Symposium EQ08—Higher-Order Topological Structures in Real Space—From Charge to Spin

Electron microscopy is often used to directly the image the atomic displacements in ferroelectrics, reaching a precision of a few picometers. As good as this is, it is still not sufficient to robustly measure many ferroic order parameters, including vorticity and higher order moments. Enabled by a new design of electron detector [1,2] that is capable of measuring the complete distribution of momentum transfers at every probe position, we construct a 4-dimensional phase space from which we solve the inverse multiple scattering problem and retrieve the underlying 3-dimensional potential of the sample. The lateral resolution of less than 20 pm is now limited not by the instrument, but by the thermal vibrations of the atoms themselves, and the precision is improved to well below 1 pm [3]. The resulting ptychographic reconstructions have allowed us to image the internal structures of both magnetic and ferroelectric vortices, skyrmions and merons, including their singular points that are critical for accurately describing the topological properties of these field textures.

[1] M. W. Tate, P. Purohit, D. Chamberlain, K. X. Nguyen, R. Hovden, C. S. Chang, P. Deb, E. Turgut, J. T. Heron, D. G. Schlom, D. C. Ralph, G. D. Fuchs, K. S. Shanks, H. T. Philipp, D. A. Muller, and S. M. Gruner. “High Dynamic Range Pixel Array Detector for Scanning Transmission Electron Microscopy” Microscopy and Microanalysis 22, (2016): 237–249.
[2] H. T. Philipp, H. T., M. W. Tate, K. S. Shanks, L. Mele, M. Peemen, P. Dona, R. Hartong, G. Van Veen, Y. T. Shao, Z. Chen, J. Thom-Levy, D. A. Muller, and S. M. Gruner. “Very-High Dynamic Range, 10,000 Frames/Second Pixel Array Detector for Electron Microscopy” Microscopy and Microanalysis 28, (2022): 425–440.
[3] Z. Chen, Y. Jiang, Y.-T. Shao, M. E. Holtz, M. Odstrčil, M. Guizar-Sicairos, I. Hanke, S. Ganschow, D. G. Schlom, and D. A. Muller. “Electron Ptychography Achieves Atomic-Resolution Limits Set by Lattice Vibrations” Science 372, (2021): 826–831

Ferroelectric domain walls strongly interact with its surroundings. In ferroelectrics thin films with exposed surfaces investigated by piezoresponse force microscopy (PFM), the main source of external screening charges is the atmosphere and the water neck, and therefore relative humidity (RH) plays a major role. In this context the speed as well as the creep-factor m describing the domain wall kinetics follow the behavior of water adsorption represented by the adsorption isotherm, indicating that the screening mechanism dominating the switching dynamics is the thickness and the structure of adsorbed water structure and its associated dielectric constant and ionic mobility.[1] On the other hand, the ferroelectrics can couple to other ferroic physical magnitudes in heterostructures such as FE/FM multilayers. In this context, the magnetic structure of magnetoelastic thin films can be manipulated by the tunable piezoelectric strain underneath: here I will show how in this case the dynamics of magnetic domain walls are dominated by the ferroelectric domain walls creating pinning sites that nucleate vortex like structures with predominant out of plane magnetic moments.[2]

Reference(s)
[1] I.Spasojevic, A.Verdaguer, G.Catalan, N.Domingo, Adv. Electron.Mater. 2021, 2100650
[2] Ch. Stefani, V. Sireus, J.Sort, E. Menendez, N. Domingo, manuscript under preparation

Local electromagnetic field distribution inside materials can be directly observed at high spatial resolution by using differential phase contrast (DPC) imaging in scanning transmission electron microscopy (STEM) [1]. In DPC STEM, momentum transfers of electrons due to electromagnetic fields are detected by a segmented detector or pixelated detector placed on the bright field region. However, as for crystalline defects such as heterointerfaces, grain boundaries, etc., concomitant diffraction contrast seriously hinders the quantitative electromagnetic fields observation by DPC STEM.
In general, diffraction contrast dramatically varies with a slight change in beam tilt or sample tilt, whereas DPC contrast originates from electric fields and is insensitive to the slight tilt changes. Therefore, by averaging multiple DPC signals acquired with slightly different tilt conditions at the same sample position, the diffraction contrast can be suppressed (averaged) while reinforcing the electric field signals [2]. We have developed tilt-scan averaged DPC (tDPC) STEM system, which can average DPC signals obtained under multiple-beam tilt conditions and suppress diffraction contrast in real-time [3] [4]. tDPC STEM has been successfully applied to observe electric field and electron carriers in GaN-based semiconductor heterointerfaces [5], demonstrating the effectiveness of tDPC STEM.
In this study, we applied tDPC STEM for observing space charge layers in yttria-stabilized zirconia (YSZ) grain boundaries. tDPC STEM observation of YSZ Σ5[001]/(310) grain boundaries revealed that an electric field diverging from the grain boundary was distributed within 15 nm on both sides of the grain boundary. This result indicates the existence of positive charges at the grain boundary core accompanied by surrounding negative charges. On the other hand, little electric field fluctuation was observed at the Σ5[001]/(210) grain boundary. These results suggest that the electric field and the width of the space charge strongly depend on the local structures of the grain boundaries [6]. Details will be discussed in the presentation.
[1] N. Shibata et al., Acc Chem Res, 50, 1502, 2017.
[2] T. Mawson et al., Ultramicroscopy, 219, 113097, 2020.
[3] Y. Kohno, et al., Microscopy, 71, 111 2022.
[4] S. Toyama et al., Ultramicroscopy, 238, 113538, 2022.
[5] S. Toyama et al., to be submitted.

Oxide interfaces are a rich source for novel physical phenomena, ranging from interfacial superconductivity to unusual (multi-)ferroic effects. Over the last decade, significant progress has been made in both the understanding and engineering of oxide interfaces, propelled by the ongoing progress in the development of atomic-scale characterization techniques¹.
Here, we introduce atom probe tomography (APT) as versatile tool for studying oxide interfaces, investigating the 3D atomic-scale structure and chemical composition of (LuFeO₃)₉/(LuFe₂O₄)₁ superlattices. This system couples together ferroelectric and ferrimagnetic response, enabling a true multiferroic material with an intriguing display of charge redistribution at polar interfaces². With our APT measurements we are able to reveal a subtle accumulation of charged oxygen vacancies at the LuFe₂O₄ layers which would typically go undetected with conventional microscopy approaches. We quantify the vacancy concentration and discuss their accumulation in relation to calculated defect formation energies, as well as their ability to stabilize an intriguing multiferroic domain structure. In general, this research establishes a new pathway for studying the interaction of interfaces and point defects in oxides, expanding related atomic-scale investigations into 3D with a new level of chemical accuracy.

References
1. Hunnestad, K. A. et al. Atomic-scale 3D imaging of individual dopant atoms in a complex oxide. arXiv:2111.00317 (2021).
2. Mundy, J. A. et al. Atomically engineered ferroic layers yield a room-temperature magnetoelectric multiferroic. Nature 537, 523–527 (2016).

Recently, improper ferroelectrics –materials in which electric polarization arises as a secondary effect of a leading order parameter– are receiving increasing attention. The family of hexagonal manganites (h-RMnO₃, R = rare earth) is a model system for improper ferroelectricity, where the electric polarization emerges as a byproduct of a primary lattice-trimerizing structural distortion, a combination of tilt and rotation of the MnO₅ bipyramids around the R³⁺ ion. The trimerization is described by a two-component order parameter Q consisting of the tilt amplitude Q and the angle φ of the MnO₅ bipyramids, but can also be related to the amplitude and phase of the corrugation of the R layer, which is easily visible and quantifiable by HAADF-STEM imaging [1]. However, while bulk h-RMnO bulk crystals have been intensively studied in the last decade, not as much of research at the atomic scale has been conducted on the improper ferroelectric behavior of technologically relevant ultrathin films.
Rather than the depolarizing field being the main challenge to achieving polar thin films, as in proper ferroelectrics, improper ferroelectricity in ultrathin films is determined by the thin-film specific behavior of its driving non-polar order parameter. In YMnO₃ thin films, substrate clamping and critical fluctuations of the order parameter lead to a lowering of the temperature of the phase transition, T_C^film. Thus, T_C^film decreases smoothly with YMnO₃ thickness and, inexplicably, at room temperature, the spontaneous polarization reaches zero for the two-unit-cell film [2].
Our current work focuses on the investigation of nanoscale confinement effects on the lattice trimerization of ultrathin YMnO₃ films. The structure and properties of the YMnO₃ films, with a special focus on the interfaces, are investigated by using a combination of quantitative (in-situ) HAADF-STEM and STEM-EELS, and density functional calculations. Our results advance the understanding of the evolution of improper ferroelectricity within the confinement of ultrathin films, which is essential for their successful implementation in nanoscale devices, such as ferroelectric tunnel junctions and resistive memories [3].
[1] E. Holtz et al. Nano Lett. 17, 5883 (2017).
[2] J. Nordlander et al. Nat. Commun. 10, 5591 (2019).
[3] A. Vogel et al. In preparation (2022).

