France



Since its early days, magnetic force microscopy (MFM) has become a truly widespread and commonly used characterization technique that has been utilised in a variety of fundamental and applied research and in industrial applications.&lt;br/&gt;In this work, we review the current state-of-the-art, analyse the challenges and outline the future of this fascinating field [1]. In comparison to other magnetic imaging techniques, MFM presents some advantages: high spatial resolution, down to 10nm; ability to work in different environments as vacuum, air or liquids [2] (despite the technical difficulties that are solved, MFM in liquids facilitates the study of biomagnetic materials) and under applied magnetic fields [3] (to study the magnetization reversal process of thin films, nanoparticles and nanostructures). Additionally, MFM exhibits high versatility and simplicity in operation.&lt;br/&gt;&lt;br/&gt;Advanced operation modes based on Variable Field MFM have proven to be very useful to visualize the magnetization reversal process [4] in one dimensional nanostructures (Figure 1). Isolated multisegmented nanowires (120nm in diameter) formed by segments of FeCo with variable length (increasing from 250nm at the left edge to 400nm the right edge) separated by Cu segments of 30nm have been characterized. The reversal process propagates always unidirectionally (ratched effect) irrespectively of the external field direction, due to the broken symmetry induced by the increasing length of the magnetic segments. Moreover, MFM studies allow us to determine the pinning centers (associated to Cu layers) that may vary from scan to scan. The so called 3D MFM imaging is used is these experiments to obtain a non-standard image where the slow scan corresponds to a continuous variation of the external magnetic field.&lt;br/&gt;&lt;br/&gt;Some emerging aspects of MFM imaging are also tackled in this work. It is worth mentioning the challenging quantitative and accurate interpretation of the MFM images [5], the probe-engineering alternatives [6] (including the analysis of the active role of the probe what could be used to gain information about the sample stray field with ultra-high resolution) or the MFM experiments on complex magnetic configurations as the skyrmionic states [7,8].&lt;br/&gt;&lt;br/&gt;Variable Field MFM and customized MFM probes [6] (growth by Focused Electron Beam Induced Deposition onto AFM probes) have been used for studying skyrmionic states. Figure 2 shows that permalloy hemispherical nanodots with a diameter of 70 nm and height of 30 nm (prepared by hole mask colloidal lithography) are able to host half-hedgehog spin textures with non-zero topological charge. Notice that they are observed at room temperature, in absence of DMI interaction and they can be further stabilized by the magnetic field arising from the Magnetic Force Microscopy probe. The movement of the structure core depends on its chirality and it is controlled by the tip stray field. Micromagnetic simulations have been used to determine the low energy magnetic configuration compatible with the MFM results.&lt;br/&gt;&lt;br/&gt;Future perspectives of MFM imaging as the characterization of 2D materials and devices for spintronic or straintronic are also address in this work; namely, the in situ combination of magnetic imaging with magnetoelectric, thermoelectric or thermomagnetic characterization.

**References:**

[1] O. Kazakova et al., J. Appl. Phys. 125, 060901 (2019)&lt;br/&gt;[2] P. Ares et al., Small, 11, 4731-4736 (2015)&lt;br/&gt;[3] E. Berganza et al., Sci. Rep. 7,11576 (2017)&lt;br/&gt;[4] C. Bran et al., Acs. Nano. 12, 5932-5939 (2018) ,&lt;br/&gt;[5] D. Martínez–Martín et al., Phys. Rev. Lett. 105, 257203 (2010)&lt;br/&gt;[6] M. Jaafar, et al., Nanoscale 12 , 10090-10097 (2020)&lt;br/&gt;[7] M. Baćani et al., Sci Rep 9, 3114 (2019).&lt;br/&gt;[8] E. Berganza et al., Nanoscale,12, 18646-18653 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/975dd1aa3a5f2f1536778690c012b565.jpg)
&lt;br /&gt;
Fig1: 3D MFM images corresponding to four branches of two pseudo-hysteresis loops. The MFM tip moves continuously along the NW axis (fast scan) while the external magnetic field sweeps (slow scan) from negative to positive fields in (a) and (c) and vice versa in (b) and (d) .

![](https://assets.underline.io/uploads/markdown_image/1/image/69d7e0603796ef2f33a8128bdd729206.jpg)
Fig 2. Sequence of MFM images corresponding to Py hemispherical-shaped nanodots. The images are obtained at different external magnetic fields applied along the X axis. The OOMMF simulations calculated for different in-plane magnetic fields reproduce the parallel to the magnetic field movement of the core, in good agreement with the MFM experiments.

INTERMAG 2021

Progress in Magnetic Force Microscopy


![](https://assets.underline.io/uploads/markdown_image/1/image/2e10c515564e9ec3287ee4c664011c20.png)

The energy cost of storing and moving data is enormous, and is growing at such a rapid pace that within a few years the power demand may overwhelm some developed nations. Non-volatile memory (NVM) and neuromorphic computing are enabling critical advances in this area, but there are many scientific and technological challenges. This conference will cover the materials challenges of different memory technologies, from the fundamental processes and mechanisms, to industry perspectives on materials specifications and manufacturing.

Materials Challenges for Memory

Since its early days, magnetic force microscopy (MFM) has become a truly widespread and commonly used characterization technique that has been utilised in a variety of fundamental and applied research and in industrial applications. In this work, we review the current state-of-the-art, analyse the challenges and outline the future of this fascinating field [1]. In comparison to other magnetic imaging techniques, MFM presents some advantages: high spatial resolution, down to 10nm; ability to work in different environments as vacuum, air or liquids [2] (despite the technical difficulties that are solved, MFM in liquids facilitates the study of biomagnetic materials) and under applied magnetic fields [3] (to study the magnetization reversal process of thin films, nanoparticles and nanostructures). Additionally, MFM exhibits high versatility and simplicity in operation. Advanced operation modes based on Variable Field MFM have proven to be very useful to visualize the magnetization reversal process [4] in one dimensional nanostructures (Figure 1). Isolated multisegmented nanowires (120nm in diameter) formed by segments of FeCo with variable length (increasing from 250nm at the left edge to 400nm the right edge) separated by Cu segments of 30nm have been characterized. The reversal process propagates always unidirectionally (ratched effect) irrespectively of the external field direction, due to the broken symmetry induced by the increasing length of the magnetic segments. Moreover, MFM studies allow us to determine the pinning centers (associated to Cu layers) that may vary from scan to scan. The so called 3D MFM imaging is used is these experiments to obtain a non-standard image where the slow scan corresponds to a continuous variation of the external magnetic field. Some emerging aspects of MFM imaging are also tackled in this work. It is worth mentioning the challenging quantitative and accurate interpretation of the MFM images [5], the probe-engineering alternatives [6] (including the analysis of the active role of the probe what could be used to gain information about the sample stray field with ultra-high resolution) or the MFM experiments on complex magnetic configurations as the skyrmionic states [7,8]. Variable Field MFM and customized MFM probes [6] (growth by Focused Electron Beam Induced Deposition onto AFM probes) have been used for studying skyrmionic states. Figure 2 shows that permalloy hemispherical nanodots with a diameter of 70 nm and height of 30 nm (prepared by hole mask colloidal lithography) are able to host half-hedgehog spin textures with non-zero topological charge. Notice that they are observed at room temperature, in absence of DMI interaction and they can be further stabilized by the magnetic field arising from the Magnetic Force Microscopy probe. The movement of the structure core depends on its chirality and it is controlled by the tip stray field. Micromagnetic simulations have been used to determine the low energy magnetic configuration compatible with the MFM results. Future perspectives of MFM imaging as the characterization of 2D materials and devices for spintronic or straintronic are also address in this work; namely, the in situ combination of magnetic imaging with magnetoelectric, thermoelectric or thermomagnetic characterization.

