microscopic spin Hamiltonian. In doing so, we suggest that the low temperature A phase order $(\uparrow\uparrow\downarrow\downarrow)$ finds its origins in the freezing of antiphase boundaries created by thermal fluctuations in a parent B phase order $(\uparrow\downarrow\uparrow\downarrow)$. The low temperature magnetic order observed in CaFe$_{2}$O$_{4}$ is thus the result of a competition between the exchange coupling along $c$, which favors the B phase, and the single-ion anisotropy which stabilizes thermally-generated antiphase boundaries, leading to static metastable A phase order at low temperatures., Comment: 16 pages, 10 figures

Novel effects induced by nonmagnetic impurities in frustrated magnets and quantum spin liquid represent a highly nontrivial and interesting problem. A theoretical proposal of extended modulated spin structures induced by doping of such magnets, distinct from the well-known skyrmions has attracted significant interest. Here, we demonstrate that nonmagnetic impurities can produce such extended spin structures in h-YMnO3, a triangular antiferromagnet with noncollinear magnetic order. Using inelastic neutron scattering (INS), we measured the full dynamical structure factor in Al-doped h-YMnO3 and confirmed the presence of magnon damping with a clear momentum dependence. Our theoretical calculations can reproduce the key features of the INS data, supporting the formation of the proposed spin textures. As such, our study provides the first experimental confirmation of the impurity-induced spin textures. It offers new insights and understanding of the impurity effects in a broad class of noncollinear magnetic systems., Comment: 18 pages, 4 figures and supplementary Information. Accepted for publication in Nature Communications

We apply neutron spectroscopy to measure the magnetic dynamics in the S=3/2 magnet $\beta$-CaCr$_2$O$_4$ (T$_N$=21 K). The low-energy fluctuations, in the ordered state, resemble large-S linear spin-waves from the incommensurate ground state. However, at higher energy transfers, these semi-classical and harmonic dynamics are replaced by an energy and momentum broadened continuum of excitations. Applying kinematic constraints required for energy and momentum conservation, sum rules of neutron scattering, and comparison against exact diagonalization calculations, we show that the dynamics at high-energy transfers resemble low-S one-dimensional quantum fluctuations. $\beta$-CaCr$_2$O$_4$ represents an example of a magnet at the border between classical N\'eel and quantum phases, displaying dual characteristics.

Terahertz vortex beams with different superposition of the orbital angular momentum $l={\pm}1$, ${\pm}2$, ${\pm}3$, and ${\pm}4$ and spin angular momentum ${\sigma}={\pm}1$ were used to study antiferromagnetic (AFM) resonances in TbFe$_3$(BO$_3$)$_4$ and Ni$_3$TeO$_6$ single crystals. In both materials we observed a strong vortex beam dichroism for the AFM resonances that are split in external magnetic field. The magnitude of the vortex dichroism is comparable to that for conventional circular dichroism due to ${\sigma}$. The selection rules at the AFM resonances are governed by the total angular momentum of the vortex beam: $j={\sigma}+l$. In particular, for $l={\pm}2$, ${\pm}3$, and ${\pm}4$ the sign of $l$ is shown to dominate over that for conventional circular polarization ${\sigma}$., Comment: 12 pages, 4 figures; Supplemental Material: 10 pages, 8 figures; Accepted for publication in Physical Review Letters

Spin density waves, based on modulated local moments, are usually associated with metallic materials, but have recently been reported in insulators which display coupled magnetic and structural order parameters. We discuss one such example, the multiferroic Cu$_3$Nb$_2$O$_8$, which is reported to undergo two magnetic phase transitions, first to a spin density wave phase at $T_N \approx 26.5K$, and then to a helicoidal structure coupled to an electric polarization below $T_2 \approx 24K$ [R. D. Johnson, et al., Phys. Rev. Lett., 107, 137205 (2011)] which breaks the crystallographic inversion symmetry. We apply spherical polarimetry to confirm the low-temperature magnetic structure, yet only observe a single magnetic phase transition to helicoidal order. We argue that the reported spin density wave originates from a decoupling of the components of the magnetic order parameter, as allowed by symmetry and driven by thermal fluctuations. This provides a mechanism for the magnetic, but not nuclear, structure to break inversion symmetry thereby creating an intermediate phase where the structure imitates a spin density wave. As the temperature is reduced, this intermediate structure destabilizes the crystal such that a structural chirality is induced, as reflected by the emergence of the electric polarization, and the imitation spin density wave relaxes into a generic helicoid. This provides a situation where the magnetic structure breaks inversion symmetry while the crystal structure remains centrosymmetric., Comment: 20 pages, 18 figures