Engineering the structural or chemical architecture of functional materials at the nano or even atomic level enables emergent properties that rely on the interplay between fundamental properties of matter such as charge, spin and local atomic-scale chemistry. A striking illustration of the relevance of this strategy is provided by placing Bi₂Se₃, a topological insulator (TI) with topologically-protected helical two-dimensional surface states and one-dimensional bulk states associated with crystal defects, in close proximity with graphene. The strong spin-orbit interaction and proximity effects result in subtle and controllable electronic band structure changes at and near the interface, with exciting potential for spintronic applications. Here we probe at high energy resolution the interfaces in a system consisting of Bi₂Se₃ films grown by chemical vapor deposition on epitaxial graphene/SiC(0001), where the number of carbon layers can be carefully controlled to tune possible proximity effects between the film and the substrate. All experiments were carried out on a monochromated Nion UltraSTEM100 MC operated at 60kV, with a probe convergence semi-angle of 31mrad and a beam current of approximately 4pA (after monochromation to ~12meV resolution). Chemical mapping confirms the atomic-level chemistry of the layers, while the specific geometry of the sample offers opportunities for probing directly the spatial localization of electronic states within the graphene layers [1] and at the SiC/graphene and graphene/Bi₂Se₃ interfaces. Strikingly, the use of a dark-field EELS geometry, using e.g. a set of custom-developed annular apertures, reveals the emergence of locally resolved fine structure in the ultra-low loss region of the spectrum. In addition to a direct interrogation of the chemical bonds between the layers via their vibrational response, these observations are linked to the interplay between the various phonon modes and the Dirac plasmons in the TI layers, whose dispersion is mapped in momentum space with nm spatial sensitivity using a recently developed methodology for nanoscale momentum-resolved spectroscopy [2].
[1] M. Bugnet et al., Phys. Rev. Lett. 128, 116401 (2022)
[2] F.S. Hage et al., Science Advances 4, eaar7495 (2018)

Complex topological configurations are a fertile playground to explore novel emergent phenomena and exotic phases in condensed-matter physics. I will describe the discovery of polar skyrmions in a lead-titanate layer confined by strontium-titanate layers by atomic-resolution scanning transmission electron microscopy (STEM). Phase-field modeling and second-principles calculations reveal that the polar skyrmions have a skyrmion number of +1 and resonant soft X-ray diffraction experiments show circular dichroism confirming chirality. Such nanometer-scale polar skyrmions exhibit a strong signature of negative permittivity at the surface of the skyrmion, which is furthermore highly tunable with an electric field. They are a new state of matter and electric analogs of magnetic skyrmions, and may be envisaged for potential applications in information technologies.

Developing a microscopic understanding of spin decoherence is essential to advancing quantum technologies. Electron spin decoherence due to atomic vibrations (phonons) plays a special role as it sets an intrinsic limit to the performance of spin-based quantum devices. Two main sources of phonon-induced spin decoherence - the Elliott-Yafet (EY) and Dyakonov-Perel (DP) mechanisms - have distinct physical origins and theoretical treatments. Here we show a rigorous framework that unifies their modeling and enable accurate predictions of spin relaxation and precession in semiconductors [1]. We compute the phonon-dressed vertex of the spin-spin correlation function, with a treatment analogous to the calculation of the anomalous electron magnetic moment in QED [2]. We find that the vertex correction provides a giant renormalization of the electron spin dynamics in solids, greater by many orders of magnitude than the corresponding correction in vacuum. Our work demonstrates a general approach for quantitative analysis of spin decoherence in materials, advancing the quest for spin-based quantum technologies.

[1] J. Park, Y. Luo, J.-J. Zhou, and M. Bernardi. "Many-body theory of phonon-induced spin relaxation and decoherence." Preprint: arXiv:2208.09575
[2] J. Park, J.-J. Zhou, Y. Luo, and M. Bernardi. "Predicting Phonon-Induced Spin Decoherence from First Principles: Colossal Spin Renormalization in Condensed Matter." Phys. Rev. Lett. (in press) Preprint: arXiv:2203.06401

Tantalum arsenide belongs to topological Weyl semimetals (WSM), with unusual electronic and magnetotransport properties. In WSM materials, the combination of distinct features of electronic structure and crystal lattice symmetry - either time reversal or inversion symmetry, leads to occurrence of so called Weyl nodes at the crossing points of two bands without spin degeneracy. The low energy excitations at the Weyl nodes behave as massless Weyl fermions with linear dispersion relations and opposite chiralities. In the band structure of TaAs 12 pairs of Weyl nodes have been identified in the distinct points of the Brillouin zone [1]; but so far TaAs has been obtained only in the form of bulk crystals [1-4]. We have grown TaAs by molecular beam epitaxy (MBE) on commonly used GaAs(001) substrates, in a III-V MBE system equipped with a valved cracker source for arsenic and e-beam source for Ta. TaAs crystallizes in a body-centred-tetragonal structure with the lattice parameters: a = b = 3.4348 Å; c = 11.641. Using in-situ reflection high energy electron diffraction (RHEED) we observe that in spite of a significant lattice mismatch to zinc-blende GaAs (with lattice parameter a=5.653Å) , TaAs grows on GaAs(001) in a fully 2-dimensional layer-by-layer mode, from the very first sub-monolayer deposition stage, with no initial 3-dimensional growth typical for epitaxy on the substrates with a high lattice mismatch. The orientation of TaAs is the same as that of the substrate, i.e. TaAs(001) planes are parallel to GaAs(001), but they are rotated by 45 degrees, hence the [110] in-plane direction of the GaAs substrate is parallel to the [010] one of TaAs. Such configuration decreases the lattice mismatch between TaAs and GaAs, but still it is as big as 19%. The twisting of TaAs(001) layers with respect to GaAs(001) substrate is observed in RHEED, and confirmed by X-ray diffraction and transmission electron microscopy (TEM) measurements. Even though no misfit dislocations are identified in TEM cross-sections visualizing the TaAs/GaAs interface, the TaAs surface morphology revealed by atomic force microscopy exhibits stripe-like structure with about 200 nm long and 20 nm thick planar columnar features parallel to GaAs[-110]. This hampers (so far) applicability of angle resolved photoemission spectroscopy (ARPES) to reveal topological properties typical to Weyl semimetals, such as bulk Dirac cones and surface Fermi arcs, due to much larger dimensions of UV-beam spot used in ARPES, but should not be an obstacle in much more local scanning tunneling spectroscopy measurements. The possibility of obtaining epitaxial layers of TaAs opens a way for integrating this WSM in heterostructures with other materials e.g. ferromagnets or superconductors, which enables investigations of proximity effects, impossible to explore using bulk TaAs crystals accessible so far.
This work has been supported by the National Science Centre (Poland), through the project No. 2017/27/B/ST5/02284, and by the Swedish Research Council through project No. 2017-04404.
[1] Su-Yang Xu, et. al. Science, 349, (2015), 613.
[2] B. Q. Lv, et al. Phys. Rev. X, 5, (2015), 031013.
[3] L. X. Yang, et. al. Nat. Phys. 11, (2015), 728.
[4] Q. R. Zhang, et, al. Phys. Rev. B 100, (2019), 115138.

Understanding chirality, the intrinsic handedness of a system, is important for future technologies using quantum magnetic materials. Of particular interest are magnetic skyrmions which are chiral and topologically protected, meaning that their spin textures can act as barriers from deformation in crystalline grains. However, most electron microscopy studies use Lorentz TEM or holography to investigate chirality of skyrmions in nearly perfect single crystals because Fresnel effects may cause signals from grain structures to be mistaken as magnetism when the two are comparable in size. In this work, we probe nanomagnetism of topological magnetic textures in sputtered thin film of B20 FeGe on Si to study the relationship between magnetic and crystal chirality. Using 4D-STEM, we find that the vorticity and helicity of these magnetic topological phases are coupled to the crystal chirality. Furthermore, our work shows that signals from magnetism can be disentangled from the crystalline effects for sub-micron grains, enabling a way to investigate topological magnetism in the presence of small polycrystalline grains. This methodology is important for spintronics and low-power magnetic memory technologies that rely on scalable techniques for large scale manufacturing of real devices.

[1] Nguyen, KX et al., Physical Review Applied, 17, 034066 (2022).

Materials exhibiting metal-insulator transitions (MITs) have a variety of potential technological applications, but in many systems the mechanism of the transition and the coupling of electronic and lattice degrees of freedom are not fully understood. The Ruddlesden-Popper ruthenate Ca₂RuO₄ is a particularly interesting example due to the tunability of its MIT and strong lattice effects. Although both the metallic and insulating phases of Ca₂RuO₄ share the same Pbca symmetry, a structural transition is closely coupled to the electronic transition in which the insulating phase is distinguished by flattened octahedra [1]. The transition is highly sensitive to a variety of external stimuli including electric fields, with a threshold field of only 40 V/cm at room temperature [2], and epitaxial strain, which can tune the transition temperature over a broad range [3]. Notably, the current driven transition can result in extended stripe patterns of metallic and insulating phase coexistence, which are suggested to mediate the significant mismatch strain between the metallic and insulating phases [4, 5].

Here, a 40 nm thick Ca₂RuO₄ film epitaxially grown on LaAlO₃ is characterized through the MIT with scanning transmission electron microscopy (STEM). The compressive epitaxial strain stabilizes a uniform metallic phase at room temperature, but cryogenic STEM measurements reveal that upon cooling below ~230 K nanometer scale stripes emerge with modulated lattice parameters consistent with the insulating phase, forming a coherent extended nanostructure. Measurement of the nanostructure at atomic-resolution over hundreds of nanometers enables visualization of the complex mesoscale phase arrangement, as well as characterization of the atomic structure within the stripes and through the interfaces of the coexisting phases. In addition, nanoscale features such as defects, local strain gradients, and the substrate-film interface can be resolved and correlated with the nanostructure. Finally, taking advantage of recent instrumentation developments [6], the film is measured at atomic-resolution at intermediate temperatures between liquid nitrogen and room temperature, capturing the evolution of the nanostructure through repeated cycles of the MIT.

[1] Braden, et al. Physical Review B, 58, 847. (1998).
[2] Nakamura, et al. Scientific reports, 3, 1-6. (2013).
[3] Dietl, et al. Applied Physics Letters, 112, 031902. (2018).
[4] Zhang, et al. Physical Review X, 9, 011032. (2019).
[5] Jenni, et al. Physical Review Materials, 4, 085001. (2020).
[6] Goodge, et al. Microscopy and Microanalysis, 26, 439-446. (2020).

*Supported by the National Science Foundation (Platform for the Accelerated Realization, Analysis, and Discovery of Interface Materials (PARADIM)) under Cooperative Agreement No. DMR-2039380 and by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-SC0019414.

Scanning electron microscopy with polarization analysis (SEMPA) is a versatile tool for high-resolution magnetic surface imaging. The capability of synchronous vector imaging is especially useful for accurately determining the in-plane angle of the local magnetization vector. Domain walls in ultrathin films with DMI and out-of-plane magnetization show a thickness-driven continuous transition from Néel to Bloch orientation, which is due to the 1/d reduction in DMI strength that is competing with the dipolar energy of the wall’s magnetic charge. By measuring the DW angle and modeling the dipolar energy the DMI strength can be determined. We present examples for epitaxial, in-situ grown layers of Co/Pt(111) and Co/Ir(111) [1,2], where due to the absence of DMI in the ferromagnet/vacuum interface exactly the DMI of one epitaxially ordered interface can be measured. While UHV conditions are required in SEMPA, there is in fact no strict limitation to imaging in-situ prepared, uncapped magnetic layers. After covering an ex-situ sputtered sample with 1 nm of Pt imaging is still possible, however at reduced magnetic contrast [3]. This enables surface imaging of sputtered multilayer stacks with varied couplings that can host three-dimensional magnetic structures. Of special interest is this for imaging synthetic antiferromagnets [4], where due to the high surface sensitivity of less than one nanometer no contrast reduction from the AF coupled second layer occurs. The combination of high-resolution surface in-plane imaging with micromagnetic simulation and additional, less surface-sensitive microscopy methods allows for successful investigation of such structures. By tilting the sample or using additional techniques like MFM the out-of-plane component of the magnetization gets accessible and thus chiral objects like skyrmions or merons can be identified.

