France



Magnetic force microscopy (MFM) is a versatile technique used to image the micromagnetic state of a sample and its dependence on an applied magnetic field and/or on the sample temperature with a spatial resolution down to about 10 nm. The high resolution and the ease of implementation in existing atomic force microscopy (AFM) tools make the MFM technique particularly desirable for the investigation of magnetic thin films and nanoscale devices. The measured signal in MFM is a change of the dynamic properties of the imaging cantilever arising from the interaction of the magnetic cantilever tip with the stray field emanating from the sample surface. The obtained MFM images are therefore only indirectly connected to the micromagnetic state of the sample. However, if the perturbations to the micromagnetic states of the tip and sample are negligible during the measurement process, the measured MFM signal can be described as the convolution of the magnetic moment of the tip with the stray field of the sample. This allows for a quantitative analysis of the stray field by the deconvolution of MFM data. Such a deconvolution of the stray field from the measured MFM signal requires the calibration of the imaging properties of the tip. The latter can be achieved by fitting multipole moments to the tip in order to fit MFM data obtained on samples with a known stray field. Nevertheless, the success of such procedures remained limited: the size and position of the tip monopole and dipole moments were found to be dependent on the size of the imaged sample structures.&lt;br/&gt;&lt;br/&gt;A concept of tip transfer function (TF) was proposed two decades ago by van Schendel &lt;i&gt;et al.&lt;/i&gt; [1]. This approach is used to specify the imaging properties of the probe and thus to access the quantitative information about the stray field emanating from the sample surface. More precisely, the method calibrates the response of the MFM tip on different spatial wavelengths of the stray field. This calibration method was then used by our group for the determination of the closure domain structure in thick Cu/Ni/Cu trilayer samples [2], for the measurement of the local density of pinned uncompensated spins in exchange-biased thin films [3], for the measurement of stray fields arising from skyrmions and the determination of the chirality in thin film systems with DMI [4], and for the detailed analysis of the complex dependence of the micromagnetic state on the external field in exchange-coupled Co/Pt-TbFe [5].&lt;br/&gt;&lt;br/&gt;Despite these successes, the tip calibration method presented by van Schendel &lt;i&gt;et al.&lt;/i&gt; has only been taken up slowly. Examples include the reconstruction of magnetic vortex state at the end of FeCo nanowires [6] and the characterization of the 3D stray field landscape above a Ir17Mn83/Co70Fe30 exchange-biased multilayer system with engineered domain walls [7]. However, more recently, quantitative MFM methods have gained renewed interest. Hu et al. have for example analyzed the reproducibility of the tip calibration methods following the TF approach in round robin tests [8]. The results presented by different groups were however based on data acquired with MFM instruments operated under ambient conditions. The limited sensitivity of these instruments and consequently the low signal-to-noise ratio largely affect the final results obtained by the quantitative procedure. Moreover, the tip-sample distance control in most of the existing work was achieved by lift-mode operation, where the sample topography is first scanned with the tip in intermittent contact with the sample. Although the reproducibility of the measurements can be ensured to some extent, tip wear is almost unavoidable as also pointed out in Ref. [8].&lt;br/&gt;&lt;br/&gt;To exploit all the advantages of quantitative MFM in the investigation of magnetic thin films and nanostructures, the instrument is preferably operated under vacuum conditions. Furthermore, a noncontact technique for tip-sample distance control should be applied to avoid the tip wear.&lt;br/&gt;&lt;br/&gt;In this work, we present a state-of-the-art MFM tip calibration procedure based on measurements performed in vacuum and with high-quality factor (Q) cantilevers. We also discuss the subtleties in data treatment specifically during tip calibration procedure, which have been largely overlooked in the past. In addition, the advantages and the limits of this TF-method are addressed.