We analyze the low-energy dynamics of quasi one dimensional, large-$S$ quantum antiferromagnets with easy-axis anisotropy, using a semi-classical non-linear sigma model. The saddle point approximation leads to a sine Gordon equation which supports soliton solutions. These correspond to the movement of spatially extended domain walls. Long-range magnetic order is a consequence of a weak inter-chain coupling. Below the ordering temperature, the coupling to nearby chains leads to an energy cost associated with the separation of two domain walls. From the kink-antikink two-soliton solution, we compute the effective confinement potential. At distances large compared to the size of the solitons the potential is linear, as expected for point-like domain walls. At small distances the gradual annihilation of the solitons weakens the effective attraction and renders the potential quadratic. From numerically solving the effective one dimensional Schr\"oedinger equation with this non-linear confinement potential we compute the soliton bound state spectrum. We apply the theory to CaFe$_{2}$O$_{4}$, an anisotropic $S=5/2$ magnet based upon antiferromagnetic zig-zag chains. Using inelastic neutron scattering, we are able to resolve seven discrete energy levels for spectra recorded slightly below the N\'eel temperature $T_\textrm{N}\approx 200$~K. These modes are well described by our non-linear confinement model in the regime of large spatially extended solitons., Comment: 11 pages, 7 figures

Ferroic materials are well known to exhibit heterogeneity in the form of domain walls. Understanding the properties of these boundaries is crucial for controlling functionality with external stimuli and for realizing their potential for ultra-low power memory and logic devices as well as novel computing architectures. In this work, we employ synchrotron-based near-field infrared nano-spectroscopy to reveal the vibrational properties of ferroelastic (90$^\circ$ ferroelectric) domain walls in the hybrid improper ferroelectric Ca$_3$Ti$_2$O$_7$. By locally mapping the Ti-O stretching and Ti-O-Ti bending modes, we reveal how structural order parameters rotate across a wall. Thus, we link observed near-field amplitude changes to underlying structural modulations and test ferroelectric switching models against real space measurements of local structure. This initiative opens the door to broadband infrared nano-imaging of heterogeneity in ferroics.

Ba$_{3}$NbFe$_{3}$Si$_{2}$O$_{14}$ (langasite) is structurally and magnetically single domain chiral with the magnetic helicity induced through competing symmetric exchange interactions. Using neutron scattering, we show that the spin-waves in antiferromagnetic langasite display directional anisotropy. On applying a time reversal symmetry breaking magnetic field along the $c$-axis, the spin wave energies differ when the sign is reversed for either the momentum transfer $\pm$ $\vec{Q}$ or applied magnetic field $\pm$ $\mu_{0}$H. When the field is applied within the crystallographic $ab$-plane, the spin wave dispersion is directionally \textit{isotropic} and symmetric in $\pm$ $\mu_{0}$H. However, a directional anisotropy is observed in the spin wave intensity. We discuss this directional anisotropy in the dispersion in langasite in terms of a field induced precession of the dynamic unit cell staggered magnetization. Directional anisotropy, or often referred to as non reciprocal responses, can occur in antiferromagnetic phases in the absence of the Dzyaloshinskii-Moriya interaction or other effects resulting from spin-orbit coupling., Comment: (6 pages, 4 figures, to be published in Phys. Rev. B)

In hybrid improper ferroelectric systems, polarization arises from the onset of successive nonpolar lattice modes. In this work, measurements and modeling were performed to determine the spatial symmetries of the phases involved in the transitions to these modes. Structural and optical measurements reveal that the tilt and rotation distortions of the MnO6 or TiO6 polyhedra relative to the high symmetry phases driving ferroelectricity in the hybrid improper Ca3X2O7 system (X=Mn and Ti) condense at different temperatures. The tilt angle vanishes abruptly at T$_T$ ~ 400 K for Ca3Mn2O7 (and continuously for X=Ti) and the rotation mode amplitude is suppressed at much higher temperatures T$_R$ ~1060 K. Moreover, Raman measurements in Ca3Mn2O7 under isotropic pressure reveal that the polyhedral tilts can be suppressed by very low pressures (between 1.4 and2.3 GPa) indicating their softness. These results indicate that the Ca3Mn2O7 system provides a new platform for strain engineering of ferroelectric properties in film based systems with substrate induced strain., Comment: Eight figures and one table in main text. Twenty-two figures and eleven tables in supplementary document

