Search

In a PN junction, the separation between positive and negative charges leads to diode transport. In the past few years, the intrinsic diode transport in noncentrosymmetric polar conductors has attracted great interest, because it suggests novel nonlinear applications and provides a symmetry-sensitive probe of Fermi surface. Recently, such studies have been extended to noncentrosymmetric superconductors, realizing the superconducting diode effect. Here, we show that, even in a centrosymmetric crystal without directional charge separation, the spins of an antiferromagnet (AFM) can generate a spatial directionality, leading to an AFM diode effect. We observe large second-harmonic transport in a nonlinear electronic device enabled by the compensated AFM state of even-layered MnBi2Te4. We also report a novel electrical sum-frequency generation (SFG), which has been rarely explored in contrast to the well-known optical SFG in wide-gap insulators. We demonstrate that the AFM enables an in-plane field-effect transistor and harvesting of wireless electromagnetic energy. The electrical SFG establishes a powerful method to study nonlinear electronics built by quantum materials. The AFM diode effect paves the way for potential device concepts including AFM logic circuits, self-powered AFM spintronics, and other applications that potentially bridge nonlinear electronics with AFM spintronics., Comment: 33+8 pages, 14+2 figures

Magnetic topological insulators provide a platform for emergent phenomena arising from the interplay between magnetism and band topology. Here we report the single crystal growth, crystal structure, magnetic and transport properties, as well as the neutron scattering studies of topological insulator series (Ge$_{1-\delta-x}$Mn$_x$)$_2$Bi$_2$Te$_5$ ($x\leq 0.47$, $0.11 \leq \delta \leq 0.20$). Upon doping up to $x = 0.47$, the lattice parameter $c$ decreases by 0.8\%, while the lattice parameter $a$ remains nearly unchanged. Significant Ge vacancies and Ge/Bi site mixing are revealed via elemental analysis as well as refinements of the neutron and X-ray diffraction data, resulting in holes dominating the charge transport. At $x = 0.47$, below 10.8 K, a bilayer A-type antiferromagnetic ordered state emerges, featuring an ordered moment of 3.0(3) $\mu_{B}$/Mn at 5 K, with the $c$ axis as the easy axis. Magnetization data unveil a much stronger interlayer antiferromagnetic exchange interaction and a much smaller uniaxial anisotropy compared to MnBi$_{2}$Te$_{4}$. We attribute the former to the shorter superexchange path and the latter to the smaller ligand-field splitting in (Ge$_{1-\delta-x}$Mn$_x$)$_2$Bi$_2$Te$_5$. Our study demonstrates that this series of materials holds promise for the investigation of the Layer Hall effect and quantum metric nonlinear Hall effect., Comment: 9 pages, 5 figures

Compared to time-reversal symmetry-protected Z2 topological insulators and Dirac/Weyl semimetals, there are significantly fewer candidates for topological crystalline insulators. SrAg4Sb2 is predicted to exhibit topological crystalline insulator behavior when considering spin-orbit coupling. In this study, we systematically investigate single crystals of SrAg4Sb2 using electrical transport and magnetic torque measurements, along with first-principles calculations. Our transport data reveals its compensated semimetal nature with a magnetoresistance up to around 700% at 2 K and 9 T. Analysis of de Haas-van Alphen oscillations uncovers a Fermi surface consisting of three distinct Fermi pockets with light effective masses. Comparison between the three-dimensional fermiology obtained from our oscillation data and the first-principles calculations demonstrates excellent agreement. This confirms the accuracy of the calculations, which indicate a band inversion centered at the {\Gamma} point and identify the existence of nontrivial tube and needle hole Fermi pockets at {\Gamma}, alongside one trivial diamond electron pocket at the T point in the Brillouin zone. Furthermore, symmetry and topology analysis results in two potential sets of topological invariants, suggesting the emergence of two-dimensional gapless Dirac surface states either on the ab planes or on both the ab planes and mirror planes, protected by crystal symmetries. Therefore, SrAg4Sb2 emerges as a promising candidate topological crystalline insulator., Comment: 9 pages, 5 figures