**References:**

[1] Schendel, H. J. Hug, B. Stiefel &lt;i&gt;et.al.&lt;/i&gt;, J. Appl. Phys. 88, 435 (2000).&lt;br/&gt;[2] M. A. Marioni, N. Pilet, T. V. Ashworth &lt;i&gt;et al.&lt;/i&gt;, Phys. Rev. Lett. 97, 027201 (2006).&lt;br/&gt;[3] A. Benassi, M. A. Marioni, D. Passerone &lt;i&gt;et al.&lt;/i&gt;, Sci Rep 4, 4508 (2014).&lt;br/&gt;[4] M. Baćani, M. A. Marioni, J. Schwenk &lt;i&gt;et al.,&lt;/i&gt; Sci Rep 9, 3114 (2019).&lt;br/&gt;[5] M. Heigl, C. Vogler, A-O Mandru &lt;i&gt;et al.&lt;/i&gt;, ACS Appl. Nano Mater. 3, 9, 9218–9225 (2020).&lt;br/&gt;[6] S. Vock, C. Hengst, M. Wolf &lt;i&gt;et al.,&lt;/i&gt; Appl. Phys. Lett. 105, 172409 (2014).&lt;br/&gt;[7] N. Zingsem, F. Ahrend, S. Vock &lt;i&gt;et.al., &lt;/i&gt;J. Phys. D: Appl. Phys.50 495006 (2017).&lt;br/&gt;[8] X. Hu, G, Daia, S. Sieversa &lt;i&gt;et al., &lt;/i&gt; J. Magn. Magn. Mater. 511, 166947 (2020).

**Images:**





INTERMAG 2021

Quantitative Magnetic Force Microscopy: Tip Transfer Function Method Revisited with High-Quality Data

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Magnetic force microscopy (MFM) is a versatile technique used to image the micromagnetic state of a sample and its dependence on an applied magnetic field and/or on the sample temperature with a spatial resolution down to about 10 nm. The high resolution and the ease of implementation in existing atomic force microscopy (AFM) tools make the MFM technique particularly desirable for the investigation of magnetic thin films and nanoscale devices. The measured signal in MFM is a change of the dynamic properties of the imaging cantilever arising from the interaction of the magnetic cantilever tip with the stray field emanating from the sample surface. The obtained MFM images are therefore only indirectly connected to the micromagnetic state of the sample. However, if the perturbations to the micromagnetic states of the tip and sample are negligible during the measurement process, the measured MFM signal can be described as the convolution of the magnetic moment of the tip with the stray field of the sample. This allows for a quantitative analysis of the stray field by the deconvolution of MFM data. Such a deconvolution of the stray field from the measured MFM signal requires the calibration of the imaging properties of the tip. The latter can be achieved by fitting multipole moments to the tip in order to fit MFM data obtained on samples with a known stray field. Nevertheless, the success of such procedures remained limited: the size and position of the tip monopole and dipole moments were found to be dependent on the size of the imaged sample structures. A concept of tip transfer function (TF) was proposed two decades ago by van Schendel et al. [1]. This approach is used to specify the imaging properties of the probe and thus to access the quantitative information about the stray field emanating from the sample surface. More precisely, the method calibrates the response of the MFM tip on different spatial wavelengths of the stray field. This calibration method was then used by our group for the determination of the closure domain structure in thick Cu/Ni/Cu trilayer samples [2], for the measurement of the local density of pinned uncompensated spins in exchange-biased thin films [3], for the measurement of stray fields arising from skyrmions and the determination of the chirality in thin film systems with DMI [4], and for the detailed analysis of the complex dependence of the micromagnetic state on the external field in exchange-coupled Co/Pt-TbFe [5]. Despite these successes, the tip calibration method presented by van Schendel et al. has only been taken up slowly. Examples include the reconstruction of magnetic vortex state at the end of FeCo nanowires [6] and the characterization of the 3D stray field landscape above a Ir17Mn83/Co70Fe30 exchange-biased multilayer system with engineered domain walls [7]. However, more recently, quantitative MFM methods have gained renewed interest. Hu et al. have for example analyzed the reproducibility of the tip calibration methods following the TF approach in round robin tests [8]. The results presented by different groups were however based on data acquired with MFM instruments operated under ambient conditions. The limited sensitivity of these instruments and consequently the low signal-to-noise ratio largely affect the final results obtained by the quantitative procedure. Moreover, the tip-sample distance control in most of the existing work was achieved by lift-mode operation, where the sample topography is first scanned with the tip in intermittent contact with the sample. Although the reproducibility of the measurements can be ensured to some extent, tip wear is almost unavoidable as also pointed out in Ref. [8]. To exploit all the advantages of quantitative MFM in the investigation of magnetic thin films and nanostructures, the instrument is preferably operated under vacuum conditions. Furthermore, a noncontact technique for tip-sample distance control should be applied to avoid the tip wear. In this work, we present a state-of-the-art MFM tip calibration procedure based on measurements performed in vacuum and with high-quality factor (Q) cantilevers. We also discuss the subtleties in data treatment specifically during tip calibration procedure, which have been largely overlooked in the past. In addition, the advantages and the limits of this TF-method are addressed.