The protected electron states at the boundaries or on the surfaces of topological insulators (TIs) have been the subject of intense theoretical and experimental investigations. Such states are enforced by very strong spin-orbit interaction in solids composed of heavy elements. Here, we study the composite particles -- chiral excitons -- formed by the Coulomb attraction between electrons and holes residing on the surface of an archetypical three-dimensional topological insulator (TI), Bi$_2$Se$_3$. Photoluminescence (PL) emission arising due to recombination of excitons in conventional semiconductors is usually unpolarized because of scattering by phonons and other degrees of freedom during exciton thermalization. On the contrary, we observe almost perfectly polarization-preserving PL emission from chiral excitons. We demonstrate that the chiral excitons can be optically oriented with circularly polarized light in a broad range of excitation energies, even when the latter deviate from the (apparent) optical band gap by hundreds of meVs, and that the orientation remains preserved even at room temperature. Based on the dependences of the PL spectra on the energy and polarization of incident photons, we propose that chiral excitons are made from massive holes and massless (Dirac) electrons, both with chiral spin textures enforced by strong spin-orbit coupling. A theoretical model based on such proposal describes quantitatively the experimental observations. The optical orientation of composite particles, the chiral excitons, emerges as a general result of strong spin-orbit coupling in a 2D electron system. Our findings can potentially expand applications of TIs in photonics and optoelectronics., Comment: 22 pages, 11 figures

Optical spectroscopy, X-ray diffraction measurements, density functional theory (DFT) and density functional theory + embedded dynamical mean field theory (DFT+eDMFT) have been used to characterize structural and electronic properties of hexagonal $M_2$Mo$_3$O$_8$ ($M$=Fe, Mn) polar magnets. Our experimental data are consistent with the room temperature structure belonging to the space group P6$_3$mc for both compounds. The experimental structural and electronic properties at room temperature are well reproduced within DFT+eDMFT method, thus establishing its predictive power in the paramagnetic phase. With decreasing temperature, both compounds undergo a magnetic phase transition and we argue that this transition is concurrent with a structural phase transition (symmetry change from P6$_3$mc) in the Fe compound and an isostructural transition (no symmetry change from P6$_3$mc) in the Mn compound. In addition, the unusual temperature dependent behavior of electronic d-d transitions in Fe$^{2+}$ ions is discussed.

Inelastic neutron scattering studies in single crystals of TbInO3 and TbIn0.95Mn0.05O3 with nearly-triangular antiferromagnetic lattice are reported. At low energies, a broad and apparently gapless continuum of magnetic excitations, located at the triangular lattice (TL) Brillouin zone boundary, is observed. The data are well described by the uncorrelated nearest-neighbor valence bonds model. At higher energies, a broad excitation branch dispersing from the TL zone boundary is observed. No signs of static magnetic order are found down to the temperatures two orders of magnitude smaller than the effective interaction energy. The fluctuating magnetic moment exceeds two thirds of the Tb3+ free-ion value and is confined to the TL plane. These observations are consistent with a TL-based spin liquid state in TbInO3.

Manipulating magnetic domains is essential for many technological applications. Recent breakthroughs in Antiferromagnetic Spintronics brought up novel concepts for electronic device development. Imaging antiferromagnetic domains is of key importance to this field. Unfortunately, some of the basic domain types, such as antiphase domains, cannot be imaged by conventional techniques. Herein, we present a new domain projection imaging technique based on the localization of domain boundaries by resonant magnetic diffraction of coherent x rays. Contrast arises from reduction of the scattered intensity at the domain boundaries due to destructive interference effects. We demonstrate this approach by imaging antiphase domains in a collinear antiferromagnet Fe2Mo3O8, and observe evidence of domain wall interaction with a structural defect. This technique does not involve any numerical algorithms. It is fast, sensitive, produces large-scale images in a single-exposure measurement, and is applicable to a variety of magnetic domain types.