[1] E.C. Corredor, et al. Phys. Rev. B 96, 060410(R), (2017).
[2] F. Kloodt-Twesten, et al. Phys. Rev. B 100, 100402(R), (2019).
[3] S. Kuhrau, et al. Appl. Phys. Lett. 113, 172403, (2018).
[4] T. Dohi et al, Nat. Commun. 10, 5153 (2019).

Charge order is the spontaneous formation of real space superstructures driven by electron-lattice coupling. Similar to other ordered structures such as crystals and magnetic lattices, charge order superlattices may exhibit a variety of defects with emergent properties. Here we use atomic-resolution scanning transmission electron microscopy (STEM) to visualize phase fluctuations and defects in charge order including dislocations, compression and shear deformations. These defects in the superlattice play a key role in nanoscale competition, incommensurate order, and long-range correlations. In particular, STEM shows how topological defects (dislocations) in the charge order lattice of a manganite destroy long-range ordering and host competing charge order instabilities. Non-equilibrium conditions can generate even more complex phase defect structures in charge order superlattices. In the case of 1T-TaS2 following ultarfast light excitation, we observe the formation of long-lived metastable charge order twins. Remarkably, these twins are delinetaed by a series of dislocations similar to low-angle grain boundaries. These atomic-resolution STEM visualizations show that charge order is a promising platform for realizing novel topological defects that are often intertwined with competing electronic instabilities.

Differential phase contrast imaging in aberration-corrected scanning transmission electron microscopy (DPC STEM) brings the possibility to probe the electromagnetic field distribution in materials and devices down to the atomic scale. Recently, it has been shown that intrinsic magnetic fields of an antiferromagnet can be visualized in real space by this technique. However, when applying this techniqe to crystal defects such as interfaces and dislocations, concomitant diffraction contrast has been a serious issue. We have developed a novel scanning system to supress diffraction contrast in DPC images, and quantitative electromagnetic field imaging at defect regions becomes possible. In this talk, serveal applications of DPC STEM to crystal interfaces will be reported.

Single-phase multiferroics intertwine ferroelectric and ferromagnetic properties, providing novel ways to manipulate data and store information, as well as providing opportunities for exploring new chemistry and physics. In practice, due to the fundamental contra-indication between ferroelectricity (empty d⁰ electronic structures) and ferromagnetism (occupied dⁿ electronic structures), single-phase multiferroics are exceedingly scarce. In recent years, we reported the design of such a novel room temperature magnetoelectric multiferroic material that could ideally be suited to future fabrication of revolutionary memory devices. To achieve this design, we took the approach of creating a new layered Aurivillius composition, Bi₆Ti_xFe_yMn_zO₁₈ (B6TFMO; x = 2.80 to 3.04; Y = 1.32 to 1.52; Z = 0.54 to 0.64), which combines differing types of A-site (Bi³⁺) and B-site (Ti⁴⁺, Fe³⁺, Mn^3+/4+) cations, to drive both ferroelectricity and ferromagnetism within the same structural phase.
While this is a rare breakthrough on its own, in this presentation I will describe how we have lately uncovered remarkable polar topological structures close to regions where the B6TFMO layering is disrupted by naturally occurring structural defects. Here, the internal elastic strain and electrostatic energy gradients are altered to give rise to an inhomogeneous polarisation distribution of polar magnitude and polar rotation angle. Atomic resolution scanning transmission electron microscopy, in conjunction with polar displacement mapping, reveals nominally charged ferroelectric domain walls and non-trivial continuous rotations of ferroelectric polarisation into exotic polar vortex structures. These emergent topological structures hitherto lay “hidden”, previously undiscovered within multiferroic B6TFMO, however they occur intrinsically, without the need for an artificial interface and in the absence of external strain engineering.
These distinctive types of 2D topologies are intriguing entities in matter, because they can offer spatially confined emergent functional properties, such as electrical conductivity within an otherwise insulating matrix. The internal characteristic length scales of these polar vortex domain walls (~5 nm) are much more compact than that of their magnetic counterparts (~10 to 100 nm), signifying potential to transcend the limits of classical data storage.

Van der Waals layered materials exhibiting robust room temperature ferroelectricity offer a versatile platform for miniaturization of ferroelectric device technology. Within this class of 2D material systems, CuInP₂S₆ has received a significant degree of interest due to the revelation of ionically mediated polarization switching pathways, multistate ferroelectricity, ionic conduction, and complex interfacial chemistry. Moreover, it is possible to form stable self-assembled heterostructures of ferroelectric CuInP₂S₆ (CIPS) and non-ferroelectric (i.e., lacking Cu) In_4/3P₂S₆ (IPS), by controlling the targeted composition and kinetics of synthesis. To date, the properties of CIPS/IPS interfaces naturally forming by in-plane epitaxy have received little attention. In this work, we use an advanced scanning probe microscopy approach to explore in detail the nanoscale variability of the AC ion-transport dependent functional properties (electromechanical, dielectric, and conductive) in CIPS-IPS flakes during the ferrielectric-paraelectric transition. First, we show evidence of a kHz ionically mediated electromechanical response of CIPS in the paraelectric phase (above TC). Second, we reveal the local dielectric constant and ionic conductivity changes across the CIPS-IPS heterostructure, by local in-situ imaging and explaining the dielectric peak of the ferroelectric phase transition with scanning probe microscopy. Finally, we find a temperature enhanced dielectric loss/ionic conductivity at the CIPS/IPS boundary that we propose is a result of enhanced Cu motion at the CIPS/IPS interface as supported by DFT calculations. Our results expose a new insight into polar properties of CIPS and open the possibility for tuning interfacial properties of the CIPS/IPS interface.

Magnetically frustrated materials offer a playground for realizing exotic magnetic ground states such as quantum spin ices and spin liquids. Synthesizing such quantum magnets in thin-film form allows further tuning of the magnetic ground state with dimensionality and epitaxial strain as well as the possibility to integrate these states with other functional materials. Here we use reactive oxide molecular beam epitaxy to synthesize thin films of hexagonal TbInO₃. This material is isostructural to the well-studied multiferroic material YMnO₃. Due to a lattice distortion accompanied by an improper ferroelectric polarization at high temperatures, the Tb³⁺ sublattice exhibits a stuffed honeycomb geometry which hosts frustrated magnetism. We study the interplay of ferroelectricity and the frustrated magnetic order in the thin film geometry.

Magnetoelectric coupling phenomena in multiferroics were initially treated almost exclusively as bulk effects exhibited by homogeneous materials. In recent years, however, attention has moved to the inhomogeneous distributions of the multiferroic order down to the nanoscale. On the one hand, magnetoelectric phase control ultimately happens on the level of the mostly sub-micrometer-sized domains. On the other hand, domain walls, interfaces and thin films are nanoscale and/or topological objects that have been proving to be the source of intriguing magnetoelectric coupling effects. In my talk, I will therefore explore the fascinating world of magnetoelectric correlations in multiferroics that are inhomogeneous at the nanoscale and demonstrate their enormous potential for new types of correlations. Examples will include [1] a seemingly contradictory coexistence of strong local and forbidden global magnetoelectric coupling; [2] conversion of a multiferroic bulk state into a multiferroic domain wall in a non-multiferroic environment; [3] magnetoelectric transfer of an order parameter with a joking reference to teleportation.

We will show how many popular real-space electric or magnetic topologies can be classified in terms of their underlying magnetoelectric multipoles. The magnetoelectric multipoles form the next-order term, beyond the magnetic dipole, in the multipole expansion of a general magnetization density in a spatially varying magnetic field. They are known to occur in all linear magnetoelectric materials, where their simultaneous breaking of time-reversal and space-inversion symmetry is both responsible for the linear magnetoelectric effect, and contributes to the surface magnetization. Here we will describe other occurences of magnetoelectric multipoles that are relevant for real-space magnetic and electric topologies in materials. First, we will show that magnetic skyrmions can be classified in terms of magnetoelectric multipoles, allowing a straightforward determination of their textures via a magnetoelectric response measurement. Then we will show that conventional, non-magnetic ferroelectric materials contain hidden reciprocal-space magnetoelectric multipoles that should be detectable using magnetic measurements such as Compton scattering. Finally, we will discuss how the magnetoelectric multipoles manifest when topologically non-trivial real-space electric structures evolve in time.

During the past decade, it has been realized that various topological structures, arising in ferroelectrics may significantly contribute to their physical properties. Even the simplest topological formation, domain walls (DWs), bring new functional complexity and open a new avenue in the operating of ferroelectric devices at the nanoscale. Here we generalize topological consideration of the nanostructured ferroelectrics to small nanoparticles, nanodots, films, and nanorods and show that the topologically stable knotting of the polarization field lines and topological chirality results in a wealth of useful functionalities such as optical activity and THz vibrations of DWs.
Importantly, despite the seeming similarity, the origin of topological structures is very different in magnetic and ferroelectric systems. In magnetic systems, it is the local built-in Dzyaloshinskii Moriya interaction that induces the long-range chiral ordering of topological excitations. At variance, a distinct feature of ferroelectrics is that the topological excitations appear as a result of the spontaneous symmetry breaking due to an interplay of the confinement and depolarization effects where the topological excitations are generated by the long-range interaction of the depolarization charges, ρ =- divP. Upon confinement the polarization field swirls to keep its divergenceless structure, the situation being similar to the incompressible liquid flow in the whirlpools or to the magnetohydrodynamic flow of the plasma interior of the stars. The topological classification scheme of these formations, unified by the constraint of the divergenceless of the vector field is by far more complex than that for the magnetic systems.
We demonstrate that the advanced 3D topological excitations, vortices, skyrmions, and Hopfions, characterized by the nontrivial linking numbers and helicity arise inside the nanostructured ferroelectrics and mimic the “topology of the Universe”. Our consideration is in-line with the ongoing paradigmatic shift in physics, marking the change from deriving properties of the matter out of the local structural symmetries to the global topological paradigm, which describes the fundamental properties of matter on the basis of their invariance under continuous transformations or perturbations.