The convergence of topology and correlations represents a highly coveted realm in the pursuit of novel quantum states of matter. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order, not possible in quantum Hall and Chern insulator systems. However, the QSH insulator with quantized edge conductance remains rare, let alone that with significant correlations. In this work, we report a novel dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator that aligns with single-particle band structure calculations, manifesting enhanced nonlocal transport and quantized helical edge conductance. Interestingly, upon introducing electrons from charge neutrality, TaIrTe4 only shows metallic behavior in a small range of charge densities but quickly goes into a new insulating state, entirely unexpected based on TaIrTe4's single-particle band structure. This insulating state could arise from a strong electronic instability near the van Hove singularities (VHS), likely leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state, marked by the revival of nonlocal transport and quantized helical edge conduction. Our observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands via CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism., Comment: 23 pages, 15 figures, submitted version

Quantum state reconstruction is an essential element in quantum information processing. However, efficient and reliable reconstruction of non-trivial quantum states in the presence of hardware imperfections can be challenging. This task is particularly demanding for high-dimensional states encoded in continuous-variable (CV) systems, as many error-prone measurements are needed to cover the relevant degrees of freedom of the system in phase space. In this work, we introduce an efficient and robust technique for optimized reconstruction based on excitation number sampling (ORENS). We use a standard bosonic circuit quantum electrodynamics (cQED) setup to experimentally demonstrate the robustness of ORENS and show that it outperforms the existing cQED reconstruction techniques such as Wigner and Husimi Q tomography. Our investigation highlights that ORENS is naturally free of parasitic system dynamics and resilient to decoherence effects in the hardware. Finally, ORENS relies only on the ability to accurately measure the excitation number of the state, making it a versatile and accessible tool for a wide range of CV platforms and readily scalable to multimode systems. Thus, our work provides a crucial and valuable primitive for practical quantum information processing using bosonic modes., Comment: Main text (6 pages with 4 figures) and Appendices (10 pages with 7 figures and 4 tables)

The diverse applications of light-matter interactions in science and technology stem from the qualitatively distinct ways these interactions manifest, prompting the development of physical platforms that can interchange between regimes on demand. Bosonic cQED employs the light field of high-Q superconducting cavities coupled to non-linear circuit elements, harnessing the rich dynamics of their interaction for quantum information processing. However, implementing fast switching of the interaction regime without deteriorating the cavity coherence is a significant challenge. We present the first experiment to achieve this feat, combining nanosecond-scale frequency tunability of a transmon coupled to a cavity with lifetime of hundreds of microseconds. Our implementation affords a range of new capabilities for quantum information processing; from fast creation of cavity Fock states using resonant interaction and interchanging tomography techniques at qualitatively distinct interaction regimes on the fly, to the suppression of unwanted cavity-transmon dynamics during idle evolution. By bringing flux tunability into the bosonic cQED toolkit, our work opens up a new paradigm to probe the full range of light-matter interaction dynamics within a single platform and provides valuable new pathways towards robust and versatile quantum information processing.

van der Waals (vdW) magnets, an emerging family of two-dimensional (2D) materials, have received tremendous attention due to their rich fundamental physics and significant potential for cutting-edge technological applications. In contrast to the conventional bulk counterparts, vdW magnets exhibit significant tunability of local material properties, such as stacking engineered interlayer coupling and layer-number dependent magnetic and electronic interactions, which promise to deliver previously unavailable merits to develop multifunctional microelectronic devices. As a further ingredient of this emerging topic, here we report nanoscale quantum sensing and imaging of atomically thin vdW magnet chromium thiophosphate CrPS4, revealing its characteristic layer-dependent 2D static magnetism and dynamic spin fluctuations. We also show a large tunneling magnetoresistance in CrPS4-based spin filter vdW heterostructures. The excellent material stability, robust strategy against environmental degradation, in combination with tailored magnetic properties highlight the potential of CrPS4 in developing state-of-the-art 2D spintronic devices for next-generation information technologies.