In order to investigate the electronic properties of the semiconducting van der Waals ferromagnet Cr$_2$Ge$_2$Te$_6$ (CGT), where ferromagnetic layers are bonded through van der Waals forces, we have performed angle-resolved photoemission spectroscopy (ARPES) measurements and density-functional-theory (DFT+U) calculations. The valence-band maximum at the {\Gamma} point is located $\sim$ 0.2 eV below the Fermi level, consistent with the semiconducting property of CGT. Comparison of the experimental density of states with the DFT calculation has suggested that Coulomb interaction between the Cr 3d electrons U$_{\rm eff}$ $\sim$ 1.1 eV. The DFT+U calculation indicates that magnetic coupling between Cr atoms within the layer is ferromagnetic if Coulomb U $_{\rm eff}$ is smaller than 3.0 eV and that the inter-layer coupling is ferromagnetic below U$_{\rm eff}$ $\sim$ 1.0 eV. We therefore conclude that, for U$_{\rm eff}$ deduced by the experiment, the intra-layer Cr-Cr coupling is ferromagnetic and the inter-layer coupling is near the boundary between ferromagnetic and antiferromagnetic, which means experimentally deduced U$_{\rm eff}$ is consistent with theoretical ferromagnetic condition., Comment: 11 pages, 3 figures

We used Raman scattering to study the lattice and magnetic excitations in the hexagonal HoMnO3 single crystals. The E2 phonon mode at 237 cm-1 is affected by the magnetic order. This mode is related to the displacement of Mn and O ions in a-b plane and modulates the Mn-O-Mn bond angles in a-b plane and the in-plane Mn-Mn superexchange interaction. The mode at 269 cm-1 associated to the displacement of the apical Ho3+ ions along the c direction presents an abrupt change of slope at TN showing that the role of the rare earth ions can not be neglected in the magnetic transition. We have identified magnon and crystal field excitations. The temperature dependence of the magnetic excitations has been compared to the Mn and Ho moment and indicates that the exchange interaction pattern between Mn and Ho atoms drives the uniaxial anisotropy gap above the Mn-spin-rotation transition.

Non-collinear two-dimensional triangular lattice antiferromagnets (2D TLAF) are currently an area of very active research due to their unique magnetic properties, which lead to non-trivial quantum effects that experimentally manifest themselves in the spin excitation spectra. Recent examples of such insulating 2D TLAF include (Y,Lu)MnO$_3$, LiCrO$_2$, and CuCrO$_2$. Hexagonal LuFeO3 is a recently synthesized 2D TLAF which exhibits properties of an ideal multiferroic material, partially because of the high spin ($S=5/2$) and strong magnetic super-exchange interactions. We report the full range of spin dynamics in a bulk single crystal of (Lu$_{0.6}$Sc$_{0.4}$)FeO$_3$ (Sc doping to stabilize the hexagonal structure) measured via time-of-flight inelastic neutron scattering. Modeling with linear spin wave theory yields a nearest neighbor exchange coupling of $J$ = 4.0(2) meV (DFT calculations for $h$-LuFeO$_3$ predicted a value of 6.31 meV) and anisotropy values of $K_D$ = 0.17(1) meV (easy plane) and $K_A$~=~-0.05(1)~meV (local easy axis). It is observed that the magnon bandwidth of the spin wave spectra is twice as large for $h$-(Lu,Sc)FeO$_3$ as it is for $h$-LuMnO$_3$., Comment: 7 pages, 4 figures

Raman spectroscopy is employed to probe directly the soft rotation and tilting modes, which are two primary order parameters predicted in the hybrid improper ferroelectric material Ca$_3$Mn$_2$O$_7$. We observe a giant softening of the 107-cm$^{-1}$ octahedron tilting mode by 26~cm$^{-1}$, on heating through the structural transition from a ferroelectric to paraelectric orthorhombic phase. This is contrasted by a small softening of the 150-cm$^{-1}$ rotational mode by 6~cm$^{-1}$. In the intermediate phase, the competing soft modes with different symmetries coexist, bringing about many-faceted anomalies in spin excitations and lattice vibrations. Our work demonstrates that the soft rotation and tilt patterns, relying on a phase-transition path, are a key factor in determining ferroelectric, magnetic, and lattice properties of Ca$_3$Mn$_2$O$_7$., Comment: accepted for publication in PRB