Over the past few years, the existence of materials capable of showing non-trivial topological textures of the polarization pattern has attracted lots of attention triggered by the presumably higher density (due to their smaller sizes) and faster response (phonon frequencies typically range in the THz regime) than their magnetic counterparts making them good candidates for next generation electronic devices. In particular, structures arising in polar oxide nanostructures, due to the delicate interplay between elastic, electrostatic and gradient energies have emerged as a fertile playground to observe novel emergent phenomena and exotic dipole textures. Most studies were performed embedding a prototype ferroelectric (PbTiO₃) in superlattices with a prototype dielectric (SrTiO₃). Theoretical predictions together with an atomically precise synthesis and characterization of materials have lead to the observation of flux-closure [1], vortices [2], skyrmions [3] or merons [4] depending on the periodicity, mechanical and electrostatic boundary conditions. This delicate balance and multiminima potential energy surface suggest a very rich phase diagram with novel phase transitions [5-7] together with exotic physical responses such as negative capacitance [8] or chirality [9]. The involved typical sizes and the will of studying the dependence of the polar texture with external stimuli such as temperature or electric fields require the development of new modelling tools. In this respect, second-principles methods [10-11] are emerging as a valuable solution for such a problems.
In this talk, I shall describe the path of phase transitions occurring in the polar vortex chiral structures upon increasing temperature and characterize them with appropriate order parameters [12]. Although the overall polarization is zero throughout the process, the system suffers a first-order first transition from a chiral-crystal to a chiral-liquid of polarization vortices upon increasing temperature. Finally, a second order phase transition is found at higher temperatures where the mirror symmetry is restored and the system becomes a disordered achiral-liquid. Moreover, in the ordered polar vortex phase, under suitable mechanical (epitaxial strain) and electrostatic boundary conditions (built in potential), a deterministic and reversible control of chirality over mesoscale regions have been found under the application of homogeneous electric fields [13]. Second-principles simulations together with second-harmonic generation based circular-dichroism measurements have shown the existence of hysteresis between left- and right-handed chiral states under the application of such electric fields.
We acknowledge the continuous feedback and support of the experimental groups leaded by Prof. R. Ramesh, L. W. Martin and S. Salahuddin from University of California-BerKeley and by D. A. Muller from University of Cornell. The authors acknowledge financial support from grant PGC2018-096955-B-C41 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF a way of making Europe”. FGO acknowledge support from grant FPU18/04661 funded by MCIN/AEI/10.13039/501100011033.
[1] Y. L. Tang et al. Science 348, 547 (2015)
[2] A. K. Yadav et al. Nature 530, 198 (2016)
[3] S. Das et al. Nature 568, 368 (2019)
[4] Y. J. Wang et al. Nat. Mater. 19, 881 (2020)
[5] Y. Nahas et al. Nature 577, 47 (2020)
[6] Y. Nahas et al, Phys. Rev. Lett. 119, 117601 (2017)
[7] L. Zhou et al. Adv. Funct. Mater. 2111392 (2022)
[8] A. K. Yadav et al. Nature 565, 468-471 (2019)
[9] P. Shafer et al. Proc. of the Natl. Acad. Sci. U.S.A., 115, 915-920 (2018)
[10] J. Wojdel et al. J. of Phys.: Condens. Matter, 25, 305401 (2013)
[11] P. García-Fernández et al. Phys. Rev. B, 93, 195137 (2016)
[12] F. Gómez-Ortiz et al. Phys. Rev. B. 105, L220103 (2022)
[13] P. Behera et al. Sci. Adv. 8, eabj8030 (2022)

The chiral anomaly is a striking signature of quantum effects which leads to violations of the continuity equation for a classically conserved current. In the case of a Weyl semimetal, this leads to a breakdown in the conservation of the chiral-charge current, which is conserved by the classical dynamics. In condensed matter systems this leads to a signature magnetoelectric response associated to anomaly due to the separation of the Weyl points in momentum space. In the presence of strong interactions however, a Weyl semimetal phase become unstable towards spontaneous symmetry breaking. If the chiral symmetry is spontaneously broken this then leads to a Goldstone mode which couples to the chiral anomaly leading to a dynamical magnetoelectric response -- a situation known as a dynamical axion insulator.

Here we consider a simple model of a charge-density wave in a Weyl semimetal and calculate the equations of motion for the Goldstone mode. Surprisingly, we find that the Goldstone mode appears to exhibit a negative phase stiffness, signalling instability of the mean-field towards finite momentum condensation. This is expected to lead to very strong fluctuations in the dynamical anomaly. We suggest a suitable long-wavelength theory which may govern the new axion dynamics in this system and comment on possible signatures.

Topological Dirac and Weyl semimetals are a 3-dimensional topological phase of matter, exhibit gapless energy bands with bulk band crossing that lead to the linear band dispersion. Degenerated Dirac bands are separated by breaking of topological symmetries, resulting in the formation of Weyl semimetal. The strong correlation effect in topological Weyl semimetal is a critical issue in condensed matter physics. Recently, one of the strong correlation effect, the Kondo effect, in Weyl semimetal was theoretically proposed but not yet realized experimental point of view. Here we suggest a coexistence of the Weyl semimetal and Kondo effect in disordered Mn-doped Mn_xVAl₃. Dilute magnetic element Mn-doping in type-II Dirac semimetal VAl₃ acts as a magnetic impurities that induces the tuning of its chemical potential so the Dirac points go closer to the Fermi energy and lifts its band degeneracy, leading to the Weyl semimetal topological phase transition. We observed the Kondo effect by several experimental points of view. Especially, the Kondo effect has confirmed by the electrical resistivity minimum at T_K = 40 K, and logarithmic increase of electrical resistivity, magnetic susceptibility, and specific heat divided by temperature with a significant Sommerfeld coefficient at low temperature. Furthermore, in order to confirm the topological phase transition from Dirac to Weyl semimetal, we affirm the experimental suggstion of Weyl semimetallic phase. One of the representative confirmation of the Weyl semimetal is the angle-resolved magnetoresistance, which has revealed the negative longitudinal magnetoresistance below Kondo temperature due to the chiral anomaly in Mn-doped Mn_xVAl₃. At low temperature below Kondo temperature (T ≤ T_K), the exchange interaction by RKKY interaction in Mn_xVAl₃ breaks time-reversal symmetry even in Kondo screening, resulting in the topological phase transition from Dirac to Weyl semimetal. Also the angle-dependent planar Hall effect can manifests the nontrivial Berry phase of matter and the chiral anomaly which elucidates the same physical origin with negative longitudinal magnetoresistance. This research shows the coexistence of the Kondo effect and Weyl semimetallic state in experimental viewpoint as well as the temperature-induced topological phase transition.

Double perovskites with an open transition-metal 5d shell are interesting materials because they are influenced by the interaction of correlation and spin-orbit coupling effects, similar to Osmate and Iridate compounds.

Here, we present our study on Ba₂MgReO₆, an insulating double perovskite with a structural transition at 33 K and a Néel temperature of 18 K. In a previous study with density-functional theory (DFT)+U [1], the authors could correctly describe the two low-symmetry phases but not the cubic, paramagnetic phase above 33 K, which came out metallic.

Using DFT+dynamical mean-field theory (DMFT), we first show that we can obtain the cubic, insulating phase with a moderate Hubbard U, showing the importance of correlations in Ba₂MgReO₆, which are due to the narrow Re-t_2g bands.

We then look at how the interplay of Hubbard U and spin-orbit coupling can trigger a metal-insulator transition to better understand the physics at play here. Finally, we analyze whether charge quadrupoles or hexadecapoles couple more strongly to the phase transition from cubic to tetragonal at 33 K and compare them quantitatively to the DFT+U results.

Our previous results on the RhPb₂ intermetallic compound [1] inspired us to search for new Rh compounds that may have topological and superconducting properties. Preliminary investigation of them in the ternary Au-Rh-Pb phase diagram has shown that AuPb₄Rh₅ exists newly [2]. Moreover, resistivity measurements of the grown crystals that had a chemical composition close to AuPb₃Rh₃ (EPMA results) have shown two superconducting transitions at 1.73 K and 2.8 K, which do not correspond to the transition temperatures of superconductors from the binary Au-Pb and Rh-Pb phase diagrams.

Further investigation of the ternary phase diagram yielded unexpected results. The EPMA measurements of grown crystals with an infrared mirror furnace similar to RhPb₂ [1] having the initial molar ratio of Au:Pb:Rh=1:4:1 showed that the crystals are Rh₂Pb₃, which seems not to exist to our knowledge or in the known binary Rh-Pb phase diagram [3]. This implies that the current understanding of the binary Rh-Pb phase diagram is incomplete.

During the RhPb₂ melting experiments[1], it was noted that Fe does react with the Rh-Pb alloy, indicating that some compounds might form. This inspired us to investigate further other phase diagrams as well. The melting experiments with a muffle furnace have shown that square-plate-like crystals can grow on the surface of the boule from the melt with an initial molar ratio of Au:Fe:Rh:Pb=2:2:1:4. Surprisingly, the EPMA measurements have shown that the grown crystals do not contain Au and Pb and it turns out finally to be FeRh. To our knowledge, this is the first time that single crystals of FeRh are grown from the melted flux of Au and Pb. The inter-metallic FeRh compound has been studied in the past intensively on peculiar ferromagnetic to antiferromagnetic transition, anomalous thermodynamical properties, crystal structural transformation, etc. near the stoichiometric 1:1 composition of Fe and Rh. However, the lack of a good single crystal has hindered understanding of these interesting properties of the RhFe intermetallic compound.The single crystal made by our method will
enaible us to uderstand more deeply the intruging RhFe intermetallic compound.

[1] N.Subotić, etc. MRS Advances (2022) https://doi.org/10.1557/s43580-022-00292-5.
[2] N.Subotić, etc. to be published
[3] “Phase Equilibria, Crystallographic and Thermodynamic Data of Binary Alloy, Pb-Rh (Lead-Rhodium)", Landolt-Börnstein -Group IV Physical Chemistry 5I (1998) 321.

