Symposium NM04—Magnetic Skyrmions and Topological Effects in Materials and Nanostructures

Non-collinear magnetic structure induces emergent magnetic field on conduction electrons, resulting in such as a geometrical Hall effect and so on [1]. Especially in helimagnets with short magnetic periods, the geometrical or topological Hall effect can dominate Hall resistivity profile [2]. Such systems have been attracting attention as a material platform where emergent magnetic fields can be utilized.
Some Mn₅Si₃-type rare-earth compounds, such as Dy₅Si3 and Ho₅Sb₃, are known for famous material examples to exhibit helimagnetic orderings. Among them, Tb₅Sb₃ has been identified as a helimagnet that hosts various magnetic structures.
We have succeeded in growing single crystals of Tb₅Sb₃ and revealed the magnetic and electric transport properties. We found peculiar magnetic-field dependences of Hall resistivity showing peak structures, which cannot be explained by anomalous Hall effect proportional to the magnetization and may indicate the emergent field contributions. We have also identified the possible formation of a disordered helimagnetic state by small-angle neutron scattering (SANS). In this poster, we will discuss the relation between the Hall resistivity profile and the disordered helical magnetic structure.
[1] S. Gao et al., Phy s . Rev. B 100, 241115(R) (2019)
[2] T. Kurumaji et al., Science 365, 6456, 914-918 (2019)

Many spintronic devices require low damping materials that also exhibit high magnetostriction.^1,2 However, the efficiency of such devices is limited by the high conductivity of metallic magnetostrictive materials, causing significant electrical losses from eddy currents and increased damping. Yttrium iron garnet (Y₃Fe₅O₁₂, or YIG) is a promising alternative to metallic magnetostrictive materials since it exhibits low Gilbert damping.^3,4Additionally, YIG exhibits acceptable magnetic properties for spintronic devices including a relatively low coercivity.^4,5 Despite these advantages, YIG intrinsically exhibits near-zero magnetostriction. Theoretical and experimental data has shown that doping YIG with cerium (substituting for yttrium) can significantly increase magnetostriction due to increased spin-orbit couplingin bulk, single crystal materials.^5,6 We utilize solution processing for facile stoichiometry control as well as integrability into a future device. The synthesis and characterization of these novel magnetostrictive YIG materials will be presented.

References: 1) J. Phys. Condens. Matter., 2017, 29, 1-22. 2) Nat. Commun., 2017, 8, 296. 3)APL Mater. 2014,2, 106. 4) Solid State Phys., 2013,64, 157-191. 5)J. Appl. Phys., 1967, 38, 3737-3739.6) AIP Conf. Proc., 1972,5, 704-706.

Spin-orbit interaction in combination with structural inversion asymmetry on magnetic surfaces, interfaces, hetero- and nanostructures is a source for a variety of spin-dependent transport phenomena and novel magnetic textures, with the chiral magnetic skyrmions [1] being the best known. In this presentation, we discuss our efforts to optimize magnetic multilayers for skyrmions [2-7] in potential applications. We elaborate on the issues of skyrmion size [7], stability and lifetime [8], and detection [9, 10]. Furthermore, we discuss multilayers of monolayer-thick films and compare those to results of stacks of thicker films. Motivated to enable efficient material screening, we report on our efforts to replace the Dzyaloshinskii–Moriya interaction (DMI) with a descriptor (e.g. work function, electric dipole moment [11]) that is easier to evaluate or measure.

Our investigations make use of a multiscale approach based on (i) density-functional theory (DFT) (the FLAPW method as implemented in the FLEUR code [12] and the Korringa-Kohn-Rostoker (KKR) method as implemented in juKKR [13]) combined with (ii) the atomistic spin dynamics code SPIRIT [14,15] by which the lifetime of the skyrmions are determined combining the Geodesic Nudged Elastic Band method (GNEB) [16] or the Systematic Saddle Point Search method [8] with the Harmonic Transition State Theory (HTST) and (iii) micromagnetic reasoning.

We acknowledge funding by the DARPA TEE program (#HR0011831554) from DOI, from Deutsche Forschungsgemeinschaft (DFG) through SPP 2137 “Skyrmionics” (Project No. BL 444/16), the Collaborative Research Centers SFB 1238 (Project C01) as well as computing time from JARA-HPC and Jülich Supercomputing Centre.

[1] Stefan Heinze et al., Nat. Phys. 7, 713 (2011).
[2] Ashis Kumar Nandy et al., Phys. Rev. Lett. 116, 177202 (2016).
[3] Abdu Belabbes et al., Phys. Rev. Lett. 117, 247202 (2016).
[4] Bertrand Dupé et al., Nat. Commun. 7, 11779 (2016).
[5] Bernd Zimmermann et al., Appl. Phys. Lett. 113, 232403 (2018).
[6] Hongying Jia et al., Phys. Rev. B 98, 144427 (2018).
[7] Hongying Jia et al., Phys. Rev. M 4, 094407 (2020).
[8] Gideon P. Müller et al., Phys. Rev. Lett. 121, 197202 (2018).
[9] Dax M. Crum et al., Nat. Commun. 6, 8541 (2015).
[10] Manuel dos Santos Dias et al., Nat. Commun. 7, 13613 (2016).
[11] Hongying Jia et al., Phys. Rev. M 4, 024405 (2020).
[12] For a program description, see www.flapw.de.
[13] For a program description, see https://jukkr.fz-juelich.de
[14] For a program description, see https://spirit-code.github.io
[15] Gideon P. Müller et al., Phys. Rev. B 99, 224414 (2019).
[16] Pavel F. Bessarab et al., Sci. Rep. 8, 3433 (2018).

Magnetic skyrmions are long-lived topological excitations in a small subset of magnetic materials, such as some heavy-metal / ferromagnet multilayers with strong interfacial spin-orbit interactions. These materials can host a high density of skyrmions without any topological counterparts, which defines these states as topological phases with a large net topological charge. A transition from a topological trivial state to a skyrmion state is hence considered a topological phase transitions. Such topological phase transitions, which involve the nucleation or annihilation of magnetic skyrmions, are in principle allowed due to the discrete nature of the lattice. However, they are still suppressed by the same strong energy barriers that also allow skyrmions to exist at room temperature [1]. Topological phase transitions are therefore expected to be of first order, with hysteresis and a transition dynamics characterized by slow and heterogeneous nucleation, as known, e.g., from freezing of water. In fact, we find that heterogeneous nucleation is the underlying principle of electrical skyrmion nucleation, which crucially relies on materials defects to break the translational symmetry [2].

Surprisingly, however, we find that picosecond homogeneous nucleation of an extended topological phase, comprising a dense array of nanometer-scale magnetic skyrmions, can be induced by a single femtosecond laser pulse.

