Atomic-scale analysis of disorder by similarity learning from tunneling spectroscopy

Rapid proliferation of hyperspectral imaging in scanning probe microscopies creates unique opportunities to systematically capture and categorize higher dimensional datasets, toward new insights into electronic, mechanical and chemical properties of materials with nano- and atomic-scale resolution. Here we demonstrate similarity learning for tunneling spectroscopy acquired on superconducting material (FeSe) with sparse density of imperfections (Fe vacancies). Popular methods for unsupervised learning and discrete representation of the data in terms of clusters of characteristic behaviors were found to produce inconsistencies with respect to capturing the location and tunneling characteristics of the vacancy sites. To this end, we applied a more general, non-linear similarity learning. This approach was found to outperform several widely used methods for dimensionality reduction and produce a clear differentiation of the type of tunneling spectra. In particular, significant spectral weight transfer likely associated with the electronic reconstruction by the vacancy sites, is systematically captured, as is the spatial extent of the vacancy region. Given that a great variety of electronic materials will exhibit similarly smooth variation of the spectral responses due to random or engineered inhomogeneities in their structure, we believe our approach will be useful for systematic analysis of hyperspectral imaging with minimal prior knowledge, as well as prospective comparison of experimental measurements to theoretical calculations with explicit consideration of disorder.

Defect-driven ferrimagnetism and hidden magnetization in MnBi$_2$Te$_4$

MnBi$_2$Te$_4$ (MBT) materials are promising antiferromagnetic topological insulators where field driven ferromagnetism is predicted to cause a transition between axion insulator and Weyl semimetallic states. However, the presence of antiferromagnetic coupling between Mn/Bi antisite defects and the main Mn layer can reduce the low-field magnetization, and it has been shown that such defects are more prevalent in the structurally identical trivial magnetic insulator MnSb$_2$Te$_4$ (MST). We use high-field magnetization measurements to show that the magnetization of MBT and MST occur in stages and full saturation requires fields of~$sim$~60 Tesla. As a consequence, the low-field magnetization plateau state in MBT, where many determinations of quantum anomalous Hall state are studied, actually consists of ferrimagnetic septuple blocks containing both a uniform and staggered magnetization component.

Direct evidence of ferromagnetism in MnSb2Te4

We report the magnetic imaging of ferromagnetic domains in the van der Waals single crystal MnSb2Te4 from two different sources using cryogenic magnetic force microscopy. The magnetic field dependence of the domains reveals very weak pinning of domain walls in MnSb2Te4, resulting in a negligibly small magnetic hysteresis loop. The temperature dependence of the domain contrast reveals a mean field like behavior, in good agreement with that of bulk magnetization measurements.

Native Defects in Antiferromagnetic Topological Insulator MnBi$_2$Te$_4$

Using scanning tunneling microscopy and spectroscopy, we visualized the native defects in antiferromagnetic topological insulator $mathrm{MnBi_2Te_4}$. Two native defects $mathrm{Mn_{Bi}}$ and $mathrm{Bi_{Te}}$ antisites can be well resolved in the topographic images. $mathrm{Mn_{Bi}}$ tend to suppress the density of states at conduction band edge. Spectroscopy imaging reveals a localized peak-like local density of state at $sim80$~meV below the Fermi energy. A careful inspection of topographic and spectroscopic images, combined with density functional theory calculation, suggests this results from $mathrm{Bi_{Mn}}$ antisites at Mn sites. The random distribution of $mathrm{Mn_{Bi}}$ and $mathrm{Bi_{Mn}}$ antisites results in spatial fluctuation of local density of states near the Fermi level in $mathrm{MnBi_2Te_4}$.

Tuning Fermi Levels in Intrinsic Antiferromagnetic Topological Insulators MnBi2Te4 and MnBi4Te7 by Defect Engineering and Chemical Doping

MnBi2Te4 and MnBi4Te7 are intrinsic antiferromagnetic topological insulators, offering a promising materials platform for realizing exotic topological quantum states. However, high densities of intrinsic defects in these materials not only cause bulk metallic conductivity, preventing the measurement of quantum transport in surface states, but may also affect magnetism and topological properties. In this paper, we show by density functional theory calculations that the strain induced by the internal heterostructure promotes the formation of large-size-mismatched antisite defect BiMn in MnBi2Te4; such strain is further enhanced in MnBi4Te7, giving rise to even higher BiMn density. The abundance of intrinsic BiMn donors results in degenerate n-type conductivity under the Te-poor growth condition. Our calculations suggest that growths in a Te-rich condition can lower the Fermi level, which is supported by our transport measurements. We further show that the internal strain can also enable efficient doping by large-size-mismatched substitutional NaMn acceptors, which can compensate BiMn donors and lower the Fermi level. Na doping may pin the Fermi level inside the bulk band gap even at the Te-poor limit in MnBi2Te4. Furthermore, facile defect formation in MnSb2Te4 and its implication in Sb doping in MnBi2Te4 as well as the defect segregation in MnBi4Te7 are discussed. The defect engineering and doping strategies proposed in this paper will stimulate further studies for improving synthesis and for manipulating magnetic and topological properties in MnBi2Te4, MnBi4Te7, and related compounds.

