United States

The spin nematic phase, which is a kind of multipole phases, has attracted a lot of interest in the field of the strongly correlated electron systems, as well as the quantum spin liquid phase. Using the numerical exact diagonalization, the density matrix renormalization group (DMRG) calculation, and the finite-size scaling analysis, it is found that some spin nematic and spin liquid phases are induced by external magnetic field in the anisotropic and frustrated quantum spin systems. In our previous work[1], it was found that a field-induced nematic phase appears at some critical field in the anisotropic spin ladder. The nematic phase is characterized by the power-law decay in the correlation function of the second-order spin moment. In addition at some higher critical field a quantum phase transition can occur to the conventional field-induced Tomonaga-Luttinger liquid. Several typical magnetization curves calculated by DMRG are presented. Recently the field-induced nematic phase was observed on the frustrated spin ladder system[2]. So we studied on a frustrated spin ladder system[3], using the numerical diagonalization and DMRG. As a result, it was found that several exotic quantum phases, including the spin-nematic liquid phase. We also reported several interesting phase diagrams of this model and some related systems[4,5]. In the present paper, we investigate the S=1 antiferromagnetic chain with the biqadratic interaction, as another candidate that exhibits the field-induced spin nematic liquid pahse. The numerical diagonalization study of finite-size clusters indicates that the spin nematic liquid pahse appears in this model under sufficiently strong magnetic field. The phase diagram in the plane of the magnetic field and the biquadratic interaction is presented.References: [1] T. Sakai, T. Tonegawa and K. Okamoto, Physica Status Solidi B 247, 583 (2010) . [2] N. Buttgen et al., Phys. Rev B 90, 134401 (2014) . [3] T. Hikihara, T. Tonegawa, K. Okamoto and T. Sakai, J. Phys. Soc. Jpn. 86, 054709 (2017). [4] T. Tonegawa, T. Hikihara, K. Okamoto, S. C. Furuya, and T. Sakai, J. Phys. So. Jpn. 87, 104002 (2018). [5] T. Sakai, K. Okamoto and T. Tonegawa, Phys. Rev. B 100, 054407 (2019) 

MMM 2020

Quantum Spin Nematic Liquid in the S=1 Antiferromagnetic Chain with the Biquadratic Interaction

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Cylindrical magnetic nanowires (CNWs) are promising candidates for the building blocks of 3D information technologies such as shift registers, magnetic recording, spintronics and logic gates1-4. Spin-polarized-current is an energy efficient way to excite magnetization dynamics in planar nanostructures. However, in CNWs this research is doing its first steps5. Magnetization dynamics in a CNW of Permalloy, 100 nm diameter and 1 µm length, is investigated under simultaneous application of electric current and magnetic field by micromagnetic simulations. The magnetization reversal process initiates with the creation of open vortex structures with different rotation senses at the nanowire ends. We conclude that the electric current by itself enlarges or reduces the length of these vortex structures according to the rotational sense of the associated Oersted field. Large enough current densities produce a vortex structure which covers the whole nanowire surface. At the same time, the magnetization in the very core of the nanowire remains the same, i.e. no complete magnetization reversal is possible in the absence of external magnetic field. The simultaneous action of the applied electric current and magnetic field allows the complete control of the vortex structures in terms of setting the polarity and vorticity. The resulting diagram of magnetic states obtained after the application of field and electric current showing the values required for the vorticity and axial magnetization switching is presented in Figure 1. This control is essential for future information technologies based on 3D vertical nanostructures. The presented state diagram will become useful for future experiments on current-induced domain wall dynamics in CNWs.References: 1. S. Parkin and S.-H. Yang, Nature Nanotechnology., Vol. 10, pp. 195 (2015). 2. F. Nasirpouri, et al., Scientific Reports., Vol. 9, pp. 9010 (2019). 3. S. Ruiz-Gómez et al., Scientific Reports., Vol. 8, pp. 16695 (2018). 4. J. Garcia et al., Journal of Magnetism and Magnetic Materials., Vol. 383, pp. 88 (2015). 5. M. Schöbitz et al., Physical Review Letters Vol. 123, pp. 217201 (2019). 