Pyrochlores are a class of metal oxide materials with the empirical formula A₂B₂O₆O’. Both the A³⁺ and B⁴⁺ sites are filled with select metal, metalloid, or lanthanide cations; the oxygen atoms coordinate roughly as a scalenohedron around the A site and as an octahedron around the B site¹. These specific oxidations and coordinations create the environment for the non-symmetric distribution of electrons in the lattice. This non-symmetric distribution is partially responsible for the ‘spin-ice’ behaviors of some pyrochlores². These metal cations also exhibit other unique magnetic properties including long-range ordered, spin-glass, and spin-liquid phases³. Here we synthesize thin films of pyrochlores using reactive-oxide molecular beam epitaxy. We study the structural and magnetic properties of rare-earth titanate pyrochlores thin films with a focus on oxidation and oxygen vacancies in these materials. Atomic-force microscopy (AFM) and x-ray diffraction (XRD) are used to verify the quality and identity of our grown films. We used SQUID magnetometry to characterize magnetic properties.

1 - Journal of Applied Physics 51, 290 (1980); https://doi.org/10.1063/1.327368
2 - Nature Materials, 13(5), 488–493. https://doi.org/10.1038/NMAT3924
3 - Reviews of Modern Physics, 82(1), 53–107. https://doi.org/10.1103/RevModPhys.82.53

For a two-dimensional time-reversal symmetric system, the quantum spin Hall phase is assumed to be the same as the Z₂ topological insulator phase in the existing literature because the spin Chern number C_s and the Z₂ invariant yield the same topological classification. Here, by investigating the topological electronic structures of monolayer α-phase group V elements, we uncover the presence of a topological phase in α-Sb, which can be characterized by a spin Chern number C_s=2, even though it is Z₂ trivial. Our analysis shows that α-As and Sb share the same band representations at high-symmetry points (HSPs) and would thus both be classified as trivial insulators in terms of topological quantum chemistry (TQC) and symmetry indicators (SIs). However, we demonstrate the existence of a phase transition between α-As and Sb, which is induced by band inversions at two generic k points. In the absence of spin-orbit coupling (SOC), α-As is a trivial insulator, while α-Sb is a Dirac semimetal with four Dirac points (DPs) located away from the high-symmetry lines. Inclusion of the SOC gaps out the Dirac points and induces a nontrivial Berry curvature, endowing α-Sb a doubled quantum spin Hall insulator with a high spin Chern number of C_s=2. We further show that monolayer α-Sb exhibits either a gapless band structure or a gapless spin spectrum on its edges as expected from topological considerations.

We study the temperature (T ) dependent electronic structure and magnetic properties of a high Curie temperature (T_c ~ 185 K) ferromagnetic topological insulator (Cr_0.35Sb_0.65)₂Te₃ using Cr L-edge and Te M-edge x-ray absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD), and angle-resolved photoemission spectroscopy (ARPES). The T-dependent XAS and XMCD results show a systematic and spin-selective splitting of Cr 3d and Te 5p unoccupied density of states, resulting in a magnetic gap opening. The T-dependent XMCD signal and magnetic gap are consistent with bulk magnetization as well as mean-field theory. The full-multiplet charge-transfer cluster model calculations with a negative charge transfer energy show a good agreement with the experimental Cr L-edge XAS and XMCD spectra. The ARPES measurements show the Dirac-cone topological surface states (SS) below and above T_c, implying that the band inversion between the Sb and Te orbital is maintained even at high Cr doping level, and is consistent with a negative charge transfer energy. These results establish a direct link between Cr 3d dopant states and the Te 5p SS forming the magnetic gap in (Cr_0.35Sb_0.65)₂Te₃.

Topologically protected magnetic structures, such as skyrmions, are currently an intensely studied topic in the nanomagnetism community due to their scientific beauty and deep fundamental insight into nanoscale spin systems, but also with regard to potential future applications towards low-power, high-density and high-speed information technologies, which are required for the Internet-of-Things (IoT) and beyond [1-3].
Skyrmions are two dimensional chiral solitons where the magnetization smoothly covers a solid angle density of radians coherently from the center of the spin texture to the opposite magnetization outside of the spin texture [4-5]. Recently, it has been realized, that expanding into the third dimension opens a door to explore highlycomplex topological magnetic structures that can only exist in 3D [6]. Among those 3D textures are magnetic Hopfions [7], which are three-dimensional knot-solitons with a topological class defined by its linking number. Theory has predicted that magnetic Hopfions can be stabilized, e.g., in chiral magnets. Those systems can host target skyrmions (TSks) which are seen as precursors to Hopfions [8-9].
Our recent research was able to stabilize magnetic Hopfions in tailored magnetic multilayers with a depth varying perpendicular anisotropy, and we confirmed the static properties of those Hopfion textures by a combination of two advanced x-ray spectromicroscopy techniques, specifically surface sensitive X-PEEM and bulk sensitive MTXM which allowed us to delineate Hopfions from TSks and torons [10].
In this presentation, we will discuss our recent experimental studies of the static character of magnetic Hopfions, using advanced X-ay microspectrosopy techniques, as well as results from micromagnetic simulations with high-performance computing (HPC), where we identified a field-driven transition from a Hopfion texture to a toron with distinct dynamics for each of the spin textures [11].
This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division Contract No. DE-AC02-05-CH1123 in the Non-Equilibrium Magnetic Materials Program (MSMAG).
[1] A. Fert, N. Reyren and V. Cros, Nature Reviews Materials 2 (7), 17031 (2017).
[2] S. Woo, K. Litzius, B. Krüger, M.-Y. Im, L. Caretta, K. Ritchter, M. Mann, A. Krone, R. Reeve, M. Weigand, P. Agrawal, P. Fischer, M. Kläui, G.S.D. Beach, Nature Materials 15, 501 (2016).
[3] S. Woo, K.M. Song, H.-S. Han, M.-S. Jung, M.-Y. Im, K.-S. Lee, K.S. Song, P. Fischer, J.-I. Hong, J W Choi, B.-C. Min, H. C. Koo, J. Chang, Nature Comm 8:15573 (2017)
[4] H.-B. Braun, Advances in Physics 61 (1), 1-116 (2012).
[5] A. N. Bogdanov and U. K. Rößler, Physical Review Letters 87 (3), 037203 (2001).
[6] A. Fernández-Pacheco, R. Streubel, O. Fruchart, R. Hertel, P. Fischer and R. P. Cowburn, Nature Communications 8, 15756 (2017).
[7] Y. Liu, R. K. Lake and J. Zang, Phys Rev B 98 (17), 174437 (2018).
[8] P. Sutcliffe, Journal of Physics A: Mathematical and Theoretical 51 (37), 375401 (2018).
[9] N. Kent, R. Streubel, C.-H. Lambert, A. Ceballos, S.-G. Je, S. Dhuey, M.-Y. Im, F. Büttner, F. Hellman, S. Salahuddin and P. Fischer, Applied Physics Letters 115 (11), 112404 (2019).
[10] N. Kent, N. Reynolds, D. Raftrey, I.T.G. Campbell, S. Virasawmy, S. Dhuey, R. V. Chopdekar, A. Hierro-Rodriguez, A. Sorrentino, E. Pereiro, S. Ferrer, F. Hellman, P. Sutcliffe, P. Fischer, Nature Communications 12 1562 (2021)
[11] D, Raftrey and P. Fischer, Phys Rev Lett 127, 257201 (2021)

Skyrmions are topologically-protected magnetic quasiparticles that are of great interest for their potential use in spintronic memory and logic. This is especially true in systems with native non-centrosymmetry, since the inherent Dzyaloshinskii-Moriya interaction can stabilize a robust topological phase at or near room temperature and zero field. Control and understanding of ensembles of skyrmions is important for realization of devices based on the technology. In particular, the order-disorder transition associated with the 2D lattice of magnetic skyrmions can have significant implications for transport and other dynamic functionality. Here, we investigate the condensation of the skyrmion phase in a polar, Van der Waals magnet. We then demonstrate that we are can engineer an ordered skyrmion crystal through structural confinement, demonstrating control over this order-disorder transition on scales relevant for device applications.

PbTiO₃/SrTiO₃ superlattices display topological dipole textures in the ferroelectric layer that have recently been found to present excitations in sub-terahertz frequencies. Moreover, a previous work discovered an ultra-reactive phase in these materials in which the thermal activation can cause the domain walls to move spontaneously, resembling the behaviour of a liquid. In this work we employ second-principles models to map the phase diagram of these superlattices, which features three phases that can be deemed as a solid, a liquid and a gas phase. We also use molecular dynamics to study and characterize the dynamic response of these phases. Our findings indicate how the response of these materials can be optimized with respect to the design parameters of the superlattices (layer thicknesses, strain) and temperature. The tuneable sub-terahertz response of these systems makes them interesting candidates for applications in high-speed telecommunications.

Van der Waals 2D magnetic materials have emerged as a novel platform that offers unique optoelectronic, magnetic, and quantum properties.¹ Such low-dimensional spin systems have vast potential in applications such as spintronics and nanoscale magnetic devices. The ability to engineer the structure and defects with respect to magnetic, optical, and electronic properties is critical. For example, an optically active single defect may have potential as a quantum emitter interacting with and embedded in the novel magnetic environment. Air-stable 2D van der Waals magnets are relatively unexplored, making the study of such materials intriguing and helpful for both fundamental research and device design.

Here, we examine the structural properties of the 2D magnet AgCrP₂S₆, a compound that is similar to the family of M₂P₂S₆. Using scanning transmission electron microscopy (STEM), we measure structural parameters, identify the 1D chain structure of magnetic atoms, and visualize the alignment of the magnetic chains between layers with atomic resolution. We also explore the nature of defects and the possibility of controlling defect location using the STEM beam. We expect this crystal structure to offer a high opportunity for anisotropy of its magnetic properties as a 2D van der Waals magnet. By parameterizing a model spin Hamiltonian based on density functional theory calculations, we predict an unusual spin structure that develops from the chain arrangement of the magnetic atoms in this material. We discuss measurements to verify the modelled spin configuration using vibrating sample magnetometry and other techniques. Lastly, we compare the defects, atomic structure transformations, and spin texture with a more studied 2D magnet, CrSBr^2,3, to better understand the fundamental properties of defects and structures in these novel air-stable 2D magnetic materials as a basis for future control and application of magnetic and optical properties.