In this talk, after giving an introduction to the stability [1] and the spin-orbit torque nucleation [2] of magnetic skyrmions, I will discuss the nucleation dynamics of this all-optical topological phase transition, which we were able to follow in real time during the early user operation of beamline SCS at the European XFEL [3]. Using time-resolved small angle x-ray scattering, we discovered that rapid, homogeneous nucleation of the skyrmion phase is mediated by a previously undisclosed transient fluctuation state. This state, which is characterized by high spatial frequency magnetic fluctuations, persists for approximately 100 ps after exciting our magnetic multilayer with a femtosecond, infrared laser pulse. The topological phase emerges from these fluctuations by nucleation and coalescence, a mechanism that goes well beyond existing theories of topological phase transitions such as the Kibble–Zurek mechanism and the Berezinskii–Kosterlitz–Thouless transition. The process is completed on a time scale of 300 ps. Using atomistic spin dynamics simulations, we confirm that the fluctuation state is key to the ultrafast increase of the global topological charge, enabled by an almost complete elimination of the topological energy barrier in this transient state of matter.

[1] F. Büttner, I. Lemesh, and G. S. D. Beach, Theory of isolated magnetic skyrmions: From fundamentals to room temperature applications. Scientific Reports 8, 4464 (2018).

[2] F. Büttner, I. Lemesh, M. Schneider, B. Pfau, C. M. Günther, P. Hessing, J. Geilhufe, L. Caretta, D. Engel, B. Krüger, J. Viefhaus, S. Eisebitt, and G. S. D. Beach, Field-free deterministic ultrafast creation of magnetic skyrmions by spin–orbit torques. Nature Nanotechnology 12, 1040 (2017).

[3] F. Büttner, B. Pfau, M. Böttcher, M. Schneider, G. Mercurio, C. M. Günther, P. Hessing, C. Klose, A. Wittmann, K. Gerlinger, L.-M. Kern, C. Strüber., C. von Korff Schmising, J. Fuchs , D. Engel, A. Churikova, S. Huang, D. Suzuki, I. Lemesh, M. Huang, L. Caretta, D. Weder, J. H. Gaida, M. Möller, T. R. Harvey, S. Zayko, K. Bagschik, R. Carley, L. Mercadier, J. Schlappa, A. Yaroslavtsev, L. Le Guyarder, N. Gerasimova , A. Scherz, C. Deiter, R. Gort, D. Hickin, J. Zhu, M. Turcato, D. Lomidze, F. Erdinger, A. Castoldi, S. Maffessanti, M. Porro, A. Samartsev, J. Sinova, C. Ropers, J. H. Mentink, B. Dupé, G. S. D. Beach, and S. Eisebitt, Observation of fluctuation-mediated picosecond nucleation of a topological phase. Nature Materials (2020).

The non-trivial topology of skyrmions in magnetic materials results in a massively enhanced coupling to spin currents and an emergent electrodynamics directly observable in the transport properties. We report an investigation of the conditions and characteristics of the unpinning and subsequent motion of skyrmions in the class of chiral magnets as inferred from the transverse and longitudinal susceptibility as well as kinetic neutron scattering.

Magnetic skyrmions have mostly been studied in cubic chiral helimagnets, in which they are Bloch-type and their axes align along the applied magnetic field. In contrast, the orientation of Néel-type skyrmions is locked to the polar axis of the host material’s underlying crystal structure. In the lacunar spinels GaV4S8 and GaV4Se8, the Néel-type skyrmion lattice phase exists for externally applied magnetic fields parallel to this axis and withstands oblique magnetic fields up to some critical angle. Here, we map out the stability of the skyrmion lattice phase in both crystals as a function of field angle and magnitude using dynamic cantilever magnetometry. The measured phase diagrams reproduce the major features predicted by a recent theoretical model, including a reentrant cycloidal phase in GaV4Se8. Nonetheless, we observe a greater robustness of the skyrmion phase to oblique fields, suggesting possible refinements to the model. Besides identifying transitions between the cycloidal, skyrmion lattice, and ferromagnetic states in the bulk, we measure additional anomalies in GaV4Se8 and assign them to magnetic states confined to polar structural domain walls.

Novel computational paradigms in combination with proper hardware solutions are required to overcome the limitations of our state-of-the-art computer technology, in particular regarding energy consumption. Due to the inherent complex and non-linear nature, spintronics offers the possibility towards energy-efficient, non-volatile hardware solutions for various unconventional computing schemes.[1-3]
In this talk, I will address the potential of magnetic skyrmions for in particular two unconventional computing schemes – reservoir computing and stochastic computing. Reservoir computing is a computational scheme that allows drastically simplifying spatial-temporal recognition tasks. We have shown that random skyrmion fabrics provide a suitable physical implementation of the reservoir [4,5] and allow to classify patterns via their complex resistance responses either by tracing the signal over time or by a single spatially resolved measurement. [6]
Stochastic computing is a computational paradigm that allows speeding up a calculation while trading for numerical precision. Information is encoded in terms of bit-streams as a probability. A key requirement and simultaneously a challenge is that the incoming bitstreams are uncorrelated. The Brownian motion of magnetic skyrmions allows creating a device that reshuffles the bit-streams. [7,8]
In any type of hardware-based computation, finally, some sort of readout of the system is needed. While often a significant effort is made in enhancing the resolution of an experimental technique to obtain further insight into the sample and its physical properties, advantageous data analysis has the potential to provide a deeper insight into a given data set. This is particularly relevant when the signal is close to the resolution limit, i.e. where the noise becomes at least of the same order as the signal. [9]

[1] J. Grollier, D. Querlioz, K. Y. Camsari, KES, S. Fukami, M. D. Stiles, Nature Electronics (2020)
[2] E. Vedmedenko, R. Kawakami, D. Sheka, ..., KES, et al., J. of Phys. D (2020)
[3] G. Finocchio, M. Di Ventra, K.Y. Camsari, KES, P. K. Amiri and Z. Zeng, arXiv:1907.07176
[4] D. Prychynenko, M. Sitte, et al, KES, Phys. Rev. Appl. 9, 014034 (2018)
[5] G. Bourianoff, D. Pinna, M. Sitte and KES, AIP Adv. 8, 055602 (2018)
[6] D. Pinna, G. Bourianoff and KES, arXiv:1811.12623
[7] D. Pinna, F. Abreu Araujo, J.-V. Kim, et al, Phys. Rev. Appl. 9, 064018 (2018)
[8] J. Zazvorka, F. Jakobs, D. Heinze, ..., KES, et al., Nat. Nanotech. 14, 658 (2019)
[9] I. Horenko, D. Rodrigues, T. O’Kane and KES, arXiv:1907.04601