Control of Vortex Structures in Individual Cylindrical Magnetic Nanowires by Simultaneous Action of Applied Magnetic Field and an Electric Current

The behavior of any physical system is governed by the order parameter, determined by the geometry of the physical space of the object, namely their dimensionality and curvature. Usually, the effects of curvature are identified using local interactions only, e.g. local spin-orbit- or curvature-induced Rashba and Dzyaloshinskii-Moriya interactions in condensed matter [1]. Lack of the framework, involving both, local and non-local interactions impedes the description of the essentially micromagnetic textures like magnetic domains, skyrmion-bubbles and vortices. Here, we present a micromagnetic theory of curvilinear ferromagnetic shells [2]. New chiral effects, originating from the magnetostatic interaction, can appear in such systems. They manifest themselves even in statics and are essentially nonlocal. This is in contrast to conventional Dzyaloshinskii--Moriya interaction (material intrinsic or curvature-induced, stemming from the exchange). The physical origin is in a non-zero mean curvature of a shell and non-equivalence between the top and bottom surfaces of the shell. To describe the new effects, we split a conventional volume magnetostatic charge into two terms: (i) magnetostatic charge, governed by the tangent to the sample's surface, and (ii) geometrical charge, given by the normal component of magnetization and the mean curvature. We classify the interplay between the symmetry of the shell, its local curvature and magnetic textures and apply the proposed formalism to analyze magnetic textures in corrugated shells with perpendicular anisotropy.References: [1] R. Streubel, J. Lee, D. Makarov et al, J. Phys. D, 49, 363001, (2016); [3] O. V. Pylypovskyi, D. D. Sheka, V. P. Kravchuk et al, Sci. Rep. Vol. 6, p. 23316 (2016); O. M. Volkov, D. D. Sheka, Y. Gaididei et al, Sci. Rep. Vol. 8, p. 866 (2018). [2] D. D. Sheka, O. V. Pylypovskyi, P. Landeros et al., Comm. Phys. 3, 128 (2019), DOI:10.1038/s42005-020-0387-2 

Magnetostatics-Induced Symmetry Breaking Effects in Curvilinear Shells

Ferromagnetic nanotubes generate continuous interest due to non-collinear spin structures which are tailored by the curvature of the ferromagnetic film [1]. If arranged vertically on a chip [2], they allow for high-density arrays and 3D device architectures in spintronics and magnonics. For their realization, coating of filamentary nanotemplates would be advantageous. However, conformal deposition of ferromagnetic metals is still a challenge. We report the fabrication of Ni nanotubes by atomic layer deposition (ALD) applied to single-crystalline semiconductor nanowires. We used nickelocene as a precursor, water as the oxidant agent and an in-cycle plasma enhanced reduction step with hydrogen. The optimized ALD pulse sequence, combined with a post-processing annealing treatment, allowed us to prepare 30 nm thick metallic Ni layers with a low resistivity of 8 μΩcm at room temperature and good conformality both on the planar substrates and nanotemplates [3]. We prepared several micrometer-long Ni nanotubes with diameters ranging from 120 to 330 nm. We report on the correlation between ALD growth and functional properties of individual Ni nanotubes characterized in terms of magneto-transport at room temperature and the confinement of spin wave modes explored by micro-focus Brillouin light scattering. For the relative variation of resistance R of a nanotube in small magnetic fields we find a value of up to 1.3 % which we attribute to the anisotropic magnetoresistance (AMR) effect. This value is larger by about 30 % compared to the best low-field AMR effect of Ni nanotubes studied previously [4,5]. In the ALD process applied to semiconductor nanowires in Refs. [4,5] the plasma enhancement of the hydrogen reduction step was not available. Together with the spin-wave resonances observed in the Ni nanotubes our findings promise Ni-based 3D device architectures for spintronic and magnonic devices prepared by ALD and operated in the GHz frequency regime. Funding by the German Science Foundation DFG via GR1640/5-2 in SPP1538 Spin caloric transport and SNF via grants 163016, BSCGI0157705, and NCCR QSIT is gratefully acknowledged.References: [1] R. Streubel, P. Fischer, F. Kronast et al., J. Phys. D: Appl. Phys., Vol. 49, p. 363001 (2016). [2] Y.-P. Wang, Z.-J. Ding, Q.-X. Liu et al, J. Mater. Chem. C, Vol. 4, p. 11059 (2016). [3] M.C. Giordano, K. Baumgaertl, S. Escobar Steinvall et al., ACS Appl. Mater. Interfaces (2020), https://doi.org/10.1021/acsami.0c06879. [4] D. Rüffer, R. Huber, P. Berberich et al., Nanoscale, Vol. 4, p. 4989 (2012). [5] D. Rüffer, M. Slot, R. Huber et al., APL Mater., Vol. 2, p. 076112 (2014). 