Realizing gapped surface states in magnetic topological insulator MnBi$_{2-x}$Sb$_{x}$Te$_{4}$

The interplay between magnetism and non-trivial topology in magnetic topological insulators (MTI) is expected to give rise to a variety of exotic topological quantum phenomena, such as the quantum anomalous Hall (QAH) effect and the topological axion states. A key to assessing these novel properties is to tune the Fermi level in the exchange gap of the Dirac surface band. MnBi$_2$Te$_4$ possesses non-trivial band topology with intrinsic antiferromagnetic (AFM) state that can enable all of these quantum states, however, highly electron-doped nature of the MnBi$_2$Te$_4$ crystals obstructs the exhibition of the gapped topological surface states. Here, we tailor the material through Sb-substitution to reveal the gapped surface states in MnBi$_{2-x}$Sb$_{x}$Te$_{4}$ (MBST). By shifting the Fermi level into the bulk band gap of MBST, we access the surface states and show a band gap of 50 meV at the Dirac point from quasi-particle interference (QPI) measured by scanning tunneling microscopy/spectroscopy (STM/STS). Surface-dominant conduction is confirmed below the Neel temperature through transport spectroscopy measured by multiprobe STM. The surface band gap is robust against out-of-plane magnetic field despite the promotion of field-induced ferromagnetism. The realization of bulk-insulating MTI with the large exchange gap offers a promising platform for exploring emergent topological phenomena.

Magnetic imaging of antiferromagnetic domain walls

The control of domain walls or spin textures is crucial for spintronic applications of antiferromagnets. Despite many efforts, it has been challenging to directly visualize antiferromagnetic domains or domain walls with nanoscale resolution, especially in magnetic field. Here, we report magnetic imaging of domain walls in several uniaxial antiferromagnets, the topological insulator MnBi$_2$Te$_4$ family and the Dirac semimetal EuMnBi$_2$, using cryogenic magnetic force microscopy (MFM). Our MFM results reveal higher magnetic susceptibility or net moments inside the domain walls than in domains. Domain walls in these antiferromagnets form randomly with strong thermal and magnetic field dependences. The direct visualization of domain walls and domain structure in magnetic field will not only facilitate the exploration of intrinsic phenomena in topological antiferromagnets, but also open a new path toward control and manipulation of domain walls or spin textures in functional antiferromagnets.

Quasi 2-D magnetism in the Kagome layer compound FeSn

Single crystals of the single Kagome layer compound FeSn are investigated using x-ray and neutron scattering, magnetic susceptibility and magnetization, heat capacity, resistivity, Hall, Seebeck, thermal expansion, thermal conductivity measurements and density functional theory (DFT). FeSn is a planar antiferromagnet below TN = 365 K and exhibits ferromagnetic magnetic order within each Kagome layer. The in-plane magnetic susceptibility is sensitive to synthesis conditions. Resistivity, Hall and Seebeck results indicate multiple bands near the Fermi energy. The resistivity of FeSn is about 3 times lower for current along the stacking direction than in the plane, suggesting that transport and the bulk electronic structure of FeSn is not quasi 2D. FeSn is an excellent metal with Rho(300K)/Rho(2K) values about 100 in both directions. While the ordered state is antiferromagnetic, high temperature susceptibility measurements indicate a ferromagnetic Curie-Weiss temperature of 173 K, reflecting the strong in-plane ferromagnetic interactions. DFT calculations show a 3D electronic structure with the Dirac nodal lines along the K-H directions in the magnetic Brillouin zone about 0.3 eV below the Fermi energy, with the Dirac dispersions at the K points gapped by spin-orbit coupling except at the H point. The magnetism, however, is highly 2D with Jin-plane/Jout-of-plane = 10. The predicted spin-wave spectrum is presented.

Long range antiferromagnetic order in a rocksalt high entropy oxide

We report for the first time the magnetic structure of the high entropy oxide $(Mg_{0.2}Co_{0.2}Ni_{0.2}Cu_{0.2}Zn_{0.2})O$ using neutron powder diffraction. This material exhibits a sluggish magnetic transition but possesses a long-range ordered antiferromagnetic ground state, as revealed by DC and AC magnetic susceptibility, elastic and inelastic neutron scattering measurements. The magnetic propagation wavevector is k=(1/2, 1/2, 1/2) based on the cubic structure Fm-3m, and the magnetic structure consists of ferromagnetic sheets in the (111) planes with spins antiparallel between two neighboring planes. Inelastic neutron scattering reveals strong magnetic excitations at 100 K that survive up to room temperature. This work demonstrates that entropy-stabilized oxides represent a unique platform to study long range magnetic order with extreme chemical disorder.

High-temperature magnetostructural transition in van der Waals-layered a-MoCl3

The crystallographic and magnetic properties of the cleavable 4d3 transition metal compound a-MoCl3 are reported, with a focus on the behavior above room temperature. Crystals were grown by chemical vapor transport and characterized using temperature dependent x-ray diffraction, Raman spectroscopy, and magnetization measurements. A structural phase transition occurs near 585 K, at which the Mo-Mo dimers present at room temperature are broken. A nearly regular honeycomb net of Mo is observed above the transition, and an optical phonon associated with the dimerization instability is identified in the Raman data and in first-principles calculations. The crystals are diamagnetic at room temperature in the dimerized state, and the magnetic susceptibility increases sharply at the structural transition. Moderately strong paramagnetism in the high-temperature structure indicates the presence of local moments on Mo. This is consistent with results of spin-polarized density functional theory calculations using the low- and high-temperature structures. Above the magnetostructural phase transition the magnetic susceptibility continues to increase gradually up to the maximum measurement temperature of 780 K, with a temperature dependence that suggests two-dimensional antiferromagnetic correlations.