**References:**

[1] Schendel, H. J. Hug, B. Stiefel et.al., J. Appl. Phys. 88, 435 (2000). [2] M. A. Marioni, N. Pilet, T. V. Ashworth et al., Phys. Rev. Lett. 97, 027201 (2006). [3] A. Benassi, M. A. Marioni, D. Passerone et al., Sci Rep 4, 4508 (2014). [4] M. Baćani, M. A. Marioni, J. Schwenk et al., Sci Rep 9, 3114 (2019). [5] M. Heigl, C. Vogler, A-O Mandru et al., ACS Appl. Nano Mater. 3, 9, 9218–9225 (2020). [6] S. Vock, C. Hengst, M. Wolf et al., Appl. Phys. Lett. 105, 172409 (2014). [7] N. Zingsem, F. Ahrend, S. Vock et.al., J. Phys. D: Appl. Phys.50 495006 (2017). [8] X. Hu, G, Daia, S. Sieversa et al., J. Magn. Magn. Mater. 511, 166947 (2020).

**Images:**

technical paper

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).

**Images:**

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).

**Images:**

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).

**Images:**

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

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.

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

Among other properties of magnetic films, the evaluation of the magnetization in response to changing external magnetic fields (magnetization reversal loops) and especially the dependence of the reversal on the magnetic field angle, which reflects the anisotropy of the material, is of particular interest for both fundamental and applied research. Measuring reversal loops at various field angles by magnetometry requires that the sensitivity of the magnetometer is aligned along the field direction for all field angles. For the commonly applied vibrating sample magnetometry (VSM) or its more advanced variants of vectorial VSM, this involves the complexity of a mechanical rotation of the sample. The anisotropic magnetoresistance can also be utilized by electric transport measurements, which requires, however, lithography and sample patterning. A powerful and extensively applied alternative method is magneto-optical Kerr Effect (MOKE) magnetometry. Apart from magnetometry, the Kerr effect is also employed in wide-field Kerr microscopy, which is an effective tool for both magnetic domain imaging. Several approaches to realize vectorial MOKE magnetometry have been reported in literature mostly based on systems that apply the longitudinal Kerr effect. However, in most cases the angular dependence is again achieved by mechanical adjustment like in VSM, i.e. the specimen has to be physically rotated to achieve alignment of the field and the sensitivity axis, possibly resulting in experimental error and spurious signals. Furthermore, it is usually assumed that the axis of the longitudinal Kerr sensitivity (the direction of magnetization at the surface, which produces the maximum Kerr signal) is precisely aligned along the plane of light incidence. As we will show in this paper, this assumption is only valid in limited cases while in general there may be transverse Kerr contributions superimposed leading to rotated sensitivity directions. In this work, we have theoretically analyzed the contrast generated in a wide-field Kerr microscope, specifically its dependence on the polarization of light and the plane of incidence, and verified it experimentally. An analytical expression for the magnetization reconstruction along the direction of an externally applied field was derived. This allowed us to develop a fully automated method for the measurement of magnetization reversal loops in magnetic films with in-plane anisotropy without any mechanical adjustment of the system or sample displacement. The subsequent analysis of the angular dependencies of the coercive field and remanent magnetization (see figure) provides insights into the magnetic anisotropy of the film. Although the method is experimentally not restricted to magnetic films, it should be granted that the magnetization does not change across the thickness if bulk specimens are investigated. The applicability and functionality of the technique was demonstrated on an FeO/Fe thin magnetic film [1], which is dominated by a uniaxial anisotropy.