Nickel nanotubes with low resistivity and coherent magnetization dynamics for 3D spintronics and magnonics prepared by atomic layer deposition

This work describes a technique for 3D printing of magnetic materials at millimeter and sub-millimeter scales for microrobotic applications using stereolithography. Traditional fabrication techniques to engineer magnetic materials become very challenging at smaller scales. The need for rapid prototyping techniques using materials with tunable magnetic properties is becoming more important [1]. Unfortunately, additive manufacturing of magnets is still in its infancy [2-3]. Most reported techniques that are based on thermoplastic bonded magnets [4-5], filament extrusion [6], binder jetting [7], or laser sintering [8], have limitations for scaling down in size. A better path towards miniaturization is offered by stereolithography [9], as presented in this work. The presented technique combines magnetic particles (NdFeB, Fe or Fe3O4) with different mixing ratios to a flexible resin that is made from aliphatic urethane diacrylate, epoxy aliphatic acrylate and a photo-initiator (Irgacure 819 - Irgacure 184) [10]. 3D printed multi-material structures are presented in Fig. 1a. This work is motivated by the need to engineer complex magnetic field patterns for MEMS actuators [11-12] and micro/soft robotics (Fig. 1B) [13]. Magnetic moment was measured to evaluate dependence of saturation magnetization and coercivity with particle material and particle concentration (Fig. 2a). Torques and forces over printed samples were measured in response to external magnetic fields (Fig. 2b), demonstrating an ability to generate highly complex 3D structures for actuation at micro- to meso-scales.References: [1] G. Chatzipirpiridis et al., “3D Printing of Thermoplastic Bonded Soft and Hard Magnetic Composites: Magnetically Tuneable Architectures and Functional Devices,” Adv. Intell. Syst., vol. 1, no. 6, p. 1900069, 2019. [2] L. Li, B. Post, V. Kunc, A. M. Elliott, and M. P. Paranthaman, “Additive manufacturing of near-net-shape bonded magnets: Prospects and challenges,” Scr. Mater., vol. 135, pp. 100–104, Jul. 2017. [3] V. Popov, A. Koptyug, I. Radulov, F. Maccari, and G. Muller, “Prospects of additive manufacturing of rare-earth and non-rare-earth permanent magnets,” Procedia Manuf., vol. 21, no. March, pp. 100–108, 2018. [4] L. Pigliaru et al., “3D printing of high performance polymer-bonded PEEK-NdFeB magnetic composite materials,” Funct. Compos. Mater., vol. 1, no. 1, p. 4, Dec. 2020. [5] P. P. Wendhausen, C. H. Ahrens, A. B. Baldissera, P. D. Pavez, and J. M. Mascheroni, “Additive manufacturing of bonded NdFeB, process parameters evaluation on magnetic properties,” in 2017 IEEE International Magnetics Conference (INTERMAG), 2017, vol. 53, no. 11, pp. 1–1. [6] B. Khatri, K. Lappe, D. Noetzel, K. Pursche, and T. Hanemann, “A 3D-Printable Polymer-Metal Soft-Magnetic Functional Composite—Development and Characterization,” Materials (Basel)., vol. 11, no. 2, p. 189, Jan. 2018. [7] C. L. Cramer et al., “Binder jet additive manufacturing method to fabricate near net shape crack-free highly dense Fe-6.5 wt.% Si soft magnets,” Heliyon, vol. 5, no. 11, p. e02804, Nov. 2019. [8] C. V. Mikler et al., “Laser Additive Manufacturing of Magnetic Materials,” JOM, vol. 69, no. 3, pp. 532–543, Mar. 2017. [9] L. Lu, P. Guo, and Y. Pan, “Magnetic-Field-Assisted Projection Stereolithography for Three-Dimensional Printing of Smart Structures,” J. Manuf. Sci. Eng., vol. 139, no. 7, pp. 1–7, Jul. 2017. [10] D. K. Patel, A. H. Sakhaei, M. Layani, B. Zhang, Q. Ge, and S. Magdassi, “Highly Stretchable and UV Curable Elastomers for Digital Light Processing Based 3D Printing,” Adv. Mater., vol. 29, no. 15, p. 1606000, Apr. 2017. [11] A. P. Taylor, C. Velez Cuervo, D. P. Arnold, and L. F. Velasquez-Garcia, “Fully 3D-Printed, Monolithic, Mini Magnetic Actuators for Low-Cost, Compact Systems,” J. Microelectromechanical Syst., vol. 28, no. 3, pp. 481–493, Jun. 2019. [12] Y. Kim, G. A. Parada, S. Liu, and X. Zhao, “Ferromagnetic soft continuum robots,” Sci. Robot., vol. 4, no. 33, p. eaax7329, Aug. 2019. [13] J. J. Abbott, E. Diller, and A. J. Petruska, “Magnetic Methods in Robotics,” Annu. Rev. Control. Robot. Auton. Syst., vol. 3, no. 1, pp. 57–90, May 2020. 