Hexagonal manganites are multiferroic materials with two highly-dissimilar phase transitions: a ferroelectric transition (from P63/mmc to P63cm) at a temperature higher than 1000 K and an antiferromagnetic transition at TN=65 - 130 K. Despite its critical relevance to the intriguing ferroelectric domain physics, the details of the ferroelectric transition are yet not well known to date primarily because of the ultra-high transition temperature. Using high-temperature X-ray diffraction experiments, we show that the ferroelectric transition is a single transition of abrupt order and R-Op displacement is the primary order parameter. This structural transition is then simultaneously accompanied by MnO5 tilting and the subsequent development of electric polarization., Comment: 15 pages, 6 figures

We report a single crystal neutron and x-ray diffraction study of the hybrid improper multiferroic Ca3Mn1.9Ti0.1O7 (CMTO), a prototypical system where the electric polarization arises from the condensation of two lattice distortion modes.With increasing temperature (T ), the out-of-plane, antiphase tilt of MnO6 decreases in amplitude while the in-plane, in-phase rotation remains robust and experiences abrupt changes across the first-order structural transition. Application of hydrostatic pressure (P) to CMTO at room temperature shows a similar effect. The consistent behavior under both T and P reveals the softness of antiphase tilt and highlights the role of the partially occupied d orbital of the transition-metal ions in determining the stability of the octahedral distortion. Polarized neutron analysis indicates the symmetry-allowed canted ferromagnetic moment is less than the 0.04 {\mu}B/Mn site, despite a substantial out-of-plane tilt of the MnO6 octahedra., Comment: 5 figures

CaFe$_{2}$O$_{4}$ is an anisotropic $S={5\over 2}$ antiferromagnet with two competing $A$ ($\uparrow \uparrow \downarrow \downarrow$) and $B$ ($\uparrow \downarrow \uparrow \downarrow$) magnetic order parameters separated by static antiphase boundaries at low temperatures. Neutron diffraction and bulk susceptibility measurements, show that the spins near these boundaries are weakly correlated and a carry an uncompensated ferromagnetic moment that can be tuned with a magnetic field. Spectroscopic measurements find these spins are bound with excitation energies less than the bulk magnetic spin-waves and resemble the spectra from isolated spin-clusters. Localized bound orphaned spins separate the two competing magnetic order parameters in CaFe$_{2}$O$_{4}$., Comment: (main text - 5 pages, 4 figures; supplementary information - 4 pages, 6 figures, to be published in Physical Review Letters). arXiv admin note: text overlap with arXiv:1606.04243

Hybrid improper ferroelectricity (HIF) denotes a new class of polar instability by the mixture of two octahedral-distortion modes and can feature the coexistence of abundant head-to-head and tail-to-tail polar domains, of which the domain walls tend to be charged due to the respective screening charges with an opposite sign. However, no such coexisting carriers are available in the materials. Using group-theoretical, microscopic, and spectroscopic analyses, we established the existence of hidden antipolar order parameter in model HIF (Ca,Sr)3Ti2O7 by the condensation of a weak, previously unnoticed antipolar lattice instability, turning the order-parameter spaces to be multicomponent with the distinct polar-antipolar intertwining and accompanied formation of Neel-type twin-like antipolar domain walls (few nm) between the head-to-head and tail-to-tail domains. The finite-width Neel walls and correlated domain topology inherently lift the polar divergences between the domains, casting an emergent exemplification of charged domain-wall screening by an antipolar ingredient. Comparisons to topological defects in improper-ferroelectrics hexagonal manganites were discussed.