After the discovery of the magnetic skyrmions in the A-phase of a chiral magnet [S. Mühlbauer et al., Science 323, 915 (2009)], the interest in non-collinear spin structures has substantially increased. Such nanoscale spin structures depend crucially on the material, temperature and energy contributions relevant to magnetically ordered states such as symmetric Heisenberg exchange, antisymmetric Dzyaloshinskii–Moriya exchange interactions, Zeeman energy, magnetocrystalline and shape anisotropy. The engineering of materials and energy terms is now decisive to harvest the promised functionalities of skyrmions e.g. as racetrack memory [A. Fert et al., Nat. Nano. 8, 152 (2013)], probabilistic computing approach [D. Pinna et al., Phys. Rev. Applied 9, 064018 (2018)] and microwave oscillator [S. Zhang et al., New J. Phys. 17, 023061 (2015)]. For all these possible applications a detailed understanding of spin dynamics in the technologically relevant GHz frequency regime [Y. Onose et al., Phys. Rev. Lett. 109, 037603 (2012), S.A. Montoya et al., Phys. Rev. B 95, 224405 (2017)] is of utmost importance. At the same time eigenresonances provide a fundamental insight into the relevant energy terms [T. Schwarze et al., Nat. Mater. 14, 478 (2015)].
In the talk we report on broadband spectroscopy performed on non-collinear spin structures supported by different materials systems such as the chiral bulk magnet Cu₂OSeO₃ and multilayers prepared from FeGd. The low magnetic damping in both systems allowed us to observe rich magnon spectra which depended characteristically on the different magnetic phases. Our experiments range from about 10 K to room temperature. Beyond broadband spin-wave spectroscopy we performed Brillouin light scattering with a focused laser beam (bulk Cu₂OSeO₃) and x-ray magnetic circular dichroism microscopy (FeGd multilayers grown on a membrane). Specific cooling cycles and magnetic field histories applied to Cu₂OSeO₃ induced metastable phases which displayed eigenmode spectra not known from the earlier publications [Y. Onose et al., Phys. Rev. Lett. 109, 037603 (2012); T. Schwarze et al., Nat. Mater. 14, 478 (2015)]. We report our latest experimental results obtained on the dynamics of non-collinear spin structures in the bulk chiral magnet Cu₂OSeO₃ and FeGd multilayers.

The work was possible due to excellent cooperation with Ping Che, and M. Albrecht, A. Bauer, K. Baumgaertl, M. Bechtel, H. Berger, E. Catapano, M. Garst, J. Gräfe, M. Heigl, A. Kúkol'ová, A. Magrez, A. Mucchietto, C. Pfleiderer, H.M. Rønnow, T. Schönenberger, G. Schütz, J.-R. Soh, I. Stasinopolous, M. Weigand, J. Waizner. The research is funded by SNSF via grant 171003 (sinergia project Nanoskyrmionics) and by DFG via transregio TRR80.

Recent experiments on twisted bilayer graphene show an anomalous quantum Hall (AQH) effect at filling of 3 electrons per moirè unit cell. The AQH effect arises in an insulating state with both valley- and ferromagnetic order. We argue [1], that weak doping of such a system leads to the formation of a novel topological spin texture, a `double-tetarton lattice'. The building block of this lattice, the `double-tetarton', is a spin configuration which covers 1/4 of the unit-sphere twice. In contrast to skyrmion lattices, the net magnetization of this magnetic texture vanishes. Only at large magnetic fields more conventional skyrmion lattices are recovered. But even for large fields the addition of a single charge to the ferromagnetic AQH state flips hundreds of spins. Our analysis is based on the investigation of an effective non-linear sigma model which includes the effects of long-ranged Coulomb interactions.
[1] Thomas Boemerich, Lukas Heinen, and Achim Rosch, Phys. Rev. B 102, 100408(R) (2020).

First discovered in 2009 to form a lattice of whirlpool-like twists in MnSi, magnetic skyrmions have since been explored extensively in other bulk magnetic crystals, and in synthetic systems such as magnetic mono- and multilayers. Regardless of the host system, the topological winding of skyrmions is the common ingredient that leads to unique physical properties attracting significant interest. In particular, it is established that skyrmions when created display a robustness against perturbation and decay that is generally referred to as topological protection. This is a central concept underlying the stability of skyrmions and their suitability for use in applications, either within equilibrium phases or far-from-equilibrium states.

In this talk, we will review our recent experimental studies of Co-Zn-Mn compounds [1-6], a family of high-temperature chiral cubic magnets discovered recently to host Bloch-type chiral skyrmions over an extended temperature range, including room temperature [1]. Amongst the remarkable properties displayed by these materials, we will focus first on how skyrmions phases fall out of thermal equilibrium remarkably easily on supercooling to form robust metastable skyrmion states [2-3]. These metastable skyrmion states extend unprecedentedly across the majority of the phase diagram, and can even display a thermally-reversible structural transformation that surprisingly does not trigger a decay to the thermodynamic ground state.

Second, we focus in on the Co7Zn7Mn6 composition, the phase diagram of which hosts two thermodynamically distinct equilibrium skyrmion phases [5]. One of these skyrmion phases is the so-called A-phase, stable just below the transition temperature and familiar to all chiral cubic magnets. The second skyrmion phase in this system is much more unusual, being stable at much lower temperatures, with this fact alone implicating multiple skyrmion stability mechanisms exist in this single system, and the existence of a new skyrmion phase stability mechanism at low temperature. From extensive recent experiments [6], we will argue that the stability of the low temperature skyrmion phase is due to a cooperative interplay between chiral magnetism and the magnetic frustration that arises due to a hyper-kagome structural motif in the crystal structure.

Overall, our experiments on Co-Zn-Mn compounds showcase this system as a rich playground for exploring the connection between topological skyrmions, the physics of far-from-equilibrium topological states and magnetic frustration.

[1] Y. Tokunaga et al., Nature Communications 6, 7638 (2015)
[2] K. Karube, J.S. White et al., Nature Materials 15, 1237 (2016)
[3] K. Karube, J.S. White et al., Phys. Rev. Materials 1, 074405 (2017)
[4] K. Karube, J.S. White et al., Science Advances 4, eaar7043 (2018)
[5] K. Karube, J.S. White et al., Physical Review B 102, 064408 (2020)
[6] V. Ukleev et al., submitted for publication.

Magnetic skyrmions are localized magnetic textures in magnetic films, behaving as particles and topologically different from the uniform ferromagnetic state. In metallic magnetic multilayers (MML) with perpendicular magnetic anisotropy (PMA), non-collinear chiral spin textures are stabilized by interfacial Dzyaloshinskii-Moriya interaction (DMI), which favours a unique sense of magnetization rotation. Magnetic skyrmions in MML were identified to be extremely promising for applications, as well as of fundamental interest. [1] The magnetism community provided a great effort during the last years to control skyrmions properties, notably size, velocity, and stability in field and temperature.

We soon realized that the increase of repetitions of the multilayers serving the thermal stability of the magnetic textures has the a priori adverse effect of stabilizing hybrid magnetic textures that is a depth dependence of the chirality (of domain walls or skyrmions) due to the competitions between dipolar fields and DMI. [2] We will describe ferromagnetic skyrmion propagation in different type of structures and discuss the role of their three-dimensional (3D) magnetic textures with hybrid chirality.