References

1. Gibertini, M., Koperski, M., Morpurgo, A. F. et al. Magnetic 2D materials an heterostructures. Nat. Nanotechnol. 14, 408-129 (2019).
2. Klein, J., Pingault, B., Florian, M. et al. The bulk van der Waals layered magnet CrSBr is a quasi-1D quantum material. arXiv:2205.13456 (2022).
3. Klein, J., Pham, T., Thomsen, J. D. et al. Atomistic spin textures on-demand in the van der Waals layered magnet CrSBr. arXiv:2170.00037 (2021)

A chiral compound FeSi is a prototypical example of the strongly-correlated d-electron insulators. Its peculiar charge and spin dynamics, which cannot be explained by a simple mean-field picture of nonmagnetic insulators, have provoked many important physical concepts such as d-electron Kondo insulator and insulator-to-metal (reversed Mott) transition due to on-site strong Coulomb interaction.
Triggered by recent new insights into topological aspects of correlated insulators, FeSi is attracting renewed attention for its unusual properties. However, it remains highly nontrivial that compounds made of light (and usually common) elements, like FeSi, can bear topological characteristics. As evidenced by the recent numerous researches, the topological insulators necessarily contain heavy (and generally rare) elements with strong spin-orbit coupling (SOC) to protect their topological band structure.
In this study, we successfully demonstrate a novel surface state hosting metallic conduction and ferromagnetic order in FeSi thin film with nonmagnetic bulk state. We identify that the surface state is not categorized into the class of topological insulators but can be described by a central concept in the modern theory of electric polarization, i.e., Zak phase. Owing to the dipolar charge distribution of Zak-phase origin, the surface state produces the strong SOC properties despite the absence of heavy-metal elements. By taking advantage of the emergent SOC, we also realize various types of nonlinear electrical conductions such as unidirectional magnetoresistance and current-induced magnetization switching. These nonlinear responses are rooted in the non-equilibrium spin accumulation and the consequent dynamics of magnetic domains.
Our results shed light on compounds made of common elements and demonstrate rich phenomena related to magnetic-domain dynamics at the new type of topological polar surface.
This work was done in collaboration with T. Hori, Y. Ohtsuka, M. Hirayama, A. Matsui, T. Nomoto, R. Arita, T. Nakajima, T. Hanashima, V. Ukleev, H. Aoki, M. Mogi, K. Fujiwara, A. Tsukazaki, M. Ichikawa, M. Kawasaki and Y. Tokura.

Novel spintronic devices can play a role in the quest for GreenIT if they are stable and can transport and manipulate spin with low power. Devices have been proposed, where switching by energy-efficient approaches is used to manipulate topological spin structures [1,2].
Firstly, to obtain ultimate stability of states, topological spin structures that emerge due to the Dzyaloshinskii-Moriya interaction (DMI) at structurally asymmetric interfaces, such as chiral domain walls and skyrmions with enhanced topological protection can be used [3-5]. Here we will introduce these spin structures ad we have investigated in detail their dynamics and find that it is governed by the topology of the spin structure [3]. By designing the materials, we can even obtain a skyrmion lattice phase as the ground state [4]. Beyond 2D structures, we recently developed systems with chiral interlayer exchange interactions that lend themselves to the formation of chiral 3D structures [6].
Secondly, for ultimately efficient spin manipulation, we use spin-orbit torques, that can transfer more than 1hbar per electron by transferring not only spin but also orbital angular momentum. We combine ultimately stable skyrmions with spin orbit torques into a skyrmion racetrack memory device [4], where the real time imaging of the trajectories allows us to quantify the skyrmion Hall effect [5]. Recently, we determined the possible mechanisms that lead to a dependence of the skyrmion Hall effect on skyrmion velocity [7]. We furthermore use spin-orbit torque induced skyrmion dynamics for non-conventional stochastic computing applications, where we developed skyrmion reshuffler devices [8] based on skyrmion diffusion, which also reveals the origin of skyrmion pinning [8]. Such diffusion can furthermore be used for Token-based Brownian Computing and Reservoir Computing [9].
Beyond dynamics excited by spin-orbit torques the next step is to use orbital currents that generate orbital torques [10]. We have demonstrated that with an additional Cu/CuOx layer, the acting torques can be increased by more than a factor 10 [10]. This effect has been interpreted as resulting from an orbital Hall current that is converted to a spin current. Finally, an interfacial Orbital Rashba Edelstein Effect has been found, highlighting that the orbital analogues of both the spin Hall effect and the spin-based Rashba Edelstein or Inverse Spin Galvanic effect exist [11].

References
[1] G. Finocchio et al., J. Phys. D: Appl. Phys., vol. 49, no. 42, 423001, 2016.
[2] K. Everschor-Sitte et al., J. Appl. Phys., vol. 124, no. 24, 240901, 2018.
[3] F. Büttner et al., Nature Phys., vol. 11, no. 3, pp. 225–228, 2015.
[4] S. Woo et al., Nature Mater., vol. 15, no. 5, pp. 501–506, 2016.
[5] K. Litzius et al., Nature Phys., vol. 13, no. 2, pp. 170–175, 2017.
[6] D. Han et al., Nature Mater., vol. 18, no. 7, pp. 703–708, 2019.
[7] K. Litzius et al., Nature Electron., vol. 3, no. 1, pp. 30–36, 2020.
[8] J. Zázvorka et al., Nature Nanotechnol., vol. 14, no. 7, pp. 658–661, 2019;
R. Gruber et al., arxiv:2201.01618 (Nature Commun. in press (2022)).
[9] K. Raab et al., arxiv: 2203.14720; M. Brems et al., Appl. Phys. Lett. 119, 132405, 2021.
[10] S. Ding et al. Phys. Rev. Lett. 125, 177201, 2020; Phys. Rev. Lett. 128, 067201, 2022.
[11] D. Go et al., EPL 135, 037002 (2021)

Engineering of domains and domain boundaries is quintessential for technological exploitation of numerous functional materials. However, it has only recently realized that the configuration of these domains/domain boundaries can have non-trivial topology. We will discuss a new topological classification scheme of domain/domain boundary configurations with Ising-type or two-dimensional order parameters: Z_m×Z_n domains (m directional variants and n translational antiphases) and Z_l vortices (where l number of domains and that of domain boundaries merge). This classification, with the concept of topological protection and topological charge conservation, has been applied to a wide range of materials such as improper ferroelectric R(Mn,Fe)O₃, antipolar In(Mn,Ga)O₃, hybrid improper ferroelectric (Ca,Sr)₃Ti₂O₇, chiral & helical Cr_1/3TaS₂, antiferromagnetic Nd₂SrFe₂O₇ & a-Fe₂O_3, antiferromagnetic & superconducting Sr₂VO₃FeAs, and CDW systems such as 2H-TaSe₂. We will also discuss the emergent physical properties of domain boundaries, distinct from those of domains. The presented topological consideration provides a basis in understanding the formation, kinetics, manipulation and property optimization of domains/domain boundaries in quantum materials.

There is significant scientific and technological interest in the epitaxial integration of ferromagnetic or antiferromagnetic materials with the topological insulators (TI). This allows the introduction of the ferromagnetic order into a topological insulator system and may lead to the development of novel spin electronic devices. It is anticipated that these heterostructures can be used as novel magnetoresistive random access memory (MRAM) devices with high charge-to-spin conversion efficiency. This implies that TI-based heterostructures can switch between 0 and 1 memory states much more efficiently, while consuming lower energy than the state-of-the-art magnetic tunneling junction-based heterostructures that use transition metals. The TI-based devices will be less susceptive to weak disorder and perturbations since writing process will occur via conventional writing field while electrical read out process will be topologically protected.
A key requirement for an operational heterojunction is a successful coupling of a TI with the magnetic material, which is facilitated by “atomically-clean” and abrupt junction interface. This should involve low-temperature deposition of the magnetic layer on the TI surface. This eliminates usage of the standard magnetic materials growth techniques, such as molecular beam epitaxy (MBE) and pulsed laser deposition, as they require the substrate temperatures greater than 300-350 ⁰C, above what TIs can survive.
Here, we report on the innovative approach to grow a room-temperature antiferromagnetic semiconductor (MnTe) using atomic layer deposition (ALD) and to epitaxially integrate it with the topological insulator (Bi₂Te₃). MnTe films were deposited at <100> GaAs and <111> InP. While the MnTe at <100> GaAs were polycrystalline, epitaxial growth was achieved at closely lattice-matched <111> InP at temperatures as low as 120 ⁰C. Bi₂Te₃ was grown by MBE at c-Al₂O₃, ex-situ transferred into the ALD system, and used as a template for MnTe growth. High-resolution X-ray diffraction studies demonstrated that epitaxial MnTe growth was achieved at 120 ⁰C. Transmission electron microscopy showed that the MnTe / Bi₂Te₃ interface was atomically sharp. No amorphous and / or disordered regions were present at the interface within the imaged regions. Magnetotransport properties of the ALD-grown MnTe were also studied and will be reported here.
In summary, ALD was successfully used for the low-temperature epitaxial integration of MnTe antiferromagnetic semiconductor with the Bi₂Te₃ topological insulator. This opens the path for the realization of near-room temperature energy-efficient spintronic devices.

Topological materials present new challenges in terms of characterization, in particular how to minimize surface and sample damage while imaging and analyzing surfaces at the direct native level. Therefore, novel approaches are needed in order to corelate materials properties with surface topology. We have adapted LEEM multi-modal techniques such as Low Energy Electron Diffraction (LEEP), Photoemission Electron Microscopy (PEEM) and in-situ ARPES with high temperature annealing to study individual surface modalities. We have examined various topological materials in the form of bulk 2D heterostructures, specifically artificially constructed metasurfaces with unique order parameters (spin, lattice, localized charge and collective excitations (such as plasmons)).