Multimaterial and flexible 3D printed magnets with sub-millimeter resolution

The extension of nanomagnetism to three dimensions is proposed as an exciting route to study new physical effects, such as the emergence of new spin textures and magneto-chiral phenomena, with the prospective of being exploited in future technologies [1,2]. Whereas a significant amount of work has been so far devoted to simulating 3D nanostructures, its fabrication and characterization has proven to be very challenging, and very few of these systems have been experimentally investigated. Our group has been recently developing new fabrication and characterization methods specifically tailored for the study of 3D nanostructures, which made it possible to control the advanced motion of domain walls in 3D straight nanowires [3,4]. Here, we will present recent advances in this realm, which now enable us to create and probe nanomagnets with more complex 3D geometries. First, we will present recent work dedicated to the 3D printing of nanomagnets using Focused Electron Beam Induced Deposition (FEBID). Based on the effective FEBID continuum model [5] and proximity effect corrections, we have developed an algorithm with the capability of modelling the deposition and defining beam scanning patterns for arbitrary 3D geometries [6]. The algorithm performance has been demonstrated in different electron microscopes and precursor gases, allowing us to create 3D nanomagnets with a wide range of geometries directly from CAD files (see Fig. 1). Complementing nanofabrication, we will present a new Kerr magneto-optical setup with the ability to probe 3D magnetic nanostructures, by exploiting the dark-field MOKE (dfMOKE), a technique that we have recently developed [3]. The unprecedented flexibility of the system to characterize these newly accessible 3D geometries will be demonstrated, thanks to the combination of mobile optics and full-3D vector magnetic fields (see Fig. 2).References: [1] Fernández-Pacheco, A. et al. Nat. Commun. 8, 15756 (2017). [2] Streubel, R. et al. J. Phys. D. Appl. Phys. 49, 363001 (2016). [3] Sanz-Hernández, D. et al. ACS Nano 11, 11066–11073 (2017). [4] Sanz-Hernández, D. et al. Nanomaterials 8, 483 (2018). [5] Toth, M., Lobo, C., Friedli, V., Szkudlarek, A. & Utke, I. Beilstein J. Nanotechnol. 6, 1518–1540 (2015). [6] Skoric, L. et al. Nano Lett. 20, 184–191 (2020). 

Advanced fabrication and magnetometry of nanostructures with complex 3D geometries