The dipolar fields are also responsible for the increase in skyrmion diameter. Both the hybrid chirality and the size increase suggest that reducing the role of dipolar fields is desirable in view of applications. A solution is to use ferromagnetic layers coupled antiferromagnetically through Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction, namely synthetic antiferromagnetic (SAF) MML. Manipulating the SAF MML is of course difficult using external magnetic fields only, and a solution using a bias layer will be discussed. [3] Studying SAF systems with conventional magnetic force microscopy (MFM) and other techniques is challenging. We will present experimental investigations using MFM in vacuum [3], NV-center microscopy, electrical transport measurement [4] and x-ray scattering techniques [5] to investigate the magnetization textures, and, in particular, the skyrmions in SAF.

Understanding precisely our observations requires a detailed understanding of the DMI. Therefore, we investigate systematically the DMI using Brillouin light scattering, stripe domain period, and domain wall propagation in several types of multilayers to measure its dependence with thickness [6] and materials [6,7]. In particular, we unravel a strong correlation between the work function and the DMI amplitude [7].

[1] A. Fert, N. Reyren and V. Cros, Nat. Rev. Materials 2, 17031 (2017)
[2] W. Legrand et al, Sci. Adv. 4, eaat0415 (2018)
[3] W. Legrand et al, Nat. Mater. 19, 34 (2020)
[4] D. Maccariello et al, to appear in Phys. Rev. Appl.
[5] C. Léveillé, E. Burgos-Parra et al, in preparation.
[6] W. Legrand et al, in preparation.
[7] F. Ajejas et al, in preparation.

French ANR grant TOPSKY (ANR-17-CE24-0025), DARPA TEE program grant (MIPR#HR0011831554), FLAG-ERA SOgraphMEM, and EU grant SKYTOP (H2020 FET Proactive 824123) are acknowledged for their financial support.

Nontrivial topological defects such as two- and three-dimensional skyrmions, skyrmion tubes and hopfions have been observed in a variety of materials including chiral magnets, nematic liquid crystals and even in ferroelectrics as well as other materials (e.g. multiferroics) and physical contexts such as condensates. I will present a comparative study of these topological entities in terms of modeling them using the relevant variable, e.g. magnetization, polarization or the director field. I will also focus on their energetics, a variety of topological invariants that characterize them and how to study their properties for potential applications.

The impact of magnetic anisotropy on the skyrmion lattice (SkL) state in non-centrosymmetric magnets has been overlooked for long, partly because a semi-quantitative description of the equilibrium SkL phase forming near the Curie temperature could often be achieved without invoking anisotropy e
ffects. Recently, anisotropy has been reported to play a crucial role in the formation of low-temperature equilibrium SkLs in cubic helimagnets, the transformation between different metastable SkLs and the deformation of skyrmions in axially symmetric polar magnets. While these findings highlight the importance of magnetic anisotropy with regard to the stability, symmetry and shape of individual skyrmions and SkLs, systematic experimental studies quantifying the strength of anisotropy in skyrmion hosts are virtually non-existing. Here, we determine the type and the strength of magnetic anisotropy in various skyrmion-host families, using multi-frequency electron spin resonance spectroscopy, and report on strong variations of anisotropy driven by composition, temperature or even by magnetic field.

Skyrmions are particle-like topological spin textures stabilized by the Dzyaloshinskii-Moriya interaction, which have recently stimulated great interests in spintronics community. The dynamics of which have been frequently studied via using magnetic fields and current-induced spin torques. On the other hand, a comprehensive understanding of thermal effects, including random thermal fluctuation and directional thermal currents, on the dynamics of skyrmions are not fully established yet.

In this talk, I will first discuss our recent experimental observation of the thermal fluctuation-induced random walk of a single isolated Néel-type magnetic skyrmion in an interfacially asymmetric Ta/CoFeB/TaO_x multilayer. In particular, an intriguing topology dependent Brownian gyromotion behavior of skyrmions has been identified. The onset of Brownian gyromotion of a single skyrmion induced by the thermal effects, including a nonlinear temperature-dependent diffusion coefficient and topology-dependent gyromotion are further formulated based on the stochastic Thiele equation.

Subsequently, I will discuss the thermal generation, manipulation and detection of nanoscale skyrmions, which were made in microstructured devices made of different multilayers – [Ta/CoFeB/MgO]₁₅, [Pt/CoFeB/MgO/Ta]₁₅ and [Pt/Co/Ta]₁₅ integrated with on-chip heaters, by using a full-field soft X-ray microscopy. In particular, the thermal generation of densely packed skyrmions at the device edge, together with the unidirectional diffusion of skyrmions from the hot region towards the cold region were experimentally observed. These thermally generated skyrmions can be further electrically detected by measuring the accompanied anomalous Nernst voltages. These results could open another exciting avenue for enabling skyrmionics, and promote interdisciplinary studies among spin caloritronics, magnonics and skyrmionics.
[1] W. Jiang, et al., Science, 349, 283 (2015).
[2] W. Jiang, et al., Nature Physics,13, 162 (2017).
[3] W. Jiang, et al., Physics Reports, 704, 1-49 (2017).
[4] J. Zázvorka et al. Nature Nanotechnology 14, 658-661 (2019).
[5] L. Zhao, et al., Phys. Rev. Letts. 125，027206 (2020).
[6] Z. Wang, et al., Nature Electronics, 3,672-679 (2020).

Off-axis electron holography is a powerful technique, which can be used to record the phase shift of an electron wave that has passed through an electron-transparent specimen in a transmission electron microscope. According to the Aharanov-Bohm equation, the phase shift is sensitive to local variations in electromagnetic potential, which are in turn dependent on nanoscale properties of a specimen of interest, such as charge density or magnetization. The determination of such properties from a recorded phase image is an ill-posed problem that is difficult to tackle. We have developed a model-based iterative reconstruction technique, which can be used to retrieve the projected in-plane magnetization distribution from the magnetic contribution to a recorded phase image, or alternatively the three-dimensional magnetization distribution from a set of at least two tilt series of magnetic phase images. The technique is based on the optimized implementation of a forward model, which maps a given magnetization distribution onto one or more phase images. The forward model utilizes sparse matrix multiplications for efficient projections and Fourier-transform-based convolutions with pre-calculated convolution kernels based on analytical solutions for the magnetic phase images of simple geometrical objects. The ill-posed problem is tackled by replacing the original problem by a least squares minimization, which is augmented by regularization techniques to find a solution for the reconstructed magnetization distribution. Tikhonov regularization of first order is used to apply smoothness constraints to the magnetization, which is justified by the minimization of exchange energy. A priori information about the positions and sizes of magnetic objects in the field of view are utilized in the form of a three-dimensional mask, which reduces the number of unknowns to be retrieved. The model-based approach is flexible and can account for arbitrary linear phase ramps and phase offsets, as well as for untrustworthy (low confidence) regions in input images. We have applied it successfully to reconstruct in-plane (projected) magnetization distributions from individual experimental magnetic phase images and three-dimensional magnetization distributions from tilt series of phase images. Diagnostic measures, which are based on optimal estimation theory, have been used to analyze the quality of the reconstruction results. The influence of the regularization strength has been assessed, in order to obtain the best solution in the presence of noise and other artefacts.