It is possible to form, via controlled growth, systems with heterointerfaces in bulk materials. We will present the structure analysis of a novel synthesized material Ba6Nb11S28 along with key physical properties. This material naturally realizes vdW coupled heterointerfaces between transition metal dichalcogenide (TMD) monolayers (hexagonal NbS2, H-NbS2) and insulating spacers Ba3NbS5. TEM diffraction taken along the c-axis shows that the hexagonal spacer and TMD layers are commensurate. The electronic band structure can be understood as that resulting from superimposing a periodic potential defined by Ba3NbS5 onto monolayer H-NbS2. This is similar to the mechanism which yields flat bands and strongly correlated physics in twisted-bilayer graphene and TMD heterostructures. LEEM techniques and Low Voltage electron microscopy has been used to characterize grown materials with high resolution at low beam voltages to directly confirm structural layers, ordering and surface diffraction and relate them to metrics of possible topolgical material performance.

Acknowledgement
This work was supported by the STC Center for Integrated Quantum Materials, NSF Grant No. DMR-1231319. This work was supported by an MRI grant from the National Science Foundation DMR-1828237 “The acquisition of a Low Energy Electron Microscope for Nanoscience research”

References
[1] Devarakonda A, Inoue H, Fang S, Ozsoy-Keskinbora C, Suzuki T, Kriener M, Fu L, Kaxiras E, Bell DC, Checkelsky J. G. Science Oct 9;370(6513):231-236 (2020).
[2] Bell D, Erdman N. Low Voltage Electron Microscopy. Bell D, Erdman N, editors. Chichester, UK: John Wiley & Sons, Ltd; (2012)

Understanding the variables that controls the size, switching, and pining of magnetic domain and structures spans the fields of fundamental physics, materials science, as well as storage and logic device technologies. Here, I will discuss our efforts in using scanning transmission electron microscopy (STEM), within differential phase contrast (DPC) imaging and electron energy-loss spectroscopy (EELS), to detect and measure magnetic phases of materials with atomic, and near atomic, spatial resolution. I will discuss the limits of the aforementioned techniques to resolve contributions from spin and orbit to magnetism, and how topological and chiral phases of matter could be investigated in the near future with an electron microscope.
This research was supported by the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725 with the DOE, and sponsored by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U.S. Department of Energy.

The advent of two-dimensional (2D) magnets [1] enables a myriad of opportunities in nano-spintronics and memory devices. A key requisite for creating nanoscale magneto-electric devices is atomic-level engineering in which materials and stacks are designed with specific properties in mind. An emerging material that is promising for atomic-level control is the magnetic semiconductor CrSBr. [2] Utilizing CrSBr requires understanding the magneto-electric [3] and magneto-optical [4] properties of the defects, involving structural characterization of individual defects by microscopy. Studies on defects are, however, often limited by the fact that few-layer samples are not stable under imaging conditions, resulting in more defects or low signal-to-noise ratio (SNR) images [2]. Recently, the emergence of machine learning (ML) in the microscopy field has opened opportunities for faster and more accurate analysis than conventional methods in SNR-dominated systems [5]. Merging ML with high-resolution microscopy techniques like scanning transmission electron microscopy (STEM) and scanning tunneling microscopy (STM) provides means to discover new key insights even in materials only a few layers thick.

Here we study defects and dopants in CrSBr and its alloy CrSBr_xCl_1-x using a combination of high-resolution microscopy (HAADF-STEM and STM) and advanced ML techniques. We investigate the quantity, type and distribution of defects with the motivation to understand their structural, electronic and magnetic properties. We apply machine learning in the form of convolutional neural networks to analyze alloys and defects and discuss its applicability to multilayer systems. Overall, we conclude that CrSBr and related compounds are interesting material platforms for applying high resolution microscopy techniques in combination with ML to study their defect properties. We expect that understanding how defects affect the structure of CrSBr and related compounds will lead to new insight into the possibilities of engineering tailor-made magneto-electric and magneto-optical devices. Furthermore, we expect that the ML models for investigating such defects can serve as a foundation for finding defects in a variety of similar materials in this challenging setting.

[1] Huang, B. et al. Nature 546, 270–273 (2017)
[2] Klein, J. et al. arXiv:2170.00037 to appear in Nature Comm. (2021)
[3] Telford, E. et al. Nature Mater. (2022)
[4] Klein, J. et al. to be submitted (2022)
[5] Lee, C., et al. Nano Lett. 20, 3369 (2020)

Energy-loss near-edge structure (ELNES) and X-ray absorption near-edge structure (XANES) are powerful tools for characterizing the local atomic and electronic structures of materials. ELNES/XANES is produced by the electronic transition from a core orbital to conduction bands, and thus it basically provides the information reflecting the partial density of states (PDOS) of the conduction band at the excited state of a given material. Although ELNES/XANES gives us valuable information such as chemical bonding and the charge state of a specific atom, the knowledge that can be extracted from the measurements is limited to the information reflecting the conduction band at the excited state. If the information reflecting the entire PDOS at the ground state can also be extracted from ELNES/XANES, materials properties based on PDOS can be evaluated directly from a single spectral measurement and materials developments would be accelerated.
In this presentation, we introduce a novel machine learning (ML) based method for determining the PDOS of valence and conduction band at the ground state from the ELNES/XANES spectra simultaneously. We have carried out density functional theory (DFT) calculations on various structures of Si and prepared a database of Si-K ELNES/XANES and the corresponding PDOS at the ground state. On this database, we have trained a ML model to predict the entire PDOS spectra at the ground state from the ELNES/XANES spectra directly. In the result, our model successfully reproduced the characteristics of the PDOS spectra near the Fermi level. Therefore, we envision the utilization of the ML could be powerful for widening the application of the ELNES/XANES measurements including simultaneous mapping of structure and property in a transmission electron microscope.

Emergent topological textures such as polar vortices and skyrmions in ferroelectric heterostructures have drawn great interest due to the richness of underlying physics and the potential applications in next generation nanodevices. Although concepts like topological protection and phase transitions as a function of temperature, strain, electric field and superlattice periodicity have been already explored in polar topological defects (vortices), the counterparts for polar topological solitons (skyrmions and merons) remain in its infancy. To understand and explore the microscopic details of these transitions requires a characterization method which can track the detailed 3D structure of individual dipole textures. By combining the full four-dimensional phase space information collected by a new generation of direct electron detectors which quantitatively records the momentum distribution of transmitted electrons at every beam position (4D-STEM), dynamical diffraction simulations, and ptychographic phase retrieval algorithm to process the data, we have been able to robustly image the local polarization and chirality in each polar texture.

Upon heating a lifted-off, freestanding [(PbTiO₃)₁₆/(SrTiO₃)₁₆]₈ superlattice membrane, we study the strain-driven emergence of tetratic meron lattice from a disordered liquid-like skyrmion state, accompanied by a change in chirality. In the case of freestanding (SrTiO₃)₁₆/(PbTiO₃)₁₆/(SrTiO₃)₁₆ trilayer membranes, we explore the creation and annihilation of polar merons and anti-merons in self-assembling labyrinthine patterns when perturbed by the electric-field gradient generated from the focused electron probe. Theoretical insights into this highly degenerate, frustrated system suggest that the transition among various metastable states originates from the intrinsic topological instabilities.

Research supported by AFOSR Hybrid Materials MURI (FA9550-18-1-0480) and ARO ETHOS MURI (W911NF-21-2-0162), facilities support from the NSF (DMR-1429155, DMR-1719875). Researchers at the University of Arkansas also thank the Vannevar Bush Faculty Fellowship Grant No. N00014-20-1-2834 from the Department of Defense.

In 1956, David Pines predicted the existence of a gapless electronic collective mode in multi-component Fermi liquids [1]. Unlike the ordinary plasmon where all electrons move in synchrony, this collective mode arises from the out-of-phase motion of electrons of different bands. This mode, which involves (D)istinct (E)lectron (M)otion was dubbed a “D.E.M.on” (or simply “demon”) by Pines. Being a gapless electronic mode, the demon has been theoretically investigated as a novel route towards superconductivity in a variety of systems [2-4], but direct experimental evidence for the existence of the demon has not been found to date. Here, we present momentum-resolved electron energy loss spectroscopy (M-EELS) measurements of Sr₂RuO₄ along with RPA calculations which suggest that the demon has finally been observed. By decomposing the charge susceptibility by band index, the RPA calculations show that the mode can be attributed to the out-of-phase motion between the γ and β bands of Sr₂RuO₄. Furthermore, the observed demon dispersion is strongly temperature-dependent, with a mode velocity of 0.70 eV*Å at 300 K and 0.5 eV*Å at 30 K, which directly ties the demon dispersion to the known low-temperature quasiparticle renormalization in Sr₂RuO₄ [5]. Our results offer a first step towards establishing the role of the demon in multiband metals and call for revisiting the consequences of this collective mode for superconductivity and other phases of matter.

References
[1]. D. Pines, Can. J. Phys. 34, 1379 (1956).
[2]. J. Ihm. M. L. Cohen, S. F. Tuan, Phys. Rev. B 23, 3258 (1981)
[3]. J. Ruvalds, Adv. Phys. 30, 677 (1981)
[4]. V. Z. Kresin, J. Opt. Soc. Am. B 6, 490-495 (1989)
[5]. J. Mravlje, et al., Phys. Rev. Lett. 106, 096401 (2011)

Recently, in the context of materials informatics, there have been many attempts to replace expensive first-principles calculations with predictions based on low-cost machine learning (ML) models. Although databases of structures and electronic states of various materials are already being developed and play an important role in the study of ML models, it is necessary to expand not only the number of data in the databases but also their contents in order to construct ML models that represent a wide variety of physical properties.
Among various physical properties, we are focusing on the core-loss spectra, which are not only computationally available but also experimentally measurable by transmission electron microscopy and synchrotron facilities. The core-loss spectra, which are excitation spectra from a core orbital to unoccupied orbitals, directly reflect partial electronic state densities (PDOS) of states excited state and indirectly contain information on ground-state PDOS, and thus on properties related to PDOS. In the context of these backgrounds, we have been performing first-principles calculations on the K-edge core-loss spectra of each independent carbon site in the organic molecules in the QM9 data set [1], which have carbon numbers of 8 or less. We have already reported that the molecular C-K edge spectra can be used to predict the molecular properties [2], and we have recently published these organic molecular C-K edge spectral database [3]. We expect that this database will be used as benchmarks for organic molecule spectral informatics or for the analysis of experimentally obtained spectra.
In this presentation, we present the results of developing a ML model using a graph neural network with the organic molecular structures and an excitation carbon site therein as input and the corresponding site C-K edge spectra as output. After training on the database, our ML model is generally successful in reproducing spectral outlines such as rough features and major peaks.