Quantum geometry - the geometry of electron Bloch wavefunctions - is central to modern condensed matter physics. Due to the quantum nature, quantum geometry has two parts, the real part quantum metric and the imaginary part Berry curvature. The studies of Berry curvature have led to countless breakthroughs, ranging from the quantum Hall effect in 2DEGs to the anomalous Hall effect (AHE) in ferromagnets. However, in contrast to Berry curvature, the quantum metric has rarely been explored. Here, we report a new nonlinear Hall effect induced by quantum metric by interfacing even-layered MnBi2Te4 (a PT-symmetric antiferromagnet (AFM)) with black phosphorus. This novel nonlinear Hall effect switches direction upon reversing the AFM spins and exhibits distinct scaling that suggests a non-dissipative nature. Like the AHE brought Berry curvature under the spotlight, our results open the door to discovering quantum metric responses. Moreover, we demonstrate that the AFM can harvest wireless electromagnetic energy via the new nonlinear Hall effect, therefore enabling intriguing applications that bridges nonlinear electronics with AFM spintronics., Comment: 19 pages, 4 figures and a Supplementary Materials with 66 pages, 4 figures and 3 tables. Originally submitted to Science on Oct. 5, 2022

Using circularly-polarized light to control quantum matter is a highly intriguing topic in physics, chemistry and biology. Previous studies have demonstrated helicity-dependent optical control of spatial chirality and magnetization $M$. The former is central for asymmetric synthesis in chemistry and homochirality in bio-molecules, while the latter is of great interest for ferromagnetic spintronics. In this paper, we report the surprising observation of helicity-dependent optical control of fully-compensated antiferromagnetic (AFM) order in 2D even-layered MnBi$_2$Te$_4$, a topological Axion insulator with neither chirality nor $M$. We further demonstrate helicity-dependent optical creation of AFM domain walls by double induction beams and the direct reversal of AFM domains by ultrafast pulses. The control and reversal of AFM domains and domain walls by light helicity have never been achieved in any fully-compensated AFM. To understand this optical control, we study a novel type of circular dichroism (CD) proportional to the AFM order, which only appears in reflection but is absent in transmission. We show that the optical control and CD both arise from the optical Axion electrodynamics, which can be visualized as a Berry curvature real space dipole. Our Axion induction provides the possibility to optically control a family of $\mathcal{PT}$-symmetric AFMs such as Cr$_2$O$_3$, CrI$_3$ and possibly novel states in cuprates. In MnBi$_2$Te$_4$, this further opens the door for optical writing of dissipationless circuit formed by topological edge states.

Cat states, with their unique phase-space interference properties, are ideal candidates for understanding fundamental principles of quantum mechanics and performing key quantum information processing tasks. However, they are highly susceptible to photon loss, which inevitably diminishes their quantum non-Gaussian features. Here, we protect these non-Gaussian features against photon loss by compressing the phase-space distribution of a cat state. We achieve this compression with a deterministic technique based on the echo conditional displacement operation in a circuit QED device. We present a versatile technique for creating robust non-Gaussian continuous-variable resource states in a highly linear bosonic mode and manipulating their phase-space distribution to achieve enhanced resilience against photon loss. Compressed cat states offer an attractive avenue for obtaining new insights into quantum foundations and quantum metrology, and for developing inherently more protected bosonic codewords for quantum error correction., Comment: 12 pages, 9 figures

The strange metal (SM) state, characterized by a linear-in-temperature resistivity, is often seen in the normal state of high temperature superconductors. It is believed that the SM state is one of the keys to understand the underlying mechanism of high-Tc superconductivity. Here we report the first observation of the concurrent breakdown of the SM normal state and superconductivity at a pressure-induced quantum critical point in an iron-pnictide superconductor, Ca10(Pt4As8)((Fe0.97Pt0.03)2As2)5. We find that, upon suppressing the superconducting state by applying pressure, the power exponent changes from 1 to 2, and the corresponding coefficient A, the slope of the temperature-linear resistivity per FeAs layer, gradually diminishes. At a critical pressure (12.5 GPa), A and Tc go to zero concurrently,where a quantum phase transition (QPT) from a superconducting state with a SM normal state to a non-superconducting Fermi liquid state takes place. Scaling analysis on the results obtained from the pressurized 1048 superconductor reveals that A and Tc have a positive relation, which exhibits a similarity with that is seen in other chemically-doped unconventional superconductors, regardless of the type of the tuning method (doping or pressurizing), the crystal structure, the bulk or film superconductors and the nature of dopant. These results suggest that there is a simple but powerful organizational principle of connecting the SM normal state with the high-Tc superconductivity., Comment: 16 pages, 4 figures