We report the magnetic excitation spectrum as measured by inelastic neutron scattering for a polycrystalline sample of Sr$_3$CuPtO$_6$. Modeling the data by the 2+4 spinon contributions to the dynamical susceptibility within the chains, and with interchain coupling treated in the random phase approximation, accounts for the major features of the powder-averaged structure factor. The magnetic excitations broaden considerably as temperature is raised, persisting up to above 100 K and displaying a broad transition as previously seen in the susceptibility data. No spin gap is observed in the dispersive spin excitations at low momentum transfer, which is consistent with the gapless spinon continuum expected from the coordinate Bethe ansatz. However, the temperature dependence of the excitation spectrum gives evidence of some very weak interchain coupling., Comment: 9 pages, 5 figures

Using polarization-resolved resonant Raman spectroscopy, we explore collective spin excitations of the chiral surface states in a three dimensional topological insulator, Bi$_2$Se$_3$. We observe a sharp peak at 150 meV in the pseudovector $A_2$ symmetry channel of the Raman spectra. By comparing the data with calculations, we identify this peak as the transverse collective spin mode of surface Dirac fermions. This mode, unlike a Dirac plasmon or a surface plasmon in the charge sector of excitations, is analogous to a spin wave in a partially polarized Fermi liquid, with spin-orbit coupling playing the role of an effective magnetic field., Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev. Lett

The symmetric splitting of two spin-wave branches in an antiferromagnetic resonance (AFR) experiment has been an essential measurement of antiferromagnets for over half a century. In this work, circularly polarized time-domain THz spectroscopy experiments performed on the low symmetry multiferroic h-HoMnO$_3$ reveal an AFR of the Mn sublattice to split asymmetrically in applied magnetic field, with an $\approx$ 50\% difference in $g$-factors between the high and low energy branches of this excitation. The temperature dependence of the $g$-factors, including a drastic renormalization at the Ho spin ordering temperature, reveals this asymmetry to unambiguously stem from Ho-Mn interactions. Theoretical calculations demonstrate the AFR asymmetry is not explained by conventional Ho-Mn exchange mechanisms alone and are only reproduced if quartic spin interactions are also included in the spin Hamiltonian. Our results provide a paradigm for the optical study of such novel interactions in hexagonal manganites and low symmetry antiferromagnets in general.

Electric and magnetic properties of multiferroic GdMn2O5 in external magnetic fields were investigated to map out the magnetoelectric phases in this material. Due to strong magnetoelectric coupling, the dielectric permittivity is highly sensitive to phase boundaries in GdMn2O5, which allowed to construct the field-temperature phase diagrams. Several phase transitions are observed which are strongly field-dependent with respect to field orientation and strength. The phase diagram for a magnetic field along the crystallographic a-axis corresponds well to a polarization step, as induced by 90 degree rotation of Gd magnetic moments. Our results support the model of two ferroelectric sublattices, Mn-Mn and Gd-Mn with strong R-Mn (4f-3d) interaction for the polarization in RMn2O5.

CuAl2O4 is a normal spinel oxide having quantum spin, S=1/2 for Cu2+. It is a rather unique feature that the Cu2+ ions of CuAl2O4 sit at a tetrahedral position, not like the usual octahedral position for many oxides. At low temperatures, it exhibits all the thermodynamic evidence of a quantum spin glass. For example, the polycrystalline CuAl2O4 shows a cusp centered at ~2 K in the low-field dc magnetization data and a clear frequency dependence in the ac magnetic susceptibility while it displays logarithmic relaxation behavior in a time dependence of the magnetization. At the same time, there is a peak at ~2.3 K in the heat capacity, which shifts towards higher temperature with magnetic fields. On the other hand, there is no evidence of new superlattice peaks in the high-resolution neutron powder diffraction data when cooled from 40 to 0.4 K. This implies that there is no long-ranged magnetic order down to 0.4 K, thus confirming a spin glass-like ground state for CuAl2O4. Interestingly, there is no sign of structural distortion either although Cu2+ is a Jahn-Teller active ion. Thus, we claim that an orbital liquid state is the most likely ground state in CuAl2O4. Of further interest, it also exhibits a large frustration parameter, f = Theta_CW/Tm ~67, one of the largest values reported for spinel oxides. Our observations suggest that CuAl2O4 should be a rare example of a frustrated quantum spin glass with a good candidate for an orbital liquid state., Comment: J. Phys. Condens Matter (accepted): 20 pages, 4 figures, 1 Table