In order to visualize the magnetization distributions of Bloch-type magnetic skyrmions in three dimensions, we have used model-based iterative recosntruction to study patterned FeGe nanostructures that host individual skyrmions in the absence of applied magnetic fields, allowing tomographic tilt series of off-axis electron holograms to be recorded. We have also identified novel superstructures of skyrmion strings in thin films of chiral magnets that form characteristic patterns in phase images recorded using off-axis electron holography.

In order to visualize the magnetization distributions of Néel-type skyrmions that are stable at room temperature, we have studied perpendicularly-magnetized multilayers of heavy metals and ferromagnets sputtered on SiN membranes by tilting the sample with respect to the incident electron beam direction in the presence of applied magnetic fields and compared experimental phase images with simulated phase images derived from atomistic models. Furthermore, we have studied two-dimensional magnetic materials, which possess strong perpendicular magnetocrystalline anisotropy and show Néel-type skyrmion bubbles after field cooling.

The main origin of the chiral symmetry breaking in magnetic materials is associated with the intrinsic Dzaloshinskii-Moriya interaction (DMI). At present, tailoring of DMI is done rather conventionally by optimizing materials, either doping a bulk single crystal or adjusting interface properties of thin films and multilayers. A viable alternative to the conventional material screening approach can be the exploration of the interplay between geometry and topology. The research field in magnetism, which is dealing with the study of the impact of geometrical curvature on magnetic responses of curved 1D wires and 2D shells is known as curvilinear magnetism [1]. The perspective of the development of curvilinear magnetism is outlined in the 2017 and 2020 Magnetism Roadmaps [2,3]. In this presentation, we will discuss on the recent achievements in the field and address the following topics:
A fully 3D approach to treat curvilinear effects in ferromagnetic nanowires and thin shells of arbitrary shape is established by Gaididei et al. back in 2014 [4] and was recently extended by Sheka et al. [5] to properly account for effects of non-locality due to the presence of long-range magnetostatic interaction. Volkov et al. has proven that the exchange-driven chiral effects in curvilinear ferromagnets are experimental observables [6] and can be used to realize nanostructures with tunable magnetochiral properties from standard magnetic materials.
In contrast to the intrinsic DMI, a concept of mesoscale Dzyaloshinskii-Moriya interaction was put forth, which is a result of the interplay between the intrinsic (spin-orbit-driven) and extrinsic (curvature-driven) DMI terms [7]. The mesoscale DMI governs the magnetochiral properties of any curvilinear ferromagnetic nanosystem and depends both on the material and geometrical parameters. Its strength and orientation can be tailored by properly choosing the geometry, which allows stabilizing distinct magnetic chiral textures including skyrmion and skyrmionium states as well as skyrmion lattices [8-10]. Interestingly, skyrmion states can be formed in a material even without an intrinsic DMI [8,10].
Sheka et al. [5] discovered a novel non-local chiral symmetry breaking effect, which does not exist in planar magnets: it is essentially non-local and manifests itself even in static spin textures living in curvilinear magnetic nanoshells. To identify this new interaction, a generalized micromagnetic theory of curvilinear ferromagnets was constructed accounting for local and nonlocal effects. The curvature leads to the emergence of the new magnetostatic charge, the geometrical charge, determined by the local characteristics of the surface. This newcomer is responsible for the appearance of novel fundamental chiral symmetry breaking effect.
The field of curvilinear magnetism was recently extended towards curvilinear antiferromagnets. Pylypovskyi et al. [11] demonstrated that intrinsically achiral one-dimensional curvilinear antiferromagnet behaves as a chiral helimagnet with geometrically tunable DMI, orientation of the Neel vector and the helimagnetic phase transition. This positions curvilinear antiferromagnets as a novel platform for the realization of geometrically tunable chiral antiferromagnets for antiferromagnetic spinorbitronics.

[1] Streubel et al., J. Phys. D: Appl. Phys. 49, 363001 (2016).
[2] Sander et al., J. Phys. D: Appl. Phys. 50, 363001 (2017).
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NV-center magnetometry emerges as a powerful technique to investigate complex magnetic textures at the nanoscale under ambient conditions. It makes use of the response to magnetic field of the single spin of an NV-center [1], which is a defect in the crystalline structure of diamond consisting of a nitrogen atom and a vacancy. We demonstrate here its imaging capabilities both on ferromagnetic skyrmions stabilized at zero external field and on antiferromagnetic domain walls and skyrmions in a synthetic antiferromagnet.

To observe non-collinear textures in ferromagnets, we operate the NV magnetometer in photoluminescence quenching mode, allowing the detection of stray field producing areas by measuring the spatial variations of the emitted NV center photoluminescence. In addition, the use of a diamond probe ensures that the experiment is carried out in the absence of external magnetic perturbation. To illustrate this, we show that skyrmions with a diameter about 60 nm [2] are stabilized by the exchange bias coming from the interface between the antiferromagnet IrMn and the ferromagnet NiFe in an optimized Pt/Co/NiFe/IrMn stack.

In addition to ferromagnets, antiferromagnets have recently attracted a great interest in spintronics owing to the robustness of their magnetic textures and their fast dynamics. However, since they exhibit no net magnetization, antiferromagnets are challenging to work with. Therefore, we introduce a new imaging mode of the scanning NV-center microscope which does not rely on the measurement of the static magnetic stray field but on the detection of magnetic noise originating from spin waves inside the non-collinear antiferromagnetic textures of interest. The presence of magnetic noise accelerates the NV spin relaxation. As a consequence, the emitted photoluminescence is reduced, allowing a simple detection of the noise sources [3].

We demonstrate this new technique on synthetic antiferromagnets [4] consisting of two ferromagnetic Co layers antiferromagnetically coupled through a Ru/Pt spacer. We first image domain walls and prove that we perform noise-based imaging by measuring a shorter NV spin relaxation time above an antiferromagnetic domain than above a domain wall. Calculations of the spin waves dispersion both in the antiferromagnetic domains and in the domains walls as well as maps of simulated magnetic noise intensity enable us to conclude that the noise which we probe arises from spin waves channelled in the domain walls.

Going further, we tune the composition of the synthetic antiferromagnet stacks in order to stabilize spin spirals or antiferromagnetic skyrmions. In both cases, our relaxometry-based technique is able to image the non-collinear structures, demonstrating its efficiency and opening new avenues of exploration in the characterization of complex structures in magnetically-compensated materials.