As the first intrinsic antiferromagnetic (AFM) topological insulator (TI), MnBi$_2$Te$_4$ has provided a material platform to realize various emergent phenomena arising from the interplay of magnetism and band topology. Here by investigating (Mn$_{1-x}$Pb$_x$)Bi$_2$Te$_4$ $(0\leq x \leq 0.82)$ single crystals via the x-ray, electrical transport, magnetometry and neutron measurements, chemical analysis, external pressure, and first-principles calculations, we reveal the magnetic dilution effect on the magnetism and band topology in MnBi$_2$Te$_4$. With increasing $x$, both lattice parameters $a$ and $c$ expand linearly by around 2\%. All samples undergo the paramagnetic to A-type antiferromagnetic transition with the N$\acute{e}$el temperature decreasing lineally from 24 K at $x=0$ to 2 K at $x=0.82$. Our neutron data refinement of the $x=0.37$ sample indicates that the ordered moment is 4.3(1)$\mu_B$/Mn at 4.85 K and the amount of the Mn$_{\rm{Bi}}$ antisites is negligible within the error bars. Isothermal magnetization data reveal a slight decrease of the interlayer plane-plane antiferromagnetic exchange interaction and a monotonic decrease of the magnetic anisotropy, due to diluting magnetic ions and enlarging the unit cell. For $x=0.37$, the application of external pressures enhances the interlayer antiferromagnetic coupling, boosting the N$\acute{e}$el temperature at a rate of 1.4 K/GPa and the saturation field at a rate of 1.8 T/GPa. Furthermore, our first-principles calculations reveal that the band inversion in the two end materials, MnBi$_2$Te$_4$ and PbBi$_2$Te$_4$, occurs at the $\Gamma$ and $Z$ point, respectively, while two gapless points appear at $x = $ 0.44 and $x = $ 0.66, suggesting possible topological phase transitions with doping., Comment: 10 pages, 7 figures

The quantum anomalous Hall (QAH) effect is characterized by a dissipationless chiral edge state with a quantized Hall resistance at zero magnetic field. Manipulating the QAH state is of great importance in both the understanding of topological quantum physics and the implementation of dissipationless electronics. Here, we realized the QAH effect in the magnetic topological insulator Cr-doped (Bi,Sb)2Te3 (CBST) grown on an uncompensated antiferromagnetic insulator Al-doped Cr2O3. Through polarized neutron reflectometry (PNR), we find a strong exchange coupling between CBST and Al-Cr2O3 surface spins fixing interfacial magnetic moments perpendicular to the film plane. The interfacial coupling results in an exchange-biased QAH effect. We further demonstrate that the magnitude and sign of the exchange bias can be effectively controlled using a field training process to set the magnetization of the Al-Cr2O3 layer. Our work demonstrates the use of the exchange bias effect to effectively manipulate the QAH state, opening new possibilities in QAH-based spintronics.