A magnetic elastomer is a type of magneto-active smart material where a magnetic field induces a mechanical response. Several methods have been used to optimize performance by controlling the microstructure, such as magnetic annealing. Optimization can also be achieved by introducing anisotropy with Fused Deposition Modeling (FDM), a 3D-printing process that extrudes viscous material in 1D lines to create 2D layers which build to a 3D part. Indeed, FDM features have been shown to manipulate the magnetic anisotropy of rigid printed parts.1 However, printing flexible composite materials presents additional challenges with FDM. Here, FDM structures were printed with thermoplastic polyurethane (TPU) polymer and either 20wt% iron (Fe), 40wt% Fe, 40wt% carbonyl iron (CI), or 40wt% magnetite (Fe3O4/Mag). In order to determine the relative effect of different parameters on the magnetic properties, a series of structures were printed combining each material type (Fe-TPU, CI-TPU, Mag-TPU) with different aspect ratios (1:1 / 2:1), infill percentages (60% / 80% / 100%), and infill orientations (parallel/perpendicular to aspect ratio). A Vibrating Sample Magnetometer was used to obtain magnetic hysteresis loops for comparing magnetic susceptibility between samples. Results demonstrated that infill orientation had the largest effect on susceptibility, aspect ratio had the next greatest effect, and infill percentage had a more nuanced effect (Fig.1). This shows that FDM allows the magnetic anisotropy to manifest through mesoscale anisotropy of a part’s internal structure. These trends were found to form a continuum of tunable magnetic responses (Fig.2). Additionally, the chosen particulate transfers its unique magnetic signature to the composite material. Overall, the highly customizable and nuanced characteristics of 3D-printed magnetic elastomer structures will allow for its use in emerging magneto-mechanical applications such as magnetic actuation and soft robotics.References: 1. M. Patton, P. Ryan, T. Calascione, N. Fischer, A. Morgenstern, N. Stenger, and B. Nelson-Cheeseman, Additive Manufacturing, Vol. 27, 482-488 (2019) 


Controlling Magnetic Properties of 3D-Printed Magnetic Elastomer Structures via Fused Deposition Modeling

In geometrically frustrated magnetism, the very nature of the ground state of Tb2Ti2O7, has remained a long standing conundrum. In this pyrochlore material, no conventional spin-ice or long-range magnetic order is stabilized, even at very low temperatures [1]. Quantum fluctuations are suspected of being at the origin of such an exotic quantum phase, yet so far no complete description is available. Using neutron scattering [2] and synchrotron-based terahertz spectroscopy [3], it has been shown that spin/lattice couplings are present in form of hybrid Tb crystal-field / phonon modes that are present across a broad temperature range from 200 K down to 6 K. This so called vibronic process affects the electronic ground state that can no longer be described solely by electronic wave functions and involve quadrupolar degrees of freedom associated with the rare earth magnetic element in its local environnement. We present here new magneto-optical investigation of vibronic spin-lattice coupling effects. We apply a static magnetic field along the cubic <111> direction while probing with linearly polarized THz radiation. Through the Zeeman effect, the magnetic field enhances splitting within the low-energy Tb crystal field transitions revealing new details in our THz spectra. Complementary magneto-optical quantum calculations including quadrupolar terms show that indeed vibronic effects are required to describe our observations at 3 K. A further prediction of our theoretical model is the presence of a novel magneto-optical birefringence as a result of this vibronic process. Together, our results [4] reveal the significance of considering quadrupolar spin-lattice effects when describing the spin-liquid ground state of Tb2Ti2O7. They also highlight the potential for future magneto-optical investigations to probe complex materials where spin /lattice couplings are present and unravel new magneto-optical activity in the THz range.References: [1] J. S. Gardner, B. D. Gaulin, A. J. Berlinsky et al., Phys. Rev. B 64, 224416 (2001) [2] T. Fennell, M. Kenzelmann, B. Roessli et al., Phys. Rev. Lett. 112, 017203 (2014) [3] E. Constable, R. Ballou, J. Robert et al., Phys. Rev. B 95, 020415(R) (2017) [4] K. Amelin, Y. Alexanian, U. Nagel et al, to be published 

THz Magneto-Optical Investigation of Quadrupolar Spin-Lattice Effects in Magnetically Frustrated Tb2Ti2O7