References
[1] R. Ramakrishnan, P. Dral, M. Rupp, and O. A. Lilienfeld, Sci Data 1, 140022 (2014).
[2] K. Kikumasa S. Kiyohara K. Shibata, and T. Mizoguchi, Adv. Intell. Syst. 4, 2100103 (2021).
[3] K. Shibata, K. Kikumasa, S. Kiyohara, and T. Mizoguchi, Sci. Data 9, 214 (2022).

When magnons propagate across a non-collinear magnetic texture, they collect a Berry phase that can be interpreted as the flux of a synthetic orbital magnetic field. This Berry flux is related to the topological skyrmion density of the magnetic texture. For a topologically non-trivial skyrmion configuration, the magnon thus experiences a synthetic Lorentz force that bends the quasi-classical trajectories of the magnons. For a skyrmion lattice, the average synthetic field is finite such that the magnons are confined to cyclotron orbits of the corresponding magnon Landau levels. This is reflected in a magnon band structure with finite Chern numbers. Here, we report on a series of spectroscopic studies of this band structure using various techniques that allow to probe different regimes in energy-momentum space: magnetic resonance spectroscopy [1], spin-wave spectroscopy [2], inelastic neutron scattering [3] and Brillouin light scattering [4,5]. These techniques have been applied to various cubic chiral magnets like MnSi, FeCoSi and Cu₂OSeO₃, that are well described by a universal effective continuum theory parametrized by a few parameters only. The combined data from all techniques are found to be in quantitative agreement with theory.

[1] R. Takagi, M. Garst, J. Sahliger, C. H. Back, Y. Tokura, S. Seki, Phys. Rev. B 104, 144410 (2021).
[2] S. Seki, M. Garst, J. Waizner, R. Takagi, N. D. Khanh, Y. Okamura, K. Kondou, F. Kagawa, Y. Otani, Y. Tokura, Nat. Commun. 11, 256 (2020).
[3] T. Weber, D. M. Fobe, J. Waizner, P. Steffens, G. S. Tucker, M. Boehm, L. Beddrich, C. Franz, H. Gabold, R. Bewley, D. Voneshen, M. Skoulatos, R. Georgii, G. Ehlers, A. Bauer, C. Pfleiderer, P. Boeni, M. Janoschek, M. Garst, Science 375, 1025 (2022).
[4] N. Ogawa, L. Koehler, M. Garst, S. Toyoda, S. Seki, Y. Tokura, PNAS 118, e2022927118 (2021).
[5] P. Che, R. Ciola, V. Kravchuk, M. Garst, D. Grundler, unpublished.

The current-induced dynamics of magnetic structures is quite complex. For example, magnetic skyrmions allow for ‘banana kicks’ in magnetism, i.e., not only a motion of the skyrmions along but also transverse to the current direction. This effect, which has become known as the skyrmion Hall effect [1,2,3], is often disruptive for device applications. In this talk, we will present possibilities of how to eliminate the skyrmion Hall effect [4,5]. As a particular example, we discuss helical phases which provide confined one-dimensional channels for high-speed skyrmion motion. We discuss how skyrmions can be generated in such helical backgrounds and analyze their stability [6].
Moreover, we will address the role played by topology in the physics of the skyrmion Hall effect. For example, it is widely believed that the skyrmion Hall effect, vanishes for overall topologically neutral structures such as (synthetic) antiferromagnetic skyrmions and skyrmioniums due to a compensation of Magnus forces. While this is true for spin-transfer torque-driven skyrmions, we show that this simple picture is generally false for spin-orbit torque-driven objects [7]. We find that the skyrmion Hall angle for spin-orbit torque-driven skyrmions is directly related to their helicity, which imposes an unexpected roadblock for developing faster and lower input racetrack memories based on spin-orbit torques.

[1] T. Schulz, et al., Nat. Phys. 8, 301 (2012)
[2] K. Litzius, et al., Nat. Phys. 13, 170 (2017)
[3] W. Jiang, et al., Nat. Phys. 13, 162 (2017)
[4] R. Zarzuela, et al., Phys. Rev. B 101, 054405 (2020)
[5] K.-W. Kim, et al., Phys. Rev. B 97, 224427 (2018)
[6] R. Knapman, et al., J. Phys. D: Appl Phys. 54, 404003 (2021)
[7] R. Msiska, et al., Phys. Rev. Appl. 17, 064015 (2022)

This contribution is aimed to address the trends in multiferroics research in a broader context of thermodynamics and symmetry theory. This would allow me to remind the conference audience about reflections about the multiferroics and their topological defects by the late Prof. Janovec from our Institute. Finally, I would like to address the incomplete analogy between physics of ferromagnets and ferroelectrics in the context of formation of spatially modulated ferroic phases and skyrmion condensate phases.

With reference to structured electron illumination (including electron vortex beams) and four-dimensional STEM algorithm developments (including DPC and ptychography), in this talk I will discuss recent developments of (S)TEM techniques enabling improved characterisation of topological structures.

The emergence of real-space topological structures, such as ferroelectric and ferromagnetic skyrmions, is an increasingly popular area of research. As the sizes of these structures approch the nanometer-scale, new characterization techniques are required to map out complex polarization profiles in three dimensions. Resonant elastic x-ray scattering (REXS) is often used to study chirality in spin textures such as magnetic skyrmions and domain walls. However, the application of this technique to analagous electric polarization textures is less established. Here, we present a framework for analyzing REXS from an arrangement of charge quadrupole moments [1], which is applied to measurements on polar skyrmions that form in PbTiO3/SrTiO3 superlattices. By utilizing circularly polarized x-rays and extended reciprocal space scans, we gain insight into their three-dimensional chiral structure. Furthermore, we determine that both right- and left-handed polar skyrmions coexist, and their relative fraction can be extracted using REXS. This technique can be extended to study ordered electric and/or magnetic phases in similar systems. We discuss how this can be appied to complex structures that emerge in multiferroic BiFeO₃/TbScO₃ superlattices.

[1] K. T. Kim, M. R. McCarter, et al., Nat. Commun. 13, 1769 (2022).

We investigate the role of polarization-photon coupling (specifically, the polarization-oscillation-induced radiation electric field) in the excitation of ferroelectric thin films by an ultrafast terahertz electric field pulse. Analytical formulas are developed to predict how the frequencies and relaxation time of three-dimensional soft mode phonons (intrinsic polarization oscillation) are modulated by the radiation electric field and epitaxial strain. Ultrafast terahertz-pulse-driven excitation of harmonic polarization oscillation in strained single-domain ferroelectric thin film is then simulated using a dynamical phase-field model that considers the coupled strain-polarization-photon dynamics. The frequencies and relaxation time extracted from such numerical simulations agree well with analytical predictions. In relatively thin films, it is predicted that the radiation electric field slightly reduces the frequencies but significantly shortens the relaxation time. These results demonstrate the necessity of considering polarization-photon coupling in understanding and predicting the response of ferroelectric materials to ultrafast pulses of terahertz and higher frequencies.

Carrier dynamics in Bi₂Se₃ topological insulator thin films of different thickness were investigated by femtosecond transient absorption spectroscopy (FTAS) at 77K and room temperature, by using selected pump energies (from 2.5 eV down to 0.6 eV) and a wide spectrum probe (from 3.6 eV down to 0.9 eV). The fabrication process for growing Bi₂Se₃, that was recently developed^[1], is quick, very inexpensive, easy to control and allows obtaining films of different thickness, endowed with topological properties, during the same procedure. In particular, ultra-thin films deposited on n-doped Si substrates with this method show good rectifying properties suitable for their use as photodetectors in the UV-Vis-IR range. The process consists of two consecutive procedures: first Bi₂Se₃ nanowires/nanobelts are deposited by standard catalyst-free vapor–solid deposition on different substrates positioned inside a quartz tube. Then, the Bi₂Se₃ stuck on the inner surface of the quartz tube is re-evaporated and deposited in the form of ultra-thin films on new substrates at a temperature below 100 °C.
FTAS measurements revealed several resolved bleaching signals that show different temporal dynamics. These spectral components can be attributed to the electron transitions at the various bulk or surface states present in the complex Bi₂Se₃ band structure and to plasmonic resonance of long-range strongly correlated electrons, as recently observed with ellipsometry in the same material.^[2] We point out that the polycrystalline films used for this work show similar absorption spectra and carrier dynamics of epitaxial layers grown by MBE.^[3,4]
Using a pump of low energy, but sufficient to give rise to interband transitions (e.g., 0.6 eV), we have observed absorption bleaching even at energies greater than that of the pump. By a careful study as a function of the pump fluence, we have been able to rule out any multiphotonic contribution to the absorption of the pump. The observation of absorption bleaching at energies larger than that of the pump is attributed to the depletion of the electron population in the bulk valence band (BVB) and/or in the lower Dirac surface states (SS1) that are involved in the interband transition permitted at 0.6 eV. Being the BVB and the SS1 also involved in high-energy transitions, that carrier depletion gives rise to a reduction of the absorption also at the higher energy resonances.
The wide experimental conditions used in our work allow a careful description of the transitions involved in the absorption spectrum and of the photoexcited carrier dynamics, thus providing novel and very useful insights into the properties that allow the fabrication of innovative, low-cost and wide-range photodetectors.

[1] M. Salvato, M. Scagliotti, M. De Crescenzi, P. Castrucci, F. De Matteis, M. Crivellari, S. Pelli Cresi, D. Catone, T. Bauch, F. Lombardi, Nanoscale 2020, 12, 12405.
[2] T. J. Whitcher, M. G. Silly, M. Yang, P. K. Das, D. Peyrot, X. Chi, M. Eddrief, J. Moon, S. Oh, A. H. Castro-Neto, M. B. H. Breese, A. T. S. Wee, F. Silly, A. Rusydi, NPG Asia Mater. 2020, 12, DOI: 10.1038/s41427-020-0218-7.
[3] Y. D. Glinka, J. Li, T. He, X. W. Sun, ACS Photonics 2021, 8, 1191.
[4] T. Jiang, R. Miao, J. Zhao, Z. Xu, T. Zhou, K. Wei, J. You, X. Zheng, Z. Wang, Chinese Opt. Lett. 2019, 17, 20005.