Activating metamagnetic transitions between ordered states in van der Waals magnets and devices bring great opportunities in spintronics. We show that external pressure, which enhances the interlayer hopping without introducing chemical disorders, triggers multiple metamagnetic transitions upon cooling in the topological van der Waals magnets Mn(Bi$_{1-x}$Sb$_x$)$_4$Te$_7$, where the antiferromagnetic interlayer superexchange coupling competes with the ferromagnetic interlayer coupling mediated by the antisite Mn spins. The temperature-pressure phase diagrams reveal that while the ordering temperature from the paramagnetic to ordered states is almost pressure-independent, the metamagnetic transitions show non-trivial pressure and temperature dependence, even re-entrance. For these highly anisotropic magnets, we attribute the former to the ordering temperature being only weakly dependent on the intralayer parameters, the latter to the parametrically different pressure and temperature dependence of the two interlayer couplings. Our independent probing of these disparate magnetic interactions paves an avenue for efficient magnetic manipulations in van der Waals magnets., Comment: 10 pages, 4 figures

Topological materials featuring exotic band structures, unconventional current flow patterns, and emergent organizing principles offer attractive platforms for the development of next-generation transformative quantum electronic technologies. The family of MnBi2Te4 (Bi2Te3)n materials is naturally relevant in this context due to their nontrivial band topology, tunable magnetism, and recently discovered extraordinary quantum transport behaviors. Despite numerous pioneering studies, to date, the local magnetic properties of MnBi2Te4 (Bi2Te3)n remain an open question, hindering a comprehensive understanding of their fundamental material properties. Exploiting nitrogen-vacancy (NV) centers in diamond, we report nanoscale quantum imaging of magnetic phase transitions and spin fluctuations in exfoliated MnBi2Te4 (Bi2Te3)n flakes, revealing the underlying spin transport physics and magnetic domains at the nanoscale. Our results highlight the unique advantage of NV centers in exploring the magnetic properties of emergent quantum materials, opening new opportunities for investigating the interplay between topology and magnetism., Comment: 19 pages, 6 figures

As the first intrinsic antiferromagnetic topological insulator, MnBi$_2$Te$_4$ has provided a platform to investigate the interplay of band topology and magnetism as well as the emergent phenomena arising from such an interplay. Here we report the chemical-vapor-transport (CVT) growth and characterization of MnBi$_2$Te$_4$, as well as the observation of the field-induced quantized Hall conductance in 6-layer devices. Through comparative studies between our CVT-grown and flux-grown MnBi$_2$Te$_4$ via magnetic, transport, scanning tunneling microscopy, and angle-resolved photoemission spectroscopy measurements, we find that CVT-grown MnBi$_2$Te$_4$ is marked with higher Mn occupancy on the Mn site, slightly higher Mn$_{\rm{Bi}}$ antisites, smaller carrier concentration and a Fermi level closer to the Dirac point. Furthermore, a 6-layer device made from the CVT-grown sample shows by far the highest mobility of 2500 cm$^2$V$\cdot$s in MnBi$_2$Te$_4$ devices with the quantized Hall conductance appearing at 1.8 K and 8 T. Our study provides a new route to obtain high-quality single crystals of MnBi$_2$Te$_4$ that are promising to make superior devices and realize emergent phenomena, such as the layer Hall effect and quantized anomalous hall effect, etc., Comment: 5 figures

While ferromagnets have been known and exploited for millennia, antiferromagnets (AFMs) were only discovered in the 1930s. The elusive nature indicates AFMs' unique properties: At large scale, due to the absence of global magnetization, AFMs may appear to behave like any non-magnetic material; However, such a seemingly mundane macroscopic magnetic property is highly nontrivial at microscopic level, where opposite spin alignment within the AFM unit cell forms a rich internal structure. In topological AFMs, such an internal structure leads to a new possibility, where topology and Berry phase can acquire distinct spatial textures. Here, we study this exciting possibility in an AFM Axion insulator, even-layered MnBi$_2$Te$_4$ flakes, where spatial degrees of freedom correspond to different layers. Remarkably, we report the observation of a new type of Hall effect, the layer Hall effect, where electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under no net electric field, even-layered MnBi$_2$Te$_4$ shows no anomalous Hall effect (AHE); However, applying an electric field isolates the response from one layer and leads to the surprising emergence of a large layer-polarized AHE (~50%$\frac{e^2}{h}$). Such a layer Hall effect uncovers a highly rare layer-locked Berry curvature, which serves as a unique character of the space-time $\mathcal{PT}$-symmetric AFM topological insulator state. Moreover, we found that the layer-locked Berry curvature can be manipulated by the Axion field, E$\cdot$B, which drives the system between the opposite AFM states. Our results achieve previously unavailable pathways to detect and manipulate the rich internal spatial structure of fully-compensated topological AFMs. The layer-locked Berry curvature represents a first step towards spatial engineering of Berry phase, such as through layer-specific moir\'e potential., Comment: A revised version of this article is published in Nature