This work was done in collaboration with Spintec in Grenoble, France, the Unité Mixte de Physique CNRS/Thalès in Palaiseau, France and the Center for Nanoscience and Nanotechnology (C2N) in Palaiseau, France. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 846597 and from the DARPA TEE Program.

[1] L. Rondin et al, Rep. Prog. Phys 77, 056503 (2014)
[2] K. Gaurav Rana et al, Phys. Rev. Appl., 13, 044079 (2020)
[3] A. Finco et al, arXiv:2006.13130 (2020)
[4] W. Legrand et al, Nat. Mater., 19, 34 (2020)

For temperatures in the range between ca. 28 and 29 K and for magnetic fields of about 0.16 − 0.21 T, the itinerant magnet MnSi features a vortex-like skyrmion order [1] of its electron spins. The study of the structure of magnetic skyrmions has generated much experimental and theoretical interest since its discovery over ten years ago. Here, we present the first comprehensive study of the dynamics of the skyrmion phase.

MnSi's non-centrosymmetric space group has profound consequences for dynamics in all ordered magnetic phases of MnSi. Namely, it introduces a Dzyaloshinskii-Moriya term which leads to magnon creation at energies that are different from those for magnon annihilation, with this phenomenon being restricted to reduced momentum transfers whose vector q has components perpendicular to the skyrmion plane. The dynamical magnetic structure factor S(q, E, H), with q = Q - G and lattice vector G, thus becomes asymmetric ("non-reciprocal") with respect to changing the sign of either q, the energy transfer E, or the magnetic field H, but is symmetric upon interchanging the signs of any two of these variables. Such an asymmetric behavior could so far also be observed for the field-polarized [2, 3], the paramagnetic [4] and the conical [5,6] phase of MnSi.

For our recently completed study [7] we fully mapped out the magnetic dynamics in the skyrmion phase of MnSi. To that end, we employed polarized triple-axis, time-of-flight and spin-echo experiments. Apart from an in-depth analysis of the non-reciprocal dynamics, we succeeded in observing a splitting of the magnon energies into closely-spaced Landau levels for momentum transfer vectors inside the skyrmion plane. Theoretically, we describe our results using a mean-field linear spin-wave model. A correction of the theory for instrumental resolution yields an excellent quantitative agreement between experiment and theory.

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[6] T. Weber, J. Waizner, P. Steffens, A. Bauer, C. Pfleiderer, M. Garst, and P. Böni; Phys. Rev. B 100, 060404(R) (2019).
[7] T. Weber, D. M. Fobes, J. Waizner, P. Steffens, G. S. Tucker, M. Böhm, L. Beddrich, C. Franz, H. Gabold, R. Bewley, D. Voneshen, M. Skoulatos, R. Georgii, G. Ehlers, A. Bauer, C. Pfleiderer, P. Böni, M. Janoschek, and M. Garst; submitted (2020).

The oxide compounds containing iron are widely studied because of many interesting phenomena including charge disproportionation, spin polarization, and the magentoresistive effect. CaFe₂O₄ crystallizes in the orthorombic Pbnm structure which consists of distorted FeO₆ distorted octahedra through edge- and corner-sharing with intercalated Ca atoms. We have recently grown a large single crystal of CaFe₂O₄ by the optical floating-zone method. The two transitions T₁~240 K and T₂~200 K are observed in our magnetic susceptibility measurements. Our neutron powder diffraction reveals two competing magnetic phases, Γ6 and Γ3, at low temperatures which are distinguished by their c-axis stacking of ferromagnetic b-axis stripes. Γ6-type magnetic phase develops below 240 K that starts to reduce with the emergence of Γ3-type magnetic phase below 200 K. The detailed magnetoresistance measurements in different crystal orientations will also be discussed in the presentation.

In superconductivity, colossal magnetoresistance, and multiferroism, emergent phenomena arise from the interplay of various degrees of freedom and competing phases that drive nanoscale complexity (i.e., chemical, ionic, electronic, etc. variations) that can be readily controlled using external stimuli and can result in colossal changes in physical responses. Leveraging advances in ab initio design, atomically precise synthesis, and multi-modal characterization of materials researchers can now induce such competition in an on-demand fashion and probe the resulting order in ways never imagined before. While non-trivial topological magnetic textures such as skyrmions have generated particular interest due to their topological protection and their potential for use in memory applications, similar effects in ferroelectrics were not expected. Such topologically protected structures or concomitant topological-phase transitions in ferroelectric were thought to be unlikely because the primary order parameter is strongly coupled to the lattice distortion and thus continuous evolution of the order parameter would result in a large elastic-energy cost. But advances in materials heterostructuring, superlatticing, nanostructuring, etc. are now opening the door to previously unexpected effects – including the observation of novel structures reminiscent of topological structures in magnetic systems in such polar materials.

Here we will summarize and highlight recent advances in the study of ferroelectric/dielectric superlattices such as (PbTiO₃)_n/(SrTiO₃)_n, wherein unit-cell-level control enables one to place the Landau, electrical, elastic, and gradient energies into competition which drives the formation of topologically non-trival structures including so-called polar vortices and skyrmions. We will introduce and explore a number of aspects of these systems, including: the fundamental nature of the features that can be produced and the mechanisms behind their formation, routes to tune the morphology of the emergent structures to produce both polar vortices and skyrmions with a skyrmion number of +1, observations of phase coexistence (mediated by a first-order phase transition) between such emergent, non-trivial phases and trivial ferroelectric phases, the potential for the formation of a novel multi-order-parameter state which belongs to a class of gyrotropic electrotoroidal compounds, the realization of electric-field control of such mixed-phase systems which permits interconversion between the non-trivial emergent states and trivial ferroelectric phases concomitant with order of magnitude changes in piezoelectric and nonlinear optical responses, the potential for a non-classical, BKT-like topological phase transition in these materials, electric-field and light susceptibilities, the potential for exotic dielectric phenomena, and much more. All told, this work will provided a primer on this growing field, highlight similarities and differences with the magnetic community, and show how multi-modal approaches are rapidly rewriting our understanding of this class of materials.

The scarcity of bulk materials capable of hosting (anti)skyrmions over a wide range of ambient temperatures remains one of the most substantial obstacles to moving from proof-of-concept experiments to practical skyrmion-based devices. We have recently demonstrated that achieving a wide temperature range for skyrmion stability requires moving from the cubic symmetry seen in conventional bulk skyrmion hosts, to uniaxial symmetries[1], alongside ensuring a high Curie temperature. Several high-temperature antiskyrmion host materials consistent with these criteria have been experimentally reported within the family of inverse Heusler alloys[2,3]. We report a comprehensive computational exploration of the inverse Heusler family of compounds in search of synthesizable compositions capable of hosting antiskyrmions and other helimagnetic phases over a wide range of temperatures near ambient conditions. We develop a universal model connecting the chemical, structural, and magnetic phase stability of these alloys, building from first-principles calculations of their structure, to finite temperature and mesoscale behavior. While very few ordered ternary inverse Heuslers may host antiskyrmions, we identify an abundance of disordered quaternary inverse Heusler alloys that are likely to support these magnetic phases, in addition to those previously reported. These results establish the first set of rational design criteria for engineering thermally-robust topological magnetism, and identify a number of promising chemical spaces for experimental exploration.