We present polarization resolved Raman scattering study of surface vibration modes in the topological insulator Bi$_2$Se$_3$ single crystal and thick films. Besides the four Raman active bulk phonons, we observed four additional modes with much weaker intensity and slightly lower energy than the bulk counterparts. Using symmetry analysis, we assigned these additional modes to out-of-plane surface phonons. Comparing with first principle calculations, we conclude that the appearance of these modes is due to $c$-axis lattice distortion and van der Waals gap expansion near the crystal surface. Two of the surface modes at 60 and 173 cm$^{-1}$ are associated with Raman active $A_{1g}$ bulk phonon modes, the other two at 136 and 158 cm$^{-1}$ are associated with infrared active bulk phonons with $A_{2u}$ symmetry. The latter become Raman allowed due to reduction of crystalline symmetry from $D_{3d}$ in the bulk to $C_{3v}$ on the crystal surface. In particular, the 158 cm$^{-1}$ surface phonon mode shows a Fano lineshape under resonant excitation, suggesting interference in the presence of electron-phonon coupling of the surface excitations., Comment: 11 pages, 5 figures and 3 tables

When magnons and phonons, the fundamental quasiparticles of the solid, are coupled to one another, they form a new hybrid quasi-particle, leading to novel phenomena and interesting applications. Despite its wide-ranging importance, however, detailed experimental studies on the underlying Hamiltonian is rare for actual materials. Moreover, the anharmonicity of such magnetoelastic excitations remains largely unexplored although it is essential for a proper understanding of their diverse thermodynamic behaviour as well as intrinsic zero-temperature decay. Here we show that in noncollinear antiferromagnets, a strong magnon-phonon coupling can significantly enhance the anharmonicity, resulting in the creation of magnetoelastic excitations and their spontaneous decay. By measuring the spin waves over the full Brillouin zone and carrying out anharmonic spin wave calculations using a Hamiltonian with an explicit magnon-phonon coupling, we have identified a hybrid magnetoelastic mode in (Y,Lu)MnO3 and quantified its decay rate and the exchange-striction coupling term required to produce it. Our work has wide implications for understanding of the spin-phonon coupling and the resulting excitations of the broad classes of noncollinear magnets.

We investigate spin dynamics in the antiferromagnetic (AFM) multiferroic TbMnO3 using optical- pump, terahertz (THz)-probe spectroscopy. Photoexcitation results in a broadband THz transmission change, with an onset time of 25 ps at 6 K that becomes faster at higher temperatures. We attribute this time constant to spin-lattice thermalization. The excellent agreement between our measurements and previous ultrafast resonant x-ray diffraction measurements on the same material confirms that our THz pulse directly probes spin order. We suggest that this could be the case in general for insulating AFM materials, if the origin of the static absorption in the THz spectral range is magnetic.

Combining high resolution scanning tunneling microscopy and first principle calculations, we identified the major native defects, in particular the Se vacancies and Se interstitial defects that are responsible for the bulk conduction and nanoscale potential fluctuation in single crystals of archetypal topological insulator Bi2Se3. Here it is established that the defect concentrations in Bi2Se3 are far above the thermodynamic limit, and that the growth kinetics dominate the observed defect concentrations. Furthermore, through careful control of the synthesis, our tunneling spectroscopy suggests that our best samples are approaching the intrinsic limit with the Fermi level inside the band gap without introducing extrinsic dopants., Comment: 9 pages, 4 figures

CaFe$_{2}$O$_{4}$ is a $S={5\over 2}$ anisotropic antiferromagnet based upon zig-zag chains having two competing magnetic structures, denoted as the A ($\uparrow \uparrow \downarrow \downarrow$) and B ($\uparrow \downarrow \uparrow \downarrow$) phases, which differ by the $c$-axis stacking of ferromagnetic stripes. We apply neutron scattering to demonstrate that the competing A and B phase order parameters results in magnetic antiphase boundaries along $c$ which freeze on the timescale of $\sim$ 1 ns at the onset of magnetic order at 200 K. Using high resolution neutron spectroscopy, we find quantized spin wave levels and measure 9 such excitations localized in regions $\sim$ 1-2 $c$-axis lattice constants in size. We discuss these in the context of solitary magnons predicted to exist in anisotropic systems. The magnetic anisotropy affords both competing A+B orders as well as localization of spin excitations in a classical magnet., Comment: (main text - 5 pages, 4 figures; supplementary information - 2 pages, 1 figure, to be published in Physical Review Letters)