In this paper we report the impact of uniaxial strain $\varepsilon$ applied along the crystalline $a$ axis on the newly discovered kagome superconductor CsV$_3$Sb$_5$. At ambient conditions, CsV$_3$Sb$_5$ shows a charge-density wave (CDW) transition at $T_{\rm CDW}=94.5$ K and superconducts below $T_C = 3.34$ K. In our study, when the uniaxial strain $\varepsilon$ is varied from $-0.90\%$ to $0.90\%$, $T_C$ monotonically increases by $\sim 33\%$ from 3.0 K to 4.0 K, giving rise to the empirical relation $T_C (\varepsilon)=3.4+0.56\varepsilon+0.12\varepsilon^2$. On the other hand, for $\varepsilon$ changing from $-0.76\%$ to $1.26\%$, $T_{\rm CDW}$ decreases monotonically by $\sim 10\%$ from 97.5 K to 87.5 K with $T_{\rm CDW}(\varepsilon)=94.5-4.72\varepsilon-0.60\varepsilon^2$. The opposite response of $T_C$ and $T_{\rm CDW}$ to the uniaxial strain suggests strong competition between these two orders. Comparison with hydrostatic pressure measurements indicate that it is the change in the $c$-axis that is responsible for these behaviors of the CDW and superconducting transitions, and that the explicit breaking of the sixfold rotational symmetry by strain has a negligible effect. Combined with our first-principles calculations and phenomenological analysis, we conclude that the enhancement in $T_C$ with decreasing $c$ is caused primarily by the suppression of $T_{\rm CDW}$, rather than strain-induced modifications in the bare superconducting parameters. We propose that the sensitivity of $T_{\rm CDW}$ with respect to the changes in the $c$-axis arises from the impact of the latter on the trilinear coupling between the $M_1^+$ and $L_2^-$ phonon modes associated with the CDW. Overall, our work reveals that the $c$-axis lattice parameter, which can be controlled by both pressure and uniaxial strain, is a powerful tuning knob for the phase diagram of CsV$_3$Sb$_5$., Comment: 8 pages, 5 figures

An intrinsic antiferromagnetic topological insulator $\mathrm{MnBi_2Te_4}$ can be realized by intercalating Mn-Te bilayer chain in a topological insulator, $\mathrm{Bi_2Te_3}$. $\mathrm{MnBi_2Te_4}$ provides not only a stable platform to demonstrate exotic physical phenomena, but also easy tunability of the physical properties. For example, inserting more $\mathrm{Bi_2Te_3}$ layers in between two adjacent $\mathrm{MnBi_2Te_4}$ weakens the interlayer magnetic interactions between the $\mathrm{MnBi_2Te_4}$ layers. Here we present the first observations on the inter- and intra-layer phonon modes of $\mathrm{MnBi_{2n}Te_{3n+1}}$ (n=1,2,3,4) using cryogenic low-frequency Raman spectroscopy. We experimentally and theoretically distinguish the Raman vibrational modes using various polarization configurations. The two peaks at 66 cm$^{-1}$ and 112 cm$^{-1}$ show an abnormal perturbation in the Raman linewidths below the magnetic transition temperature due to spin-phonon coupling. In $\mathrm{MnBi_4Te_7}$, the $\mathrm{Bi_2Te_3}$ layers induce Davydov splitting of the A$_{1g}$ mode around 137 cm$^{-1}$ at 5 K. Using the linear chain model, we estimate the out-of-plane interlayer force constant to be $(3.98 \pm 0.14) \times 10^{19}$ N/m$^3$ at 5 K, three times weaker than that of $\mathrm{Bi_2Te_3}$. Our work discovers the dynamics of phonon modes of the $\mathrm{MnBi_2Te_4}$ and the effect of the additional $\mathrm{Bi_2Te_3}$ layers, providing the first-principles guidance to tailor the physical properties of layered heterostructures., Comment: 9 pages, 4 figures