The structural inversion symmetry plays an important role in low-dimensional nanomagnets, due to its strong influence on magnetic and electrical properties. It can lead to the appearance of chiral effects, such as the topological Hall effect [1], or to the formation of chiral noncollinear magnetic textures, as skyrmions [2] and chiral domain walls (DWs) [3]. These chiral structures can be the key components for realizing novel concepts for magnonics [4], antiferromagnetic spintronics [5], spin-orbitronics [6], and oxitronics [7]. So far, the main chiral symmetry breaking effect considered as being the origin for the presence of chiral noncollinear magnetic textures is the intrinsic Dzyaloshinskii-Moriya interaction (DMI) [8,9], which appears in certain magnetic crystals in which the unit cell lacks inversion symmetry, such as the gyrotropic magnetic crystals, or appear typically in ultrathin films or bilayers due to the inversion symmetry breaking on the film interface [3]. At present, tailoring of DMI is done 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. This interplay is of fundamental interest throughout many disciplines in condensed matter physics, including thin layers of superconductors [10] and superfluids [11], nematic liquid crystals [12], cell membranes [13], semiconductors [14]. In the emergent field of curvilinear magnetism chiral effects are associated to the geometrically broken inversion symmetries [15]. Those appear in curvilinear architectures of even conventional materials. There are numerous exciting theoretical predictions of exchange- and magnetostatically-driven curvature effects, which do not rely on any specific modification of the intrinsic magnetic properties, but allow to create non-collinear magnetic textures in a controlled manner by tailoring local curvatures and shapes [16,17]. Until now the predicted chiral effects due to curvatures remained a neat theoretical abstraction. Very recently, we provided the very first experimental confirmation of the existence of the curvature-induced chiral interaction with exchange origin in a conventional soft ferromagnetic material. It is experimentally explored the theoretical predictions, that the magnetisation reversal of flat parabolic stripes shows a two step process [18,19]. At the first switching event, a domain wall pinned by the curvature induced exchange-driven DMI is expelled leading to a magnetisation state homogeneous along the parabola's long axis. Measuring the depinning field enables to quantify the effective exchange-driven DMI interaction constant. The magnitude of the effect can be tuned by the parabola's curvature. It is found that the strength of the exchange-induced DMI interaction for the experimentally realised geometries is remarkably strong, namely ~0.4 mJ/m2, compared the surface induced DMI. The presented study legitimates the predictive power of full-scale micromagnetic simulations to design the properties of ferromagnets through their geometry, thus stabilising chiral textures. We explore these curvilinear magnetic thin films for the realization of novel artificial magnetoelectric materials based on curvilinear helimagnets embedded in piezoelectric matrix [20], to enable the geometrical tuning of the magnetochirality in curvilinear 1D architectures [21], tailoring of magnetic states in flat nanospirals [22] and as components of shapeable magnetoelectronics for interactive wearables [23].References: [1] N. Nagaosa, et al., Nature Nanotech. 8, 899 (2013) [2] U. K. Rößler, et al., Nature 442, 797 (2006) [3] A. Fert, et al., Nature Rev. Mat. 2, 17031 (2017) [4] A. V. Chumak, et al., Nature Physics 11, 453 (2015) [5] T. Jungwirth, et al., Nature Nanotech. 11, 231 (2016) [6] I. M. Miron, et al., Nature 476, 189 (2011) [7] V. Garcia, et al., Nature 460, 81 (2009) [8] I. Dzyaloshinsky, J. Phys. Chem. Solids 4, 241 (1958). [9] T. Moriya, Phys. Rev. Lett. 4, 228 (1960). [10] J. Tempere, et al., Phys. Rev. B 79, 134516 (2009) [11] H. Kuratsuji, Phys. Rev. E 85, 031150 (2012) [12] T. Lopez-Leon, et al., Nature Physics 7, 391 (2011) [13] H. T. McMahon, et al., Nature 438, 590 (2005) [14] C. Ortix, Phys. Rev. B 91, 245412 (2015) [15] Y. Gaididei, et al., Phys. Rev. Lett. 112, 257203 (2014) [16] J. A. Otálora, et al., Phys. Rev. Lett. 117, 227203 (2016) [17] V. P. Kravchuk, et al., Phys. Rev. Lett. 120, 067201 (2018) [18] O. Volkov et al., PRL 123, 077201 (2019). [19] O. Volkov et al., PSS-RRL 13, 1800309 (2019). [20] O. Volkov et al., J. Phys. D: Appl. Phys. 52, 345001 (2019). [21] O. Volkov et al., Scientific Reports 8, 866 (2018). [22] M. Nord, et al., Small 1904738 (2019). [23] J. Ge, et al., Nature Comm. 10, 4405 (2019).