[1] Kitchaev, D. A., Schueller, E. C., Van der Ven, A. Physical Review B, 101(5), 054409. (2020)
[2] Nayak, A. K., Kumar, V., Ma, T., et al. Nature, 548(7669), 561-566. (2017)
[3] Jena, J., Stinshoff, R., Saha, R., et al. Nano letters, 20(1), 59-65. (2019)

Tetragonal Heusler compounds that lack inversion symmetry was shown to stabilize an antiskyrmion lattice, even above room temperature. Recently, multiple distinct Skyrmion states have been proposed to emerge in the Heusler ferromagnetic metal Mn_1.4PtSn. The compound displays a transition from A.S.K. to Bloch-type Skyrmions, as seen from Lorentz transmission electron microscope results, placing Mn_1.4PtSn in a select category. This Heusler compound forms in a superstructure with the D_2d symmetry, which allows for an anisotropic Dzyaloshinskii-Moriya interaction (D.M.I.) perpendicular to the tetragonal axis. We use density functional theory calculations of Mn_1.5XY and Mn₂XY to extract the relevant exchange interactions that determine the rich phase diagrams in these materials. The exchange interactions are between the comparatively large moments on the Mn atoms ~4 μ_B, which show magnetic states that are ferrimagnetic non-collinear up to the spin reorientation. The D.M.I. and anisotropy's primary source is the X ion, either Rh, Pd, Ir, or Pt, which also influences the exchange interactions. The Fermi level can be tuned by the Y ion, either In, Sn or Sb. The interplay of these microscopic exchange interactions leads to a rich phase diagram that can display distinct skyrmion phases in external fields.
The Topological Hall effect (THE), a direct measurement of the topological magnetic excitations in conductive compounds, has proven a subject in detecting Skyrmion lattice phases. We calculate the anomalous Hall effect and topological Hall effects in these regimes to capture the electronic structure's influence on the Berry curvature. Here we report new insights of the magnetotransport, which is compared to experimental findings in the magneto-optical Kerr effect, magnetic force microscopy studies, ferromagnetic resonance, specifically in the intriguing magnetic properties of Mn_1.4PtSn. We show how the contribution of Skyrmions can be detected in transport devices. Our results provide evidence for the existence of antiskyrmions and ferrimagnetic in-plane Skyrmions depending on a wide range of temperatures and the orientation of an external magnetic field. These findings lead to a unique possibility to stabilize distinct skyrmions and for detection by all-electrical means.

Nanostructured platform for materials with real space (magnetic skyrmion) and momentum space (Weyl fermions) topological features could enable efficient memory and quantum computing devices. We have developed “bottom-up” chemical vapor deposition (CVD) techniques to synthesize single-crystal nanostructures of non-centrosymmetric cubic B20 FeGe (magnetic skyrmion host) and CoSi (Weyl semimetal). Magnetic skyrmions are depicted as two-dimensional spin texture, in reality, they possess a three-dimensional structure of skyrmions that looks like elongated strings extending throughout the thickness of the sample. We report the creation and annihilation of skyrmion strings in FeGe nanostructures under in-plane magnetic field (H_||) using magnetotransport and defocused Lorentz transmission electron microscopy (LTEM) detection techniques for the first time. Unusual asymmetric and hysteretic magnetoresistance (MR) features are observed during magnetic phase transitions within the skyrmion strings stability regime when H_|| is along the nanostructure’s long edge, which increase the sensitivity of MR detection. On the other hand, CoSi are found to possess unconventional chiral fermions with higher Chern number and chirality dependent band dispersion. We synthesized novel merohedral twinned nanowires of Weyl semimetal that could possess a topological defect (exhibits spontaneous symmetry breaking) connecting/separating two enantiomeric atomic arrangements inside the crystal itself. We discuss here the notable synthesis results, experimental techniques, and challenges to explore the topological nature of magnetic and electronic structures in nanostructure morphology.

Topological skyrmions and antiskyrmions have attracted enormous attention due to their different emergent phenomena and potential applications to spintronics. In this talk, we will present the real-space observations of skyrmions/antiskyrmions and their transformation in two kinds of non-centrosymmetric magnets^[1,2] by Lorentz transmission electron microscopy. We will show the stability and manipulation of the square-shape antiskyrmions in a square lattice and elliptically-deformed skyrmions with opposite helicities as determined by the interplay of magnetic dipole interaction and anisotropic Dzyaloshinskii–Moriya interaction. We then show that their topological nature, such as topological charge, helicity, and lattice form, is highly controllable by manipulating the in-plane and out-of-plane magnetic fields, temperature, and thickness, etc..

References:
[1] L. C. Peng, R. Takagi, W. Koshibae, K. Shibata, K. Nakajima, T. Arima, N. Nagaosa, S. Seki, X. Z. Yu and Y. Tokura. Nat. Nanotech. 15, 181-186 (2020)
[2] K. Karube*, L. C. Peng*, J. Masell, X. Z. Yu, F. Kagawa, Y. Tokura & Y. Taguchi, submitted (2020) (*equally contributed)

We report on the inductor function as designed and realized via emergent electromagnetic field (EEMF) in metallic magnets with helical spin orders. An inductor is one of the most fundamental circuit elements for modern electronic device. The magnitude of such a conventional inductance is proportional to the volume of an inductor’s coil, which is known as a hardly-solvable hindrance to miniaturization of inductors. Here, we demonstrate an inductance of quantum-mechanical origin, that is originating from the emergent electric field induced by current-driven dynamics of spin helices in a magnet. In microscale rectangular-shaped devices of a magnet with nanoscale spin helices, e.g. Gd₃Ru₄Al₁₂, we observed that the inductance is prominently enhanced in spin helically-modulated phases, showing a typical inductance value (L) as large as sub micro-henry for the device whose volume is ~10^-6 times smaller than the inductor available at present. The observed inductance is enhanced by the nonlinearity in current and shows non-monotonous frequency dependence, both of which result from the current-driven dynamics of the spin-helix structures. We discuss the possibility of the highly inductive helimagnets working beyond room temperature as a most distinct outcome of EEMF in quantum materials.