**References:**

 [1] J. Zehner, I. Soldatov, S. Schneider, R. Heller, N. B. Khojasteh, S. Schiemenz, S. Fäahler, K. Nielsch, R. Schäfer, and K. Leistner, Adv. Electron. Mater. n/a, 2000406 (2020). [2] I. Soldatov and R. Schafer, Review of Scientific Instruments 88, 073701 (2017).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/8e5dc939abb697a0ae5d76d5e34bb13d.jpg)
(a) and (b) Hysteresis loops, obtained with complimentary sensitivities: (a) s-polarised light along the y-axis and (b) p-polarised light along the x-axis. In (c) the field is applied at an angle of 40o to the x-direction. The magnetisation along this field direction was reconstructed from (a) and (b) The incidence plane is defined by activating proper LEDs as indicated by the circular insets that show the ends of the glass fibre cross in the conoscopic imaging mode [2]. (b) and (c) Angular dependencies of coercive field and remanent magnetisation, respectively (the black points are measured and the red curve is an extrapolation by mirroring with respect to the y-axis). The data is obtained on the Fe/FeO film with 10 nm thickness

Advanced, Kerr-microscopy-based MOKE magnetometry for the anisotropy characterization of magnetic films

Discovery of the Dzyaloshinskii-Moriya Interaction (DMI) in magnetic thin films has launched an intense research effort into its effects on the structure of magnetic bubbles and domain walls including the formation of topological excitations like skyrmions. While it is well established that the internal structure of a DW transitions from a Bloch to a Néel domain wall when there is sufficient DMI, less attention has been paid to excitations contained within the domain wall. For example, recently, a new feature known as a domain wall (DW) skyrmion has been theoretically predicted and observed experimentally [1,2]. These are 360 degree rotations of the internal magnetization of a DW, which are the post-DMI analogue of a vertical Bloch line (VBL), where there is a 180 degree rotation. Moving forward, it will be important to probe excitations like these in situ to understand their dynamic behavior. Here we demonstrate the manipulation of VBLs via in-plane magnetic fields observed in situ using Lorentz transmission electron microscopy (LTEM). In this work, (Co/Ni)M multi-layers are deposited via magnetron sputtering directly onto custom-sized Si3N4 TEM membranes. We chose to examine an M=10 sample as we have previously observed an abundance of 1-π and 2-π VBLs along its DWs [3]. We note that 2-π VBLs are topologically equivalent to DW skyrmions. Fresnel mode Lorentz TEM was performed on an FEI Tecnai F20 in Lorentz mode (objective lens turned off). In-plane magnetic fields are applied in situ through the use of a Hummingbird Scientific magnetic biasing holder; the specific holder used here has a field range of ±300 Oe. In the as-prepared state, many VBLs are observed along Bloch DWs in Fresnel-mode micrographs (Fig. 1). Upon application of in-plane magnetic fields of increasing strength, we observe the movement of VBLs along DWs. When the field direction is reversed, we observe the same VBLs to move in the opposite direction. Additionally, we observe the annihilation of VBLs following the impingement of their movement by VBLs of the same winding direction. The winding of these VBLs can be reasoned to be the same sign as one another because those with opposite winding would have a zero-energy barrier to annihilation as seen in Fig. 2. Details regarding challenges to imaging, observations in high-DMI samples, and other implications of this technique will be further discussed in this presentation [4].

**References:**

 [1] R. Cheng, M. Li, A. Sapkota, A. Rai, et al., Phys. Rev. B, Vol. 99, p. 184412 (2019). [2] M. Li, A. Sapkota, A. Rai, A. Pokhrel, et al., arXiv: 2004.07888, (2020). [3] M. Li, D. Lau, M. De Graef, and V. Sokalski, Phys. Rev. Mater., Vol. 3, p. 064409, (2019). [4] This research is supported by the Defense Advanced Research Project Agency (DARPA) program on Topological Excitations in Electronics (TEE) under grant number D18AP00011. The authors also acknowledge use of the Materials Characterization Facility at Carnegie Mellon University supported by grant MCF-677785.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/9dd928d7fad895994fe561ade50c29b7.jpg)
Micrographs of magnetic domain walls in [Co/Ni]10 samples with magnetic fields applied in the (left) ``positive" and (right) ``negative" directions. Arrows highlight positions of vertical Bloch lines whereas dotted circles indicate locations of 2-π vertical Bloch lines that have annihilated.

![](https://assets.underline.io/uploads/markdown_image/1/image/4e2179244bbc8d33a73434151e51b02a.jpg)
Micrographs of two vertical Bloch lines ``unwinding" as magnetic field strength is increased. Insets depict magnified view of circled regions with potential domain wall configuration labeled with arrows. Scale bar is 1 μm.

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