Curvature-driven Chiral Effects in Nanomagnetism INVITED

The discovery of chiral spin textures such as domain walls, skyrmions, merons and bobbers, with their associated non-trivial topology and superior spintronic properties, is one of the most exciting landmarks in nanomagnetism and spintronics in recent years. Until now, these spin textures have been mostly realised by exploiting symmetry-breaking effects in non-centrosymmetric bulk crystals and synthetic ultra-thin film heterostructures. An emerging alternative route to the generation of chiral spin interactions is geometry [1]. In thin films, for example, curvature can provide the breaking of inversion-symmetry necessary for the generation of localized DMI-like spin interactions [2]. In this work, we employ state of the art 3D nanofabrication [3] to demonstrate the generation of complex chiral spin states using only geometrical effects, with no special material requirements. To do so, we fabricate an artificial magnetic double-helix system (Figure 1a) and perform magnetic X-ray microscopy [4]. This nanostructure is formed by two strongly-interacting strands (Figure 2) with dimensions comparable to fundamental magnetic lengths. By designing geometrical chirality, a wide variety of complex chiral 3D states is imprinted into the internal magnetization vector field. This includes helical magnetic domain walls (Figure 1b), vortex tubes and topologically-induced point-like structures [4]. In this presentation we will describe in detail how the topological mismatch caused by matching a left-handed and a right-handed double helix (See * in Figure 1a) leads to the generation of a localized Néel defect and the formation of an asymmetric vortex state [4]. These results showcase the power of using geometry for the localized generation of complex spin states, opening new paths for the study of non-trivial spin textures.References: [1] Streubel, R. et al. Journal of Physics D: Applied Physics 49.36 (2016): 363001. [2] Kravchuk, V. P., et al. Physical review letters 120.6 (2018): 067201. [3] Skoric, L. et al. Nano Letters 20.1 (2019): 184-191. [4] Sanz-Hernández, D., et al. arXiv:2001.07130 [cond-mat.mes-hall]

Creating and Interfacing Chiral Spin Textures Using 3D Geometries INVITED

When applied to C2V ferromagnetic/heavy metal interfaces, Moriya’s rules do not deterministically predict the orientation of interatomic DM vectors. Low-symmetry magnetic systems can exhibit both Rashba (DR) and Dresselhaus (DD) forms of the Dzyaloshinskii-Moryia interaction (DMI), as both spin-orbit couplings are generally present [1]. We assert that the spatial variation of the DM vectors—and thus that of the strength and direction of the effective DMI field—is determined by the DMI’s character (i.e., ||DD||/||DR||), as well as the unit cell’s aspect ratio [2]. Overall, the DMI is thus nominally anisotropic and hybridized—potentially stabilizing antiskyrmions and Bloch-Néel (i.e. mixed) skyrmions [2-3]. Ascertaining the existence and tunability of [anti]skyrmions in such systems is of technological interest and would elucidate the nature of DMI [2]. Employing the Wulff construction [3], ξ-vector formalism [4], and an augmented wall energy that accounts for DMI character, this work models the equilibrium shape and wall magnetization profile of bubble domains and skyrmions in thin films with C2v symmetry. We show that for sufficiently large DMI, square-shaped antiskyrmions are stable for certain DM vector orientations while lens- and oval-shaped mixed skyrmions are favored otherwise. A symmetry-breaking applied in-plane field stabilizes domain shapes resembling ovals and Reuleaux triangles. The impact of the unit cell’s aspect ratio, the DM vector’s orientation, and other material parameters on the shape of bubble domains and skyrmions are discussed. Moreover, our results reveal unusual relationships between faceting behavior and wall stiffness under rather reasonable conditions. Elucidating the interplay between the different effective fields present, we explore the validity of these results based on pedal plots, discontinuities in the magnetization profiles, and local extrema in the wall energy.References: U. Güngördü et al., Physical Review B., 93, 064428 (2016) M. Hoffman et al., Nature Communications., 8, 308 (2017) J. P. Pellegren, D. Lau, and V. Sokalski, Physical Review Letters., 119, 027203 (2017) A. A. Wheeler, Journal of Statistical Physics., 95, 1245–1280 (1999)

Energetics, equilibrium shape, and vorticity of skyrmions and antiskyrmions stabilized by the anisotropic Dzyaloshinskii-Moriya interaction in thin films with C2v symmetry

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