When a magnetic insulator is subject to a temperature gradient, an effective magnon current flows from the hot to the cold side of the sample. It was theoretically proposed that this magnon current exerts a torque on the magnetization, similar to a spin-transfer torque in a bulk magnet, which can move magnetic skyrmions towards the source of heat [1,2,3].
I will present recent experimental observations which confirm the directed motion of skyrmions in the chiral magnetic insulator Cu₂OSeO₃ when a heat gradient is applied. The experimentally observed skyrmion velocity is in qualitative agreement with our theoretical predictions. Moreover, our theoretical analysis predicts an enhancement of the magnon current at the phase transition from a conical to a field-polarized background. The embedding phase is therefore expected to have a strong impact on the motion of skyrmions in a thermal gradient, including a critical speed-up at the aforementioned phase transition, which I will discuss in this presentation.

[1] L. Kong and J. Zang, Phys. Rev. Lett. 111, 067203 (2013)
[2] A. A. Kovalev, Phys. Rev. B 89, 241101(R) (2014)
[3] S.-Z. Lin, C. D. Batista, C. Reichhardt, and A. Saxena, Phys. Rev. Lett. 112, 187203 (2014)

Exotic topological spin textures¹⁾ and their dynamics attract much attention to fundamental physics²⁾ and applications to novel electron-devices³⁾ owing to their topological nature and emergent electromagnetic properties. Here, I will present how to control, drive and manipulate nanometer-scale topological spin textures and their lattice forms, such as (anti) skyrmion, (anti) meron and their transformations between antiskyrmions and skyrmions, merons and skyrmions, and transformations of their lattice forms between square lattice (sq.-ML) and triangular lattice (hex-SkL), with finely tuning the external magnetic field in several magnets^4-6) with non-centrosymmetric crystalline structure. On the other hand, the minute (atomic-scale) skyrmions have been successfully manipulated in centrosymmetric magnets with Ruderman–Kittel–Kasuya–Yoshida (RKKY)-type electronic coupling^7-8). To manipulate and track individual skyrmions and its lattice form using a relatively low electric current, we make a microdevice composed a thin helimagnet of FeG with a small notch⁹⁾, which allowed the spin current to be localized in a specific area near the corner of the notch. Drift, Hall and torque motions of single 80-nm-size skyrmions and their clusters are tracked with directional current at low current density, a thousand times weaker than those used in that for drives of magnetic domain walls.

These works were done in collaborations with Profs. Yoshinori Tokura, Naoto Nagaosa, Masashi Kawasaki, Taka-hisa Arima, Yusuke Tokunaga, Shinichro Seki and Masahiko Mochizuki and Drs. Tasujiro Taguchi, Fumitaka Kagawa, Max Hirschberger, Wataru Koshibae, Naoya Kanazawa, Kosuke Karube, Jan Masell, Licong Peng, Fehmi Yasin, Khanh Nguyen Daisuke Morikawa, Masao Nakamura, Kiyou Shibata, and Rina Takagi.

References:
¹⁾ X. Z. Yu, J. Masell, et al., Nano Lett. 20, 7313 (2020)
²⁾ N. Nagaosa and Y. Tokura, Nat. Nanotechnol. 8, 899 (2013).
³⁾ W. Legrand, Nat. Mater. 19, 34 (2020).
⁴⁾ L.C. Peng, et al., Nat. Nanotechnol. 15, 181 (2020)
⁵⁾ F. Yasin, Adv. Mater. (2020) DOI: 10.1002/adma.202004206
⁶⁾ X. Z. Yu, et al., Nature 564, 95 (2018)
⁷⁾ M. Hirschberger, et al., Nat. Commun. 10, 5831 (2019)
⁸⁾ K. Nguyen, et al., Nat. Nanotechnol. 15, 444 (2020)
⁹⁾ X.Z. Yu, et al., Sci. Adv., 6, eaaz9744 (2020)

As the charge carriers in 3D materials are not confined and free to move in all spatial dimensions, Quantum Hall Effect (QHE) in 3D is rare and it is relatively unexplored in experiments due to the limited choice of viable candidate materials. Here, we report on the observation of weak antilocalization (WAL) and QHE followed by Shubnikov de-Haas (SdH) oscillations with oscillation frequency 314 T and effective mass in bulk CaCuSb single crystal. It crystallizes in the hexagonal structure (P6₃/mmc). One of the unique features of this crystal structure is to possess two Cu-Sb layers in the unit cell that act as the conduction channels. Significant anisotropy in electrical transport measurements along crystallographic a- and c- direction suggests that magneto-transport effect is due to charge diffusion on Cu-Sb planes but not along c- axis. A cusp like behavior in the low field region of magnetoresistance reveals WAL in this compound, as observed in ABC- type hexagonal structure CaAgBi ^[1]. Magnetoconductance (MC) follows 2D scaling law as reflection of merging MC data as a function of normal component of magnetic field for different angles. Quantized Hall plateaus are observed in the 1/ρ_xy vs 1/B plot are attributed to the multiple 2D conduction channels in the system. The first-principles calculations show that CaCuSb is a semimetal with dominant hole carriers at the Fermi level. Our study shows that CaCuSb can provide a unique platform to study QHE in high magnetic fields.

Reference:
[1] Souvik Sasmal et al., J. Phys.: Condens. Matter 32, 335701 (2020)

Magnetic skyrmions are topologically distinct spin textures and can be stable with quasi-particle like behavior.¹ This makes them interesting for information technologies,² where data is envisioned to be encoded in topological charges, instead of electronic charges as in conventional semiconducting devices. Using magnetic multilayers we demonstrated that inhomogeneous charge currents allow the generation of skyrmions at room temperature in a process that is remarkably similar to the droplet formation in surface-tension driven fluid flows.³ Micromagnetic simulations reproduce key aspects of this transformation process and suggest a second mechanism at higher currents that does not rely on preexisting magnetic domain structures.⁴ Indeed, we demonstrated this second mechanism experimentally using non-magnetic point contacts.⁵ Using this approach, we demonstrated that the topological charge gives rise to a transverse motion on the skyrmions, i.e., the skyrmion Hall effect.⁶ Finally, I will provide an outlook on dynamic excitations of magnetic skyrmions.^7,8

This work was supported by the U.S. Department of Energy, Office of Science, Materials Sciences and Engineering Division and by NSF through I-MRSEC.

References:
1. W. Jiang, et al., Phys. Rep. 2017, 704, 1–49.
2. A. Hoffmann and S. D. Bader, Phys. Rev. Appl. 2015, 4, 047001-1–047001-18
3. W. Jiang, et al., Science 2015, 349, 283–286.
4. O. Heinonen, et al., Phys. Rev. B 2016, 93, 094407-1–094407-6.
5. Z. Wang, et al., Phys. Rev. B 2019, 100, 184426-1–184426-9.
6. W. Jiang, et al., Nature Phys. 2017, 13, 162–169.
7. M. Lonsky and A. Hoffmann, Phys. Rev. B 2020, 102, 104403-1–104403-11.
8. M. Lonsky and A. Hoffmann, APL Mater. 2020, 8, 100903-1–100903-12.