MnBi2nTe3n+1(MBT) is the first intrinsic magnetic topological insulator and is promising to hostemergent phenomena such as quantum anomalous Hall effect. They can be made ferromagnetic by having n >= 4 or with Sb doping. We studied the magnetic dynamics in a few selected ferromag-netic (FM) MBT compounds, including MnBi8Te13and Sb doped MnBi2nTe3n+1(n= 2,3) usingAC susceptibility and magneto-optical imaging. Slow relaxation behavior is observed in all threecompounds, suggesting its universality among FM MBT. We attribute the origin of the relaxationbehavior to the irreversible domain movements since they only appear below the saturation fieldswhen ferromagnetic domains form. The very soft ferromagnetic domain nature is revealed by thelow-field fine-structured domains and high-field sea-urchin-shaped remanent-state domains imagedvia our magneto-optical measurements. Finally, we ascribe the rare "double-peak" behavior ob-served in the AC susceptibility under small DC bias fields to the very soft ferromagnetic domainformations., Comment: 5 figures

Two-dimensional van der Waals MnBi$_{2n}$Te$_{3n+1}$ (n = 1, 2, 3, 4) compounds have been recently found to be intrinsic magnetic topological insulators rendering quantum anomalous Hall effect and diverse topological states. Here, we summarize and compare the crystal and magnetic structures of this family, and discuss the effects of chemical composition on their magnetism. We found that a considerable fraction of Bi occupies at the Mn sites in MnBi$_{2n}$Te$_{3n+1}$ (n = 1, 2, 3, 4) while Mn is no detectable at the non-magnetic atomic sites within the resolution of neutron diffraction experiments. The occupancy of Mn monotonically decreases with the increase of n. The polarized neutron diffraction on the representative MnBi$_{4}$Te$_{7}$ reveals that its magnetization density is exclusively accumulated at the Mn site, in good agreement with the results from the unpolarized neutron diffraction. The defects of Bi at the Mn site naturally explain the continuously reduced saturated magnetic moments from n = 1 to n = 4. The experimentally estimated critical exponents of all the compounds generally suggest a three-dimensional character of magnetism. Our work provides material-specified structural parameters that may be useful for band structure calculations to understand the observed topological surface states and for designing quantum magnetic materials through chemical doping., Comment: 5 figures, typos corrected

TaAs and NbAs are two of the earliest identified Weyl semimetals that possess many intriguing optical properties, such as chirality-dependent optical excitations and giant second harmonic generation (SHG). Linear and nonlinear optics have been employed as tools to probe the Weyl physics in these crystals. Here we extend these studies to address two important points: determining the complete anisotropic dielectric response, and to explore if and how they can reveal essential Weyl physics. For the first time, we determine the complete anisotropic dielectric functions of TaAs and NbAs by combining spectroscopic ellipsometry and density functional theory (DFT). Parameterized Lorentz oscillators are reported from 1.2-6 eV (experiment) and 0-6 eV (DFT), and good agreement is shown between them. Both linear and nonlinear optical properties have been reported to reveal Weyl physics. We suggest that strong optical resonances from trivial bands are the likely origin of the large optical second harmonic generation previously reported at these energies. Furthermore, by comparing the contribution of a small k-space centered around the Weyl cones to the total linear dielectric function, we find that these contributions are highly anisotropic and are <25% of the total dielectric function below 0.5 eV; above 1eV, these contributions are negligible. Thus, the study of Weyl physics using optical techniques requires very low energies and even there, a careful assessment is required in distinguishing the much smaller contributions of the Weyl bands from the dominant contributions of the trivial bands and Drude response to the total dielectric function., Comment: 42 pages, 13 figures for the main text