**References:**

[1] O. Kazakova et al., J. Appl. Phys. 125, 060901 (2019) [2] P. Ares et al., Small, 11, 4731-4736 (2015) [3] E. Berganza et al., Sci. Rep. 7,11576 (2017) [4] C. Bran et al., Acs. Nano. 12, 5932-5939 (2018) , [5] D. Martínez–Martín et al., Phys. Rev. Lett. 105, 257203 (2010) [6] M. Jaafar, et al., Nanoscale 12 , 10090-10097 (2020) [7] M. Baćani et al., Sci Rep 9, 3114 (2019). [8] E. Berganza et al., Nanoscale,12, 18646-18653 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/975dd1aa3a5f2f1536778690c012b565.jpg)
 
Fig1: 3D MFM images corresponding to four branches of two pseudo-hysteresis loops. The MFM tip moves continuously along the NW axis (fast scan) while the external magnetic field sweeps (slow scan) from negative to positive fields in (a) and (c) and vice versa in (b) and (d) .

![](https://assets.underline.io/uploads/markdown_image/1/image/69d7e0603796ef2f33a8128bdd729206.jpg)
Fig 2. Sequence of MFM images corresponding to Py hemispherical-shaped nanodots. The images are obtained at different external magnetic fields applied along the X axis. The OOMMF simulations calculated for different in-plane magnetic fields reproduce the parallel to the magnetic field movement of the core, in good agreement with the MFM experiments.

technical paper

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X-ray circular magnetic dichroism (XMCD) is a powerful tool for highly-sensitive and element-specific investigations of magnetic materials. This effect can be utilized in Scanning Transmission X-ray Microscopy (STXM) in the soft X-ray range for magnetic imaging at spatial resolutions down to 20 nm. When combined with a pump-probe excitation and single-photon detection scheme, magneto-dynamic imaging can be achieved with a stroboscopic time-resolution of the order of 20 ps. These capabilities have been widely used in the field of magnetism, including vortex core dynamics [1], magnonics in real-space on the scale of tens of nm[2,3,4] and room temperature skyrmionics [5,6] As a photon-based technique, STXM is very tolerant to the sample environments and allows for diverse detection methods. For example, the use of strong magnetic fields can be combined with surface sensitive electron yield imaging, as well as with helium cryostats to provide sample temperatures down to 20K at multi-GHz bandwidths for dynamic excitation. Examples for research utilizing these features will be presented, as well as recent developments such as CCD-Ptychography for super-resolution or using a high- repetition-rate laser as an optical pump source for time-resolved measurements. As an outlook, it will be discussed how STXM can profit from the current developments in high-brilliance x-ray sources.

**References:**

[1] Van Waeyenberge et al., Nature 444, 461 (2006). [2] S Wintz et al., Nat. Nanotech. 11, 948 (2016). [3] V. Sluka et al., Nat. Nanotech. 14, 328 (2019). [4] N. Träger et al., Phys. Status Solidi RRL , 14: 2000373 (2020). [5] S Woo et al., Nat. Mater. 15, 501 (2016). [6] K Litzius et al., Nat. Phys. 13, 170 (2017). [7] S. Mayr et al. (unpublished) (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/ab4ee7588fc632d843781219a2c096de.jpg)

Schematics and time-resolved STXM image (normalized snapshot) revealing the coherent flow of magnons in a ferrimagnetic insulator [7]

Advanced Scanning Transmission X-Ray Microscopy for the Investigation Magnetic Phenomena

The magnetic fields generated by spins and currents provide a unique window into the physics of correlated-electron materials and devices. Proposed only a decade ago, magnetometry based on the electron spin of nitrogen-vacancy (NV) defects in diamond is emerging as a platform that is exceptionally suited for probing condensed matter systems [1]: it can be operated from cryogenic temperatures to above room temperature, has a dynamic range spanning from DC to GHz, and allows sensor-sample distances as small as a few nanometers. As such, NV magnetometry provides access to static and dynamic magnetic and electronic phenomena with nanoscale spatial resolution. While pioneering work focused on proof-of-principle demonstrations of its nanoscale imaging resolution and magnetic field sensitivity, now experiments are starting to probe the correlated-electron physics of magnets and superconductors and to explore the current distributions in low-dimensional materials [1]. In this talk, I will review some of our recent work that uses NV center magnetometry to image skyrmions in thin magnetic films [2], measure the spin chemical potential in magnetic insulators [3], and image hydrodynamic electron flow in layered materials [4,5].

**References:**

1. F. Casola et al., Nat. Rev. Mater. 2018 2. Y. Dovzhenko et al., Nature Comm. 2018. 3. C. Du et al., Science 2017. 4. M. Ku et al., Nature 2020. 5. Uri Vool et al., arXiv2009.04477

Quantum Sensing of Quantum Materials using NV-Center Microscopy

Three dimensional magnetic systems promise significant opportunities for applications, for example providing higher density devices and new functionality associated with complex topology and greater degrees of freedom [1,2]. For the experimental realisation of these new properties, appropriate characterisation techniques are required to determine both the three-dimensional magnetic structure, and its response to external stimuli. In this talk, I will describe our recent progress in the development of new capabilities for the imaging of three-dimensional magnetic systems, and their dynamic behaviour. For three-dimensional magnetic imaging, we have developed X-ray magnetic nanotomography [3]. By measuring high resolution 2D XMCD projections [4] of the sample for many angles about a dual rotation axis experimental setup, and combing these with a new iterative reconstruction algorithm [5], we determine the complex three-dimensional magnetic patterns within the bulk of a micrometre-sized soft magnetic pillar with 100 nm spatial resolution, as shown in Figure 1. The internal magnetic configuration reveals a complex network of topological magnetic features such as vortices, antivortices and domain walls and, at the crossing points of these structures, we observe the presence of Bloch point singularities [3]. The identification, and interpretation, of nanoscale topological objects within the complex reconstructed magnetic configurations – that consist of millions of pixels – represents a significant challenge. To address this, we have recently implemented calculations of the magnetic vorticity [6,7], a vector that represents the flux of the skyrmion number density, and thus encodes the topology of the magnetic configuration. In this way, not only can we locate and identify the presence of topological structures (Figure 1e,f), but we gain new insights into 3D magnetic solitons, leading to the first observation of magnetic vortex rings [7], as shown in Figure 1g. Lastly, in addition to the static magnetic configuration, the dynamic response of the 3D magnetic configuration to excitations is key to our understanding of both fundamental physics, and applications. With our recent development of X-ray magnetic laminography [8,9] (Figure 2), it is now possible to determine the magnetisation dynamics of a three-dimensional magnetic system [8]. In this way, we have been able to map the dynamics of a magnetic microdisc in response to the excitation of a 500 MHz magnetic field, revealing the motion of vortex domain walls within the bulk of the structure, as well as mapping the coherent rotation modes of the magnetisation in three dimensions (Figure 2c,d), with spatial and temporal resolutions of 50 nm and 70 ps, respectively. These new experimental capabilities of X-ray magnetic imaging open the door to the elucidation of complex three-dimensional magnetic structures, and their dynamic behaviour.

**References:**

[1] A. Fernández-Pacheco, et al., “Three-dimensional nanomagnetism” Nat. Comm. 8, 15756 (2017) [2] C. Donnelly & V. Scagnoli, “Imaging three-dimensional magnetic systems with X-rays” J. Phys. D: Cond. Matt. (2019). [3] C. Donnelly et al., “Three-dimensional magnetization structures revealed with X-ray vector nanotomography” Nature 547, 328 (2017). [4] C. Donnelly et al., “High-resolution hard x-ray magnetic imaging with dichroic ptychography” PRB 94, 064421 (2016). [5] C. Donnelly et al., “Tomographic reconstruction of a three-dimensional magnetization vector field” NJP 20, 083009 (2018). [6] N. R. Cooper, “Propagating magnetic vortex rings in ferromagnets.” PRL. 82, 1554 (1999). [7] C. Donnelly et al., “Experimental observation of vortex rings in a bulk magnet” Nat. Phys. (2020) [8] C. Donnelly et al., “Time-resolved imaging of three-dimensional nanoscale magnetization dynamics”, Nat. Nano. 15, 356 (2020). [9] K. Witte et al., “From 2D STXM to 3D Imaging: Soft X-ray Laminography of Thin Specimens”, Nano Lett. 20, 1305 (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/0e2d9057483d2b7b45d4d6c5b16ede99.jpg)
Figure 1. X-ray magnetic tomography of a GdCo micropillar (a) reveals a complex internal magnetic configuration. A horizontal slice (b) contains a number of vortices (c) and antivortices (d). Through calculations of the magnetic vorticity vector, we can identify the presence of topological structures (e) and magnetisation singularities (f) within the bulk of the micropillar. By plotting the magnetic vorticity, we identify magnetic vortex rings of circulating vorticity (g). a-d are reproduced from [3], and e-g are reproduced from [8].

![](https://assets.underline.io/uploads/markdown_image/1/image/72ea02148e85a8623efddf043a46be9a.jpg)
Figure 2 Pump-probe X-ray magnetic laminography (a) allows for the mapping of the magnetization dynamics of a magnetic microdisc (b) with spatial and temporal resolutions on the order of nanometers and picoseonds, respectively. Coherent rotation modes of the magnetization are shown for a cross section (c) and a lower slice of the structure containing vortex domain walls (d). a-d reproduced from [8].

Imaging 3D magnetic configurations with X-rays

The increasing exploration of nanomagnetism into the third dimension lead to the discovery of novel frustration mechanisms and ensuing magnetic configurations and textures, many with unprecedented properties [1]. The fundamental understanding of these configurations and the interactions stabilizing them requires a quantitative microscopy technique revealing 3D magnetic structures with a spatial resolution below characteristic magnetic length scales pertaining to a given problem. In our contribution we introduce holographic vector-field electron tomography (VFET), a combination of off-axis electron holography (EH) and electron tomography in the transmission electron microscope (TEM), facilitating sub-10 nanometer spatial resolution [2, 3]. Off-axis EH utilizes an interferometric setup to determine the phase shift of an electron wave that passed through the sample. The Aharonov-Bohm phase shift of ferro-magnetic samples is proportional to projections of both electric potential (mainly mean inner potential) and magnetic flux density (B-field), which allows to reconstruct them in 3D from a tilt series of 2D phase images by tomographic methods [2]. The principle and workflow of holographic VFET is illustrated in Fig. 1. In addition to the comprehensive workflow of recording and reconstructing the 3D data, crucial steps of alignment and image processing, e.g., precise displacement correction of 2D projections and 3D tomograms, phase unwrapping, denoising, etc. are addressed. Fig. 2 shows two examples, how holographic VFET is applied to reveal 3D magnetic configurations in nanoscale magnetic materials. In Figs. 2a,b, we present 3D remanent states in a Co-rich CoNi cylindrical nanowire (NW) with a diameter of 70 nm and the hcp c-axis oriented almost perpendicular to the NW axis [4]. We observed two different remanent states after the application of an external saturation field of 2 T perpendicular (Fig. 2a) and parallel (Fig. 2b) to the NW axis. The external field direction perpendicular to both the wire axis and the magnetocrystalline easy axis resulted in a transverse-vortex chain configuration, whereas a field direction parallel to the wire axis produced longitudinal vortex domains with their cores aligned along the applied field, but with alternately opposite chirality. Micromagnetic simulations confirm our findings and enable us to understand the origin of the observed complex magnetic states, in particular, reveal a large influence of the NW morphology on the remanent state. In Fig. 2c, the first 3D reconstruction of Bloch-Skyrmions in a FeGe needle-shaped FIB sample taken at 90K temperature is depicted. The reconstructed textures provide insights into a variety of previously unseen local deviations from a homogeneous Bloch character within the skyrmion tubes (SkTs), details of the collapse of the skyrmion texture at surfaces, and a correlated modulation of the SkT in FeGe along their tube axes. [5]

**References:**

[1] A. Fernandez-Pacheco et al., Nat Commun 8, p.15756 (2017) [2] D. Wolf et al., Chem Mater 27, p. 6771 (2015) [3] D. Wolf et al., Comm Phys 2, p. 87 (2019) [4] I.M. Andersen et al., submitted (2021) [5] D. Wolf et al., to be submitted (2021) [6] DW and AL have received funding from the European Research Council (ERC) under the Horizon 2020 research and innovation program of the European Union (grant agreement number 715620). AL, and SS acknowledge financial support through the Priority Program SPP2137 of the German Research Foundation (DFG) within projects LU-2261/2-1 and RE-1164/6-1.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/d41934af339cca9f9876429c2fd07a66.jpg)
Principle and workflow of holographic vector-field electron tomography (VFET) in the transmission electron microscope (adapted from Ref. [3]). (1) Modulation of electron waves by magnetic sample, (2) Interference of modulated object wave with unmodulated reference wave by an electrostatic biprism building up an electron hologram, (3) Reconstruction of hologram yielding amplitude and phase shift of object wave, (4) Acquisition of two tilt series around two tilt axes, X and Y, providing two (ideally 360°) phase tilt series, (5/6) Calculation of half the sum/difference of opposite projections (green/red arrow) resulting in electric/magnetic phase tilt series, (7) 3D reconstruction of electric potential from electric phase tilt series, (8) 3D Reconstruction of the two magnetic B-field components Bx (By) from the derivatives in y (x) - direction of the magnetic phase tilt series, (9) Computation of Bz component by solving divB=0.


![](https://assets.underline.io/uploads/markdown_image/1/image/5510c31e0fc0dc100ad286c0cc5a0e09.jpg)
Holographic VFET of magnetic nanostructures. (a,b) Volume rendering of the By component of the reconstructed magnetic induction B of two remanent magnetic states (a) and (b) in a Co-rich CoNi nanowire (70 nm diameter) after external field HSat applied perpendicular (a) and parallel (b) to the wire axis. The magnified regions with vectors slices show transverse vortex chains in (a) and longitudinal vortex domains of alternating chirality separated by a domain wall in (b). (c) Volume rendering of the in-plane components Bx, By according to the colorwheel and iso-surface of the mean inner potential reconstruction highlighting the FeGe FIB-prepared specimen shape (grey, bottom half only). The magnified views visualize a single skyrmion tube (SkT) in which the three vectors slices plot the 3D spin texture inside the SkT at different z-heights.

3D Mapping of Magnetic Nanotextures with Nanometer Resolution Using Holographic Vector-Field Electron Tomography

Smart materials can change key physical properties in response to external stimuli. To achieve adaptive design performance regardless of environmental changes, demand for smart materials technology has greatly increased. Magnetorheological (MR) composites are a class of smart materials that can rapidly and reversibly control adjust their damping and stiffness properties in response to external magnetic field. MR composites consist of micron-size soft magnetic particles in a non-magnetic carrier matrix. MR composites can be divided into three major classes based on matrix materials: MR fluids (MRFs), MR foams, and MR elastomers (MREs). The rheological properties of MRFs, which use liquid as the carrier matrix, can be controlled in response to an external magnetic field. MRFs have been widely applied to a variety of hydraulic actuators to produce a controllable damper force or torque. MR foams are composed of either non-magnetic porous metal foam filled with MRF or have particles embedded in a porous elastomeric foam. Because of their light weight and high compliance, MR foams exhibit large changes in baseline stiffness and are candidate smart materials for space applications, as well as vibration and acoustic absorption applications. MREs, which use a non-porous solid elastomer as the carrier matrix, have controllable viscoelastic properties. MREs can used to retrofit passive rubber isolators and mounts in vibration and shock mitigation systems to provide improved and adaptive performance. MRFs typically exhibit sedimentation because of the large density difference between carbonyl Fe particles (density of 7.9 g/ml) and the non-magnetic carrier fluid (e.g., silicone oil has a density of 0.97 g/ml). Unlike MRFs, the Fe particles in MR foams and MREs are permanently dispersed. Because particles are embedded in the carrier matrix, MR foams and MREs show less MR effect than MRFs where particles can migrate and agglomerate. To increase MR effects in MREs, research [1-4] to encapsulate MRFs in MREs has been reported. It should be noted that MR foams have porous carrier matrix and may be not possible to encapsulate MRF into MR foam. In this study, MRF encapsulated elastomers (MREEs) are fabricated and their controllable stress behaviors are experimentally evaluated. Two design configurations are studied for MREEs: the first is MRF and permanent magnet (PM) embedded inside MREEs, and the second is MRF only embedded in MREEs. MREEs with PM can be passively and actively activated, but MREEs without PM can be only activated by external magnetic field produced by an electromagnet. A sample MREE (Figure 1) encapsulates an MRF composed of 35 vol% carbonyl Fe dispersed in a 1,000 cSt silicone oil. The silicone rubber was as soft as 00-20. The diameter and height of this sample was nominally 2.6” and 0.37”, respectively. The compressive stress-strain curve of the MREEs both without and with applied magnetic field were measured by a MTS machine. Figure 2 presents the measured field-dependent compressive stress curves of the MREE. As seen in this figure, the compressive stress curves of the MREE can be continuously adjusted in response to current input. Also, the hysteresis loop also increased as the applied current inputs. This physically implies that the dissipated energy increased. In the full paper, the effect of two different magnetic flux directions (i.e., positive and negative coil currents) will be presented. The compressive stress curve of the MREEs can also be affected by the strain rate, as in impact events. To illustrate such strain rate effects, the compressive stress curves over a range of strain rates will be also presented. From the measured hysteresis loop, the dissipated energy can also determined. In addition, the MREEs can be stacked for accommodating larger compressive displacement. In this study, the effect of two different stackable situations (one is attractive PMs configuration and the other is repulsive PMs configuration) on the compressive stress curve will be evaluated. From the results presented in this study, the controllable stress capability of the MREEs will be presented for a range of operating conditions.

**References:**

[1] D. York, X. Wang, and F. Gordaninejad, “A new MR fluid-elastomer vibration isolator,” J. Intel. Mater. Syst. and Struct, 18: 1221-1225 (2007). [2] D. York, X. Wang, F. Gordnaniejad, “A new magnetorheological mount for vibration control,” J. Vibr Acoust., 133: 031003 (2011). [3] A. K. Bastola, L. Li and M. Paudel, |A hybrid magnetorheological elastomer developed by encapsulation of magnetorheological fluid,” Journal of Materials Science, Vol. 53, pp. 7004-7016 (2018). [4] A. K. Bastola, E. Ang, M. Paudel, L. Li, “Soft hybrid magnetorheological elastomer: gap bridging between MR fluid and MR elastomer,” Colloids and Surfaces A, Vol. 583, 123975 (2019).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c7b4531d44116ed3566e15610b99a51e.jpg)
Figure 1. MRF encapsulated elastomers (MREEs).

![](https://assets.underline.io/uploads/markdown_image/1/image/84dd4f6d08b64d7a6a8dcdde1ea3c75f.jpg)
Figure 2. Field-dependent compressive stress curves of the MREE.

 Controllable Stress of Magnetorheological Fluid Encapsulated Elastomers

Magnetorheological (MR) elastomers as composite materials of magnetizable particles in an elastomer matrix are the soft solid relatives of the better known MR fluids [1]. They preferably consist of silicone elastomer filled with dispersed iron particles [2]. MR elastomers exhibit interesting viscoelastic properties, which strongly depend on the elastomer stiffness and the particle concentration and are controllable by a magnetic field. With rising iron particle concentration, the basic stiffness in terms of the elastic storage modulus increases, as expected. In a strong magnetic field, the storage modulus can be enhanced by a factor of about 10 (see Figure 1). A corresponding increase is observed also for the viscous loss modulus (see Figure 1). These effects are particularly pronounced for MR elastomers with soft silicone matrices, which exhibit low molecular crosslinking densities. In common MR elastomers, the iron particles are randomly distributed in the surrounding matrix material due to the mixing of the particles with the liquid silicone precursors in the preparation process. However, it is also possible to prepare MR elastomers with anisotropic particle distribution [3]. In order to achieve this modification, a magnetic field is applied already in the preparation procedure before and during the chemical crosslinking of the silicone elastomer in a thermal process, where the particles are arranged to chains along the magnetic field, in analogy to MR fluids. The magneto-mechanical properties of anisotropic MR are significantly different from those of their isotropic counterparts. A strong increase of the storage modulus of the anisotropic composites is observed already with lower iron particles concentrations. In other investigations, the magnetic properties of MR elastomer cubes with isotropic and anisotropic particle arrangements were studied and compared. Similar to MR fluids, even with high concentrations of iron particles, the magnetic susceptibility of MR elastomers is extremely low in comparison with pure solid iron, which is due to the dispersed distribution of the iron particles in the composite. The measured susceptibility of the anisotropic MR elastomer with a magnetic field perpendicular to the iron particle chains is comparable to the corresponding values of the isotropic samples. However, it could be shown that the susceptibility parallel to the particle chains in the anisotropic MR elastomer is significantly higher due to the particle contacts in this direction. Numerous interesting applications become possible with MR elastomers. Generally known are applications in vibration reduction. Here, the focus is on tunable vibration absorbers due to the dominant elastic behavior of elastomers [4] in contrast to the more viscous characteristics of MR fluids. However, promising exploitation potential of MR elastomers arises also for actuation devices, where an MR elastomer body deforms in a magnetic field. A speciality of these MR elastomer-based actuators is the possibility to realize different types of actuation depending on the orientation of the magnetic field. A basic type of actuation is caused by the linear deformation of an MR elastomer body in a corresponding magnetic field. Due to magnetic attraction forces on the soft-magnetic iron particles by a specially shaped yoke part in the magnetic circuit, the MR elastomer body such as a disk is deformed into a preferred direction. This type of actuator can be used for human-machine interfaces, where haptic feedback is required, when the user touches the interface. Another interesting application of linear MR elastomer actuators are pumping units. In these units, the periodic linear deformation of the actuator sucks the medium to be transported through a non-return valve into a chamber and pushes it out through another non-return valve. Moreover, with MR elastomers also another type of actuators with radial motion may be realized. In a magnetic field with radial orientation between an inner yoke and an annular outer yoke, a ring-shaped body of MR elastomer between the two yokes leaving an annular gap to the inner yoke can expand radially and close the gap (see Figure 2). This unusual kind of radial actuation offers a high potential for various applications. Especially interesting are valves with a ring-shaped opening, where the degree of closing is controlled by the magnetic field strength, i.e. the current in the coil of the electromagnet, and the corresponding radial deformation of the MR elastomer ring. With this mechanism, proportional valves can be realized. Another possible application of radial MR elastomer actuators are locking devices. Here, MR elastomer rings bridge the annular gaps between an inner rotatable shaft and an outer housing, Thereby blocking the rotation, when the magnetic field is activated. It could be demonstrated that locking torques of about 5 Nm can be achieved in a device with two MR elastomer rings. The locking effect is stronger than with an MR fluid in a device with a corresponding geometrical configuration. In this symposium contribution, material properties of MR elastomers and various actuator designs for different applications are discussed.

**References:**

[1] J. D. Carlson and M. R. Jolly, MR fluid, foam and elastomer devices. Mechatronics 10, 555-569 (2000) [2] W. H. Li and M. Nakano, Fabrication and characterization of PDMS based magnetorheological elastomers, Smart Materials and Structures 22, 055035 (2013) [3] H. Böse and R. Röder, Magnetorheological Elastomers with high variability of their mechanical properties, J. Phys.: Conf. Ser. 149, 012090 (2009) [4] X. Z. Zhang and W. H. Li, Adaptive Tuned Dynamic Vibration Absorbers Working with MR Elastomers, Smart Structures & Systems 5, 517-529 (2009)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/6744c1ad7d09ab43fe3a6705230d8b92.jpg)
Figure 1: Dependence of the storage modulus (left) and the loss modulus (right) of MRE composites with different carbonyl iron particle (CIP) concentrations on the magnetic flux density

![](https://assets.underline.io/uploads/markdown_image/1/image/9279471e448a328b9b3c131a71d3e93a.jpg)
Figure 2: MRE actuator with radial expansion for proportional valve applications in the inactivated state (annular gap open, left) and activated state (annular gap closed, right)

 Magnetorheological Elastomers – Material Properties and Actuation Capabilities

The work presents the fabrication and characterisation of a new liquid metal filled magnetorheological elastomer (LMMRE) comprising liquid metal microdroplets and metallic magnetic microparticles1. The conductive network formed by liquid metal droplets and solid metal microparticles in the matrix imparts conductivity to LMMRE (Fig. 1). Both isotropic and anisotropic LMMREs were fabricated either without or with an external magnetic field. For the case of isotropic LMMRE, compared to conventional composites, this LMMRE uniquely reaches a maximum resistance in the relaxed state and can drop sharply under any mechanical deformation, including compression, stretching, bending, and twisting. This indicates that the LMMRE can exhibit an unconventional negative piezoresistive effec. The mechanical and thermal properties of LMMRE were further studied. Several proof-of-concept applications based on LMMRE such as wearable joint sensors and intelligent heating devices were also demonstrated. For example, the LMMRE can be used to detect the movement of human joints. A LMMRE strip was attached to the index finger, then the finger bent repeatedly with the maximum bending angles of 45° and 90°, respectively. The resistance change-time curve reflects the accurate response of the LMMRE sensor to different angles and its stability under cyclic loading (Fig. 2). Therefore, this LMMRE has the potential to be applied for developing highly sensitive flexible sensors for wearable devices. After that, we created and studied an anisotropic LMMRE using the magnetic field alignment method. We show that magnetically aligning the particles prior to curing the LMMRE produces different results. Namely, the conductivity of the anisotropic LMMRE—in the absence of deformation—improves significantly by several orders of magnitude in all directions compared to the isotropic LMMRE with the same composition. In addition, the resistivity changes of the anisotropic LMMRE under mechanical deformation and its anisotropic piezoresistive properties are also significantly different from isotropic LMMRE. Along the particle alignment direction, the resistivity of anisotropic LMMRE increases sharply with strain. In contrast, in the direction perpendicular to the particle chains, its resistivity decreases monotonically with strain. Besides, the anisotropic LMMRE is also more sensitive to mechanical deformation along the particle alignment direction. Furthermore, we discovered that the mechanical, magnetic and thermal properties of the anisotropic LMMRE also exhibit significant anisotropy. Harnessing these unique properties, we demonstrated several applications based on anisotropic LMMRE such as soft tactile logic devices and an improved intelligent heating device.

**References:**

1. G. Yun, S.Y. Tang, S. Sun, D. Yuan, Q. Zhao, L. Deng, S. Yan, H. Du, M.D. Dickey and W. Li, Nature Communications, Vol. 10, p.1300 (2019)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/c920a6082af6d7e2d2bc3e1355244050.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/302bb7031997fbedf454e3f6f4b4f302.jpg)

 Study of Liquid Metal Filled Magnetorheological Elastomers

Magnetorheological elastomer (MRE) is a magnetic particle reinforced elastomer composite, which its mechanical properties can be controlled with the application of a magnetic field.1 The magnetorheological effect induces changes in stiffness and damping properties in the composite with the response of the magnetic particles to the external magnetic field.2 Smart sensor and actuator components can be fabricated for adaptive vibration control systems where mechanical properties can be controlled by the application of magnetic field. Typically, composites are prepared by mixing magnetic particles with the uncured rubber matrix and then the mixture is poured into a mold for curing. Recently low-cost 3D printers are widely available, utilizing various polymers. Manufacturability of MRE composites using additive manufacturing (AM) process has gained great attention so the geometrical design of the MRE composite fabrication can be achieved.3 In this research, development of filament of MRE for fused filament fabrication based on additive manufacturing is performed. The magnetorheological effect depends on the particle’s magnetic properties and volume fraction, and distribution, etc. Filament materials are developed by mixing thermoplastic polyurethane (TPU) pellets with the magnetic particles (iron oxide, carbonyl Fe particles), followed by extrusion process to produce rolls of filament. Due to the nature of the mixing process relying on gravity to feed material into the extruder, denser and much smaller magnetic particles (~10 μm) than the TPU pellets (~mm) tend to fall to the bottom of the hopper, leading non-uniform distribution of magnetic particle along the filament thru extrusion process. Therefore, the trickling systems with a screw feeder were developed to provide consistent trickling rate of each TPU and magnetic particles respectability. [Figure 1 (a)] The trickling rate of TPU was fixed at ~4.9 g/min and the trickling rate of iron oxide was varied from 0.0 to 2.5 g/min. Five sets of filaments were produced with different trickling rates of iron oxide.[Figure 1(b)]. Diameter ranges from 1.45 ± 0.01 to 1.55 ± 0.06 mm. The density of filament increases with the higher trickling rate of magnetic powder and the densities change from 1.33 ± 0.05 to 1.46 ± 0.05 g/cc, indicating that the volume fraction control of magnetic particles in the extrusion process was successful. The grayscale level plot [Figure 1 (c)] indicates the iron oxide concentration in each filament in the yellow box region. The grayscale plot profiles the images with each point represents the average pixel intensity. This data shows that the filaments produced with lower trickling rate (0.6 and 1.0 g/min) did not show significant difference but the lower gray scale values of filaments with 1.5 and 2.5 g/min indicate that there are more iron oxide particles. Micro-focus X-ray tomography scans were performed on the produced composite filament (Figure 2). The results show that magnetic particles are well dispersed in the matrix. The small grains are &lt; ~30 mm and the larger grains are ~60 mm. The iron oxide volume fraction ranges from 9.31% to 12.95%. This demonstrates that MRE filament feedstock materials can be successfully manufactured for use in fused filament deposition processes.

**References:**

1. S. S. Kang, K. Choi, and J. D. Nam, Materials., Vol.13, p.4597 (2020) 2. O. Padalka, H. J. Song, N. M. Wereley, J. A. Filer, IEEE Transactions on Magnetics, Vol. 46, p.2275 (2010) 3. A. K. Bastola, M. Paudel, L. Li, Smart Materials and Structures, Vol. 29, p.123002 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/b3aba021d44c39dfd0f2da3a1c22aa82.jpg)
Figure 1 (a) Schematic drawing and image of developed trickling system. (b) coils of TPU filaments produced with different amount of iron oxide. (c) image of extruded filaments and plot profile of the yellow box.

![](https://assets.underline.io/uploads/markdown_image/1/image/f2f413611412f4c079a9eb2b2e621762.jpg)
Figure 2 X-ray tomography scan performed on the produced composite filament. Iron oxide particles are highlighted with color coding by volume. The TPU matrix is colored in light gray to easily visualize the pores and iron oxide dispersions.

 Magnetic Particle Reinforced Elastomer Composites for Additive Manufacturing

Antiferromagnetism, discovered by Louis Néel, is a very interesting and complex physical phenomenon which has led to much new physics and important applications. Many antiferromagnetic materials were found since its discovery. Recent development of novel bulk and thin film synthesis techniques and materials genomic computational methods have accelerated and broadened considerably the plethora of antiferromagnetic materials. Antiferromagnets become particularly interesting when incorporated into inhomogeneous hetero- and/or nano-structures. This has led to interesting phenomena such as Exchange Bias and important recent applications in the field of Spintronics. I will describe the main features of antiferromagnetism, the interesting physical phenomena, unique devices and the principal open research issues. The research at UCSD was supported by the Office of Basic Energy Science, U.S. Department of Energy, BES-DMS funded by the Department of Energy’s Office of Basic Energy Science, DMR under grant DE FG02 87ER-45332.

**References:**



**Images:**

Antiferromagnetism: Celebrating 50 years since the Nobel Prize

Being able to observe atomic-scale spin structures and to probe magnetic properties atom-by-atom is decisive for the discovery of new magnetic phenomena, the optimization of magnetic materials as well as the development of nano- or even atomic-scale spintronic devices. Spin-Polarized Scanning Tunneling Microscopy (SP-STM) [1] being based on the observation of vacuum tunneling of spin-polarized electrons between a highly spin-polarized and atomically sharp probe tip and a sample under investigation [2] allows for atomic-scale studies of magnetic order of ferro- [3], antiferro- [4] and ferrimagnetic [5] materials, including the internal structure of magnetic domain walls down to the atomic level [6,7]. By combining SP-STM with energy-resolved tunneling spectroscopy, the powerful method of Spin-Polarized Scanning Tunneling Spectroscopy (SP-STS) evolved providing access to spin-resolved electronic states of ferro- [8] and antiferromagnetic [9] or even molecular [10,11] materials with atomic-scale spatial resolution. Magnetic field-dependent SP-STM studies led to the development of nano-scale [12] or even single-atom magnetometry [13] allowing the probing of single-atom magnetization in metallic [14] or diluted magnetic semiconductor systems [15]. A very important issue for SP-STM studies is the appropriate choice of a highly spin-polarized and atomically sharp probe tip with a minimum magnetic stray field in order to avoid disturbances of the magnetic state of atomic-scale systems. Half-metallic ferromagnetic CrO2 thin film probe tips were used in the very early studies in order to achieve an almost 100% spin polarization [2]. However, these tips exhibit a non-negligible stray field, so that they were only useful in applications to antiferromagnetic materials. On the other hand, magnetic stray fields can be avoided by making use of antiferromagnetic probe tips, e.g. Cr thin film [16] or bulk [17] tips, which have proven to be very useful for imaging magnetic domain walls [16] or magnetic vortex states [18] in ferromagnetic nanostructures. However, Cr tips usually offer a spin polarization of around 20% only, thereby the spin contrast is not as high as it could be. Recently, we were able to prepare atomically sharp SP-STM tips offering both, a very high spin polarization and a negligible magnetic stray field: By picking up a single magnetic atom from a sample surface with a superconducting STM tip, we created a magnetic bound state within the superconducting energy gap, a so-called Yu-Shiba-Rusinov state, being 100% spin-polarized [19], and subsequently made use of that state to probe the magnetic structure of artificially created spin chains made up of manganese atoms on a niobium substrate [20]. Thanks to the capability of SP-STM to combine real-space atomic resolution with spin sensitivity, numerous discoveries could be made in magnetic thin films and nanostructures, such as the first experimental observations of chiral domain walls [21-23], spin spirals [24] and skyrmionic lattice states [25,26] due to interfacial Dzyaloshinskii-Moriya (DM) interactions. Moreover, SP-STM allowed the first observation of the internal spin structure of individual chiral magnetic skyrmions [27, 28] as well as their local manipulation, i.e. creation and annihilation, by local (vertical) spin current injection [27] and local electrical fields [29] which is an important prerequisite for any application of magnetic skyrmions in magnetic data storage or logic devices [30]. It has been realized in recent years that complex magnetic states in thin film systems can arise from the competition of various magnetic interactions, including isotropic and anisotropic as well as higher-order exchange interactions. It is extremely important to probe the nature of these interactions down to the atomic scale in order to be able to design novel types of magnetic materials and devices based on that knowledge. SP-STM has allowed probing the distance and directional dependencies of RKKY interactions directly in real space at the atomic level [31], yielding important information about the distance regimes for which maximum ferro- or antiferromagnetic coupling between individual magnetic atoms is achieved. Based on this kind of insight, artificial magnets [14] and even prototype atomic-scale spin logic devices [32] could be fabricated. Moreover, the stabilization of spin systems via symmetrically tailored RKKY interactions [33] could be demonstrated recently. Similarly, SP-STM has recently been applied to study the distance dependence of interfacial DM interactions [34] which subsequently allowed tailoring non-collinear chiral spin structures at the atomic level [35]. Chiral spin chains are of considerable interest for realizing information transfer by vector spin chirality in finite magnetic chains [36]. Moreover, when combined with superconducting substrates, atomic-scale model systems for topological superconductivity and Majorana bound states can be realized [37, 38] offering great potential for topological quantum computation. Finally, time-resolved SP-STM measurements have provided novel insight into the dynamics of nano-scale classical [39] or even quantum magnetic systems [40]. Local spin-current injection from a highly spin-polarized tip into nano-scale magnetic systems [41] has proven to be a very valuable method to induce and manipulate the spin dynamics of small clusters or even single magnetic atoms on surfaces [40]. Studying the influence of the dynamical states of chiral spin chains on superconducting substrates on the dynamics of Majorana states is one of the exciting directions of ongoing research activities.

**References:**

[1] R. Wiesendanger, Rev. Mod. Phys. 81, 1495 (2009): "Spin mapping at the nanoscale and atomic scale". [2] R. Wiesendanger, H.-J. Güntherodt, G. Güntherodt, R.J. Gambino, and R. Ruf, Phys. Rev. Lett. 65, 247 (1990): "Observation of vacuum tunneling of spin-polarized electrons with the scanning tunneling microscope". [3] O. Pietzsch, A. Kubetzka, M. Bode, and R. Wiesendanger, Phys. Rev. Lett. 84, 5212 (2000): "Real-Space Observation of Dipolar Antiferromagnetism in Magnetic Nanowires by Spin-Polarized Scanning Tunneling Spectroscopy". [4] S. Heinze, M. Bode, A. Kubetzka, O. Pietzsch, X. Nie, S. Blügel, and R. Wiesendanger, Science 288, 1805 (2000): "Real-space imaging of two-dimensional antiferromagnetism on the atomic scale". [5] R. Wiesendanger, I.V. Shvets, D. Bürgler, G. Tarrach, H.-J. Güntherodt, J.M.D. Coey, and S. Gräser, Science 255, 583 (1992): "Topographic and magnetic-sensitive scanning tunneling microscopy study of magnetite". [6] M. Pratzer, H. J. Elmers, M. Bode, O. Pietzsch, A. Kubetzka, and R. Wiesendanger, Phys. Rev. Lett. 87, 127201 (2001): "Atomic-scale magnetic domain walls in quasi-one-dimensional Fe nanostripes". [7] M. Bode, E. Y. Vedmedenko, K. von Bergmann, A. Kubetzka, P. Ferriani, S. Heinze, and R. Wiesendanger, Nature Materials 5, 477 (2006): "Atomic spin structure of antiferromagnetic domain walls". [8] M. Bode, M. Getzlaff, and R. Wiesendanger, Phys. Rev. Lett. 81, 4256 (1998): "Spin-Polarized Vacuum Tunneling into the Exchange-split Surface State of Gd(0001)". [9] M. Kleiber, M. Bode, R. Ravlić, and R. Wiesendanger, Phys. Rev. Lett. 85, 4606 (2000): "Topology-induced spin frustrations at the Cr(001) surface studied by spin-polarized scanning tunneling spectroscopy". [10] J. Brede, N. Atodiresei, S. Kuck, P. Lazic, V. Caciuc, Y. Morikawa, G. Hoffmann, S. Blügel, and R. Wiesendanger, Phys. Rev. Lett. 105, 047204 (2010): "Spin- and energy-dependent tunneling through a single molecule with intramolecular spatial resolution". [11] J. Schwöbel, Y. Fu, J. Brede, A. Dilullo, G. Hoffmann, S. Klyatskaya, M. Ruben, and R. Wiesendanger, Nature Communications 3, 953 (2012): "Real-space observation of spin-split molecular orbitals of adsorbed single-molecule magnets". [12] O. Pietzsch, A. Kubetzka, M. Bode, and R. Wiesendanger, Science 292, 2053 (2001): "Observation of magnetic hysteresis at the nanometer scale by spin-polarized scanning tunneling spectroscopy". [13] F. Meier, L. Zhou, J. Wiebe, and R. Wiesendanger, Science 320, 82 (2008): "Revealing magnetic interactions from single-atom magnetization curves”. [14] A. A. Khajetoorians, J. Wiebe, B. Chilian, S. Lounis, S. Blügel, and R. Wiesendanger, Nature Physics 8, 497 (2012): "Atom-by-atom engineering and magnetometry of tailored nanomagnets". [15] A. A. Khajetoorians, B. Chilian, J. Wiebe, S. Schuwalow, F. Lechermann, and R. Wiesendanger, Nature 467, 1084 (2010): "Detecting excitation and magnetization of individual dopants in a semiconductor". [16] A. Kubetzka, M. Bode, O. Pietzsch, and R. Wiesendanger, Phys. Rev. Lett. 88, 057201 (2002): "Spin-Polarized Scanning Tunneling Microscopy with Antiferromagnetic Probe Tips". [17] A. Schlenhoff, S. Krause, G. Herzog, and R. Wiesendanger, Appl. Phys. Lett. 97, 083104 (2010): "Bulk Cr tips with full spatial magnetic sensitivity for spin-polarized scanning tunneling microscopy". [18] A. Wachowiak, J. Wiebe, M. Bode, O. Pietzsch, M. Morgenstern, and R. Wiesendanger, Science 298, 577 (2002): "Direct Observation of Internal Spin-Structure of Magnetic Vortex Cores". [19] L. Cornils, A. Kamlapure, L. Zhou, S. Pradhan, A. A. Khajetoorians, J. Fransson, J. Wiebe, and R. Wiesendanger, Phys. Rev. Lett. 119, 197002 (2017): "Spin-polarization of the Yu-Shiba-Rusinov state of an individual atom". [20] L. Schneider, Ph. Beck, J. Wiebe, and R. Wiesendanger, Science Advances 7, eabd7302 (2021): "Atomic-scale spin-polarization maps using functionalized superconducting probes". [21] A. Kubetzka, O. Pietzsch, M. Bode, and R. Wiesendanger, Phys. Rev. B 67, 020401 (2003): "Spin-polarized scanning tunneling microscopy study of 360° walls in an external magnetic field". [22] E. Y. Vedmedenko, L. Udvardi, P. Weinberger, and R. Wiesendanger, Phys. Rev. B 75, 104431 (2007): "Chiral magnetic ordering in two-dimensional ferromagnets with competing Dzyaloshinsky-Moriya interactions". [23] S. Meckler, N. Mikuszeit, A. Pressler, E. Vedmedenko, O. Pietzsch, and R. Wiesendanger, Phys. Rev. Lett. 103, 157201 (2009): "Real-space observation of a right-handed inhomogeneous cycloidal spin spiral by spin-polarized scanning tunneling microscopy in a triple axes vector magnet". [24] M. Bode, M. Heide, K. von Bergmann, P. Ferriani, S. Heinze, G. Bihlmayer, A. Kubetzka, O. Pietzsch, S. Blügel, and R. Wiesendanger, Nature 447, 190 (2007): "Chiral magnetic order at surfaces driven by inversion asymmetry". [25] K. von Bergmann, S. Heinze, M. Bode, E. Y. Vedmedenko, G. Bihlmayer, S. Blügel, and R. Wiesendanger, Phys. Rev. Lett. 96, 167203 (2006): "Observation of a complex nano-scale magnetic structure in a hexagonal Fe monolayer". [26] S. Heinze, K. von Bergmann, M. Menzel, J. Brede, A. Kubetzka, R. Wiesendanger, G. Bihlmayer, and S. Blügel, Nature Physics 7, 713 (2011): "Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions". [27] N. Romming, Ch. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Science 341, 636 (2013): "Writing and deleting single magnetic skyrmions". [28] N. Romming, A. Kubetzka, Ch. Hanneken, K. von Bergmann, and R. Wiesendanger, Phys. Rev. Lett. 114, 177203 (2015): "Field-dependent size and shape of single magnetic skyrmions". [29] P.-J. Hsu, A. Kubetzka, A. Finco, N. Romming, K. von Bergmann, and R. Wiesendanger, Nature Nanotechnology 12, 123 (2017): "Electric-field-driven switching of individual magnetic skyrmions". [30] R. Wiesendanger, Nature Reviews Materials 1, 16044 (2016): "Nanoscale magnetic skyrmions in metallic films and multilayers: a new twist for spintronics". [31] L. Zhou, J. Wiebe, S. Lounis, E. Vedmedenko, F. Meier, S. Blügel, P. H. Dederichs, and R. Wiesendanger, Nature Physics 6, 187 (2010): "Strength and directionality of surface RKKY-interaction mapped on the atomic scale". [32] A. A. Khajetoorians, J. Wiebe, B. Chilian, and R. Wiesendanger, Science 332, 1062 (2011): "Realizing all-spin based logic operations atom by atom". [33] J. Hermenau, S. Brinker, M. Marciani, M. Steinbrecher, M. dos Santos Dias, R. Wiesendanger, S. Lounis, and J. Wiebe, Nature Commun. 10, 2565 (2019): "Stabilizing spin systems via symmetrically tailored RKKY interactions". [34] A. A. Khajetoorians, M. Steinbrecher, M. Ternes, M. Bouhassoune, S. Lounis, M. dos Santos Dias, J. Wiebe, and R. Wiesendanger, Nature Commun. 7, 10620 (2016): "Tailoring the chiral magnetic interaction between two individual atoms". [35] M. Steinbrecher, R. Rausch, K. T. Ton, J. Hermenau, A. A. Khajetoorians, M. Potthoff, R. Wiesendanger, and J. Wiebe, Nature Commun. 9, 2853 (2018): "Non-collinear spin states in bottom-up fabricated atomic chains". [36] M. Menzel, Y. Mokrousov, R. Wieser, J. E. Bickel, E. Vedmedenko, S. Blügel, S. Heinze, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, Phys. Rev. Lett. 108, 197204 (2012): "Information transfer by vector spin chirality in finite magnetic chains". [37] H. Kim, A. Palacio-Morales, T. Posske, L. Rózsa, K. Palotas, L. Szunyogh, M. Thorwart, and R. Wiesendanger, Science Advances 4, eaar5251 (2018): "Towards tailoring Majorana bound states in artificially constructed magnetic atom chains on elemental superconductors". [38] L. Schneider, S. Brinker, M. Steinbrecher, J. Hermenau, T. Posske, M. dos Santos Dias, S. Lounis, R. Wiesendanger, and J. Wiebe, Nature Commun. 11 4707 (2020): "Controlling in-gap end states by linking nonmagnetic atoms and artificially-constructed spin chains on superconductors". [39] M. Bode, O. Pietzsch, A. Kubetzka, and R. Wiesendanger, Phys. Rev. Lett. 92, 067201 (2004): "Shape dependent Thermal Switching Behavior of Superparamagnetic Nanoislands". [40] A. A. Khajetoorians, B. Baxevanis, Ch. Hübner, T. Schlenk, S. Krause, T. Wehling, S. Lounis, A. Lichtenstein, D. Pfannkuche, J. Wiebe, and R. Wiesendanger, Science 339, 55 (2013): "Current-driven spin dynamics of artificially constructed quantum magnets". [41] S. Krause, L. Berbil-Bautista, G. Herzog, M. Bode, and R. Wiesendanger, Science 317, 1537 (2007): "Current-induced magnetization switching with a Spin-Polarized Scanning Tunneling Microscope".

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