France



&lt;br/&gt;I Introduction&lt;br/&gt;The iron core residual flux density is one of the two reasons that cause the no-load closing of the large power transformer to generate magnetