France



Fluctuations are ubiquitous in magnetically and charge ordered systems. Spanning multiple orders of magnitude in space and time, they often lead to a wealth of fascinating physical effects. Recent examples of such dynamics are fluctuations of spin- and charge density waves in antiferromagnets [1], diffusion-like motion of magnetic skyrmions in low pinning magnetic multilayer or spontaneous fluctuations between ordered stripe and skyrmion lattices phases [2].&lt;br/&gt;High-resolution real-space imaging can resolve the spatial information. However, due to insufficient signal on a timescale faster than the relevant dynamics, averaging over an extended period of time (or repetitions) is key for the majority of high-resolution imaging experiments. So far, averaging has been performed blindly and continuously, leading to a trade-off between extracting either spatial or temporal information, especially in weak contrast systems.&lt;br/&gt;Here, we present coherent correlation imaging (CCI) – a high-resolution, full-field imaging technique that realizes multi-shot, time-resolved imaging of stochastic processes. The key of CCI is the classification of camera frames that correspond to that same physical state by combining a correlation-based similarity metric with powerful classification algorithm developed for nanoparticle tomography and genome research (see Fig. 1) [3]. CCI extends these algorithms to the temporal domain, realizing informed, non-sequential signal averaging while maintaining single frame temporal resolution. CCI does not require prior knowledge of the imaged system, rendering it the first time-resolved x-ray imaging technique capable of accessing systems with entirely unknown dynamics.&lt;br/&gt;To develop and demonstrate CCI, we study thermal hopping of magnetic domain walls – a prototypical example of stochastic nanometer-scale dynamics – on timescales ranging from sub-seconds to hours under equilibrium conditions. Our material is [Pt (2.7 nm)/Co&lt;sub&gt;60&lt;/sub&gt;Fe&lt;sub&gt;20&lt;/sub&gt;B&lt;sub&gt;20 &lt;/sub&gt;(0.8 nm)/MgO (1.5 nm)]&lt;sub&gt;15&lt;/sub&gt;, a chiral ferromagnet with magnetic pinning low enough to exhibit stochastically recurring dynamics that resemble thermally induced Barkhausen jumps near room temperature [4]. Imaging is performed through Fourier-transform x-ray holography with contrast provided by the x-ray magnetic circular dichroism [5].&lt;br/&gt;CCI reconstructs sharp, high-contrast images of all domain states and, unlike previous approaches, also tracks the time when these states occur (see Fig. 2). This uniquely reveals not only the occupation probabilities of all states, but further, the complex network of stochastic transition trajectories between states. The full potential of this technique will manifest at the next generation of pulsed high-coherence x-ray sources, where it promises to resolve a wealth of previously hidden dynamic processes, such as the nucleation dynamics of externally-induced phase transitions and the intrinsic fluctuations of weakly pinned textures in spin and charge ordered systems.

**References:**

[1] - Shpyrko, O. G. &lt;i&gt;et al.&lt;/i&gt; Direct measurement of antiferromagnetic domain fluctuations. &lt;i&gt;Nature&lt;/i&gt; 447, 68–71 (2007)&lt;br/&gt;[2] - Seaberg, M. H. &lt;i&gt;et al.&lt;/i&gt; Nanosecond X-Ray Photon Correlation Spectroscopy on Magnetic Skyrmions. &lt;i&gt;Physical Review Letters&lt;/i&gt; 119, 067403 (2017)&lt;br/&gt;[3] - Eisen, M. B. &lt;i&gt;et al&lt;/i&gt;. Cluster analysis and display of genome-wide expression patterns. &lt;i&gt;Proceedings of the National Academy of Sciences&lt;/i&gt; 95, 14863–14868 (1998)&lt;br/&gt;[4] - Lemesh, I. &lt;i&gt;et al.&lt;/i&gt; Current-Induced Skyrmion Generation through Morphological ThermalTransitions in Chiral Ferromagnetic Heterostructures. &lt;i&gt;Advanced Materials&lt;/i&gt; 30, 1805461 (2018)&lt;br/&gt;[5] - Eisebitt, S. &lt;i&gt;et al.&lt;/i&gt; Lensless imaging of magnetic nanostructures by X-ray spectro-holoraphy. &lt;i&gt;Nature&lt;/i&gt; 432, 885–888 (2004)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/02c68b10457f8b0b09df682b3321c147.jpg)
Figure 1| Single-frame correlation and single-frame imaging. a, CCI two-time correlation&lt;br /&gt;
analysis showing the similarity between the states recorded at different times. b, Cross-section of the two-time correlation function at &lt;i&gt;t&lt;sub&gt;2&lt;/sub&gt; = 28&lt;/i&gt; s (red line in (a)). The colored shades define frames that correspond to the same physical state of the system. c, Image corresponding to the blind average of all frames. High-contrast regions indicate stationary behavior of the local out-of-plane magnetization &lt;i&gt;m&lt;sub&gt;z&lt;/sub&gt;&lt;/i&gt;, while seemingly semi-transparent features correspond to a superposition of two different magnetic states. d,e, Images obtained by selectively averaging the blue and yellow shaded regions in (b), respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/d7e9df838294c2b83f25a91cbc1552ab.jpg)
Figure 2| CCI-resolved dynamics in our sample. a, Real-space images of all domain states. Field of view is 720 nm in diameter. b, Temporal evolution of the states. The horizontal axis indicates the measurement time. The vertical axis shows which state has existed at the given time.

INTERMAG 2021

Coherent Correlation Imaging: High-resolution imaging of stochastic dynamics INVITED

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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MMM 2022

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Fluctuations are ubiquitous in magnetically and charge ordered systems. Spanning multiple orders of magnitude in space and time, they often lead to a wealth of fascinating physical effects. Recent examples of such dynamics are fluctuations of spin- and charge density waves in antiferromagnets [1], diffusion-like motion of magnetic skyrmions in low pinning magnetic multilayer or spontaneous fluctuations between ordered stripe and skyrmion lattices phases [2]. High-resolution real-space imaging can resolve the spatial information. However, due to insufficient signal on a timescale faster than the relevant dynamics, averaging over an extended period of time (or repetitions) is key for the majority of high-resolution imaging experiments. So far, averaging has been performed blindly and continuously, leading to a trade-off between extracting either spatial or temporal information, especially in weak contrast systems. Here, we present coherent correlation imaging (CCI) – a high-resolution, full-field imaging technique that realizes multi-shot, time-resolved imaging of stochastic processes. The key of CCI is the classification of camera frames that correspond to that same physical state by combining a correlation-based similarity metric with powerful classification algorithm developed for nanoparticle tomography and genome research (see Fig. 1) [3]. CCI extends these algorithms to the temporal domain, realizing informed, non-sequential signal averaging while maintaining single frame temporal resolution. CCI does not require prior knowledge of the imaged system, rendering it the first time-resolved x-ray imaging technique capable of accessing systems with entirely unknown dynamics. To develop and demonstrate CCI, we study thermal hopping of magnetic domain walls – a prototypical example of stochastic nanometer-scale dynamics – on timescales ranging from sub-seconds to hours under equilibrium conditions. Our material is [Pt (2.7 nm)/Co60Fe20B20 (0.8 nm)/MgO (1.5 nm)]15, a chiral ferromagnet with magnetic pinning low enough to exhibit stochastically recurring dynamics that resemble thermally induced Barkhausen jumps near room temperature [4]. Imaging is performed through Fourier-transform x-ray holography with contrast provided by the x-ray magnetic circular dichroism [5]. CCI reconstructs sharp, high-contrast images of all domain states and, unlike previous approaches, also tracks the time when these states occur (see Fig. 2). This uniquely reveals not only the occupation probabilities of all states, but further, the complex network of stochastic transition trajectories between states. The full potential of this technique will manifest at the next generation of pulsed high-coherence x-ray sources, where it promises to resolve a wealth of previously hidden dynamic processes, such as the nucleation dynamics of externally-induced phase transitions and the intrinsic fluctuations of weakly pinned textures in spin and charge ordered systems.

**References:**

[1] - Shpyrko, O. G. et al. Direct measurement of antiferromagnetic domain fluctuations. Nature 447, 68–71 (2007) [2] - Seaberg, M. H. et al. Nanosecond X-Ray Photon Correlation Spectroscopy on Magnetic Skyrmions. Physical Review Letters 119, 067403 (2017) [3] - Eisen, M. B. et al. Cluster analysis and display of genome-wide expression patterns. Proceedings of the National Academy of Sciences 95, 14863–14868 (1998) [4] - Lemesh, I. et al. Current-Induced Skyrmion Generation through Morphological ThermalTransitions in Chiral Ferromagnetic Heterostructures. Advanced Materials 30, 1805461 (2018) [5] - Eisebitt, S. et al. Lensless imaging of magnetic nanostructures by X-ray spectro-holoraphy. Nature 432, 885–888 (2004)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/02c68b10457f8b0b09df682b3321c147.jpg)
Figure 1| Single-frame correlation and single-frame imaging. a, CCI two-time correlation 
analysis showing the similarity between the states recorded at different times. b, Cross-section of the two-time correlation function at t2 = 28 s (red line in (a)). The colored shades define frames that correspond to the same physical state of the system. c, Image corresponding to the blind average of all frames. High-contrast regions indicate stationary behavior of the local out-of-plane magnetization mz, while seemingly semi-transparent features correspond to a superposition of two different magnetic states. d,e, Images obtained by selectively averaging the blue and yellow shaded regions in (b), respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/d7e9df838294c2b83f25a91cbc1552ab.jpg)
Figure 2| CCI-resolved dynamics in our sample. a, Real-space images of all domain states. Field of view is 720 nm in diameter. b, Temporal evolution of the states. The horizontal axis indicates the measurement time. The vertical axis shows which state has existed at the given time.

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

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.

Progress in Magnetic Force Microscopy



Since the 80’s, when Brillouin light scattering emerged as a powerful tool for investigating magnetization dynamics in thin films and multilayers, it developed into a versatile microscopic probe for studying collective spin excitations. Following a short introduction on studies of millimeter-sized films, we will give examples how to investigate individual magnetic structures down to tens of nanometers in dimension. We will introduce the concepts of time- and phase-resolved Brillouin light scattering which give full access to the spatio-temporal evolution of the optically accessible spin-wave spectrum. During our talk, we will provide hands-on demonstrations how to drive spin waves via spin currents and microwave excitations in magnetic nanostructures using the build in dc/ac probe station in our laboratory and show the capabilities of Brillouin light scattering for quantifying spin-wave phenomena. Furthermore, we will highlight similarities and differences to other optical scanning probe techniques such as time-resolved magneto-optical Kerr microscopy and optically detected magnetic resonance based on vacancy centers. We will outline how those techniques can potentially be combined with Brillouin light scattering to access complementary information.

**References:**



**Images:**





Brillouin Light Scattering Revisited

The modernization of steel industry has brought up an interest in development of novel and fast characterization techniques that analyze the material from different aspects with the same instrument setup. In recent years, development of magnetic characterization techniques arose for investigating the microstructure and mechanical properties of certain steels [1]. However, these techniques display limited flexibility in terms of surface specific measurements and defect analysis that can become an important part in quality assurance of a produced material. Within this work, a novel utilization of magneto-optical Kerr effect (MOKE) microscopy for microstructural and stress evaluation of martensitic steels is discussed. MOKE has been proven to be a very powerful and versatile characterization technique [2], that allows investigation of magnetic domains and magnetic properties that emerge from the investigated material’s surface. With domain analysis and evaluation of magnetization change with external magnetic field, the surface magnetic properties can be correlated to the bulk magnetic properties of the material [3]. Furthermore, the technique allows high-resolution imaging and investigation of microstructural characteristics of the material without the usage of etchants that can potentially modify the microstructure and ending results. By correlating the microstructural attributes to the magnetic behavior of the material’s surface, the different phases of the material can be distinguished and morphologically analyzed. The method also allows clear identification of austenite in the matrix of martensitic steels, since austenite is non-magnetic opposite to other matrix phases. As a result, the method is highly versatile and allows investigation of steels on different aspects of its properties on a microstructural level. We present the applicability of MOKE on an example of martensitic high-speed steels with micrometer sized microstructural features. The presented data will provide insight into the correlation of the magnetic information to the microstructure. The novelty of this research lies in the application of MOKE microscopy on steels that are relatively magnetically hard and have a fine grain size (under 10 µm). The utilization of MOKE microscopy for phase and microstructure investigation on such steels has until now not been performed. To further display the practicality of MOKE, the steel is investigated with two different processing states, conventionally heat treated and deep cryogenic treated (DCT) [4]. DCT exposes the steel to sub-zero temperatures down to the temperature of liquid nitrogen (-196 °C) inducing further transformation of retained austenite into martensite, which is beneficial for the mechanical properties [5]. The presented examples display the capability of MOKE to identify small quantities of retained austenite of volumetric fraction under 1 %, which is challenging to evaluate with other commonly used techniques such as electron back scattering diffraction (EBSD) and X-ray diffraction (XRD) [6]. In addition to microstructural analysis, we also explore the possibility to use MOKE for residual stress analysis. The technique involves the application of a Vickers indenter that imposes localized stress changes through an indentation imprint on the material’s surface. The resulting stress extends radially from the indentation and decreases in magnitude with distance from the edge of the indentation. With local magnetometry and domain analysis of the material’s surface before and after the stress state modification, a correlation to the residual stress of the material is established. The applicability of the method is presented on the example of the conventionally treated and DCT steel, for which the DCT is reported to reduce tensile residual stresses. MOKE analysis confirms the reduction of residual stresses as well as confirms the change of tensile residual stresses to compressive residual stresses as reported by previous researchers [7]. With the discussed results we present that MOKE microscopy shows high potential as a fast and in-depth microstructural and stress characterization technique applicable on an industrial scale.

**References:**

[1] J. Liu, J. Wilson and M. Strangwood, J. Magn. Magn. Mater., vol. 401, pp. 579–592 (2016). [2] J. McCord, J. Phys. D. Appl. Phys., vol. 48, no. 33, p. 333001 (2015). [3] F. Qiu, M. J. Klug and G. Tian, J. Phys. D. Appl. Phys., vol. 52, no. 26, p. 265001 (2019). [4] B. Podgornik, V. Leskovsek, and J. Vizintin, Mater. Manuf. Process., vol. 24, no. 7–8, pp. 734–738 (2009). [5] P. Jovičević-Klug, B. Podgornik, J. Mater. Res. Technol. Vol. 9, 13118–27 (2020). [6] Y. Zhang, P. Lai and H. Jia, Metals, vol. 9, no. 1, p. 94 (2019). [7] D. Senthilkumar, I. Rajendran and M. Pellizzari, J. Mater. Process. Technol. Vol. 211, pp. 396–401 (2011).

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Microstructural and Residual Stress Evaluation of Bulk Martensitic Steels with Micrometer-sized Grains through Magneto-optical Kerr Effect

Spintronic devices based on antiferromagnetic (AFM) materials has drawn significant attention due to its potential for information storage with low power consumption and ultrafast switching speeds. Since all the information storage in AFM spintronics devices rely on the switching of AFM domains, there is an urgent requirement to directly measure the AFM domain in real space during the spin switching process. Recently, we developed a novel method to image the AFM domains in single crystal CoO and NiO thin films grown on MgO(001) substrates with the magneto-optical birefringence effect[1,2]. The magneto-optical birefringence effect is found to strongly depend on the photon energy of incident light. Utilizing this optical method, we demonstrated the first real-time imaging of the AFM domain switching process in Fe/CoO system through the spin-flop coupling. While applying a constant field, the domain nucleation dominates the switching process, but while applying an alternative field, the AFM domain switching process is found to be dominated by domain wall motion. Our studies demonstrate that the AFM domain imaging under external fields or current pulse can be achieved in real time, which could be helpful for the understanding of the dynamics of AFM materials and the development of AFM spintronics storage devices.

**References:**

Jia Xu, et. al, New J. Phys. 22, 083030 (2020). Jia Xu, et. al, Phys. Rev. B 100, 134413 (2019).

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Imaging the dynamical switch of antiferromagnetic domains by optical microscopy INVITED

A quantum diamond microscope (QDM) uses a uniform sheet of magnetically-sensitive nitrogen-vacancy (NV) centers in diamond placed on top of a flat magnetic sample [1,2]. In a QDM, we illuminate the NVs with laser light, probe the NV transitions with a microwave field, and image the NV fluorescence with a microscope and camera. This allows us take pictures of the magnetic field in every pixel. Compared to other magnetic imaging tools (SQUID, MOKE, and MFM), the recently-developed QDM has the following advantages, enabling new measurements that were previously unfeasible and generating interest in the physics, geomagnetism, and biomagnetism communities: 1. Large field of view (~1 mm) 2. Parallelized camera readout of 1E6 pixels, with no raster scanning 3. Minimal sample-sensor separation (as small as a few nanometers), which enables high signal-to-noise ratio and sub-micron spatial resolution 4. Capability for full-vector or scalar-projection magnetic imaging, over a wide range of magnetic field frequencies (DC to 100 GHz) and temperatures (0 to 600 K) This talk will discuss how we apply the QDM instrumentation techniques in interdisciplinary applications in related physics and engineering disciplines. I will highlight our recent success with imaging fabricated 2D magnetic materials, reconstructing the electric currents in integrated circuits to troubleshoot and diagnose their behavior, hunting for failures in fabricated silicon electronics, and measuring previously-inaccessible characteristics of ion chip traps used for quantum computing. I will conclude this talk with a preview of upcoming new directions for NV diamond magnetic imaging with color centers, such as NV magnetic sensing in extreme environments and promising alternative color-center candidates. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International, Inc., for the DOE's National Nuclear Security Administration under contract DE-NA0003525.

**References:**

1. Geochem. Geophys. Geosyst. 18, 8 (2017) 2. Nanophotonics 8 11 1945-1973 (2019).

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Developing High-Resolution Magnetic Microscopy Applications Using NV Centers in Diamond INVITED

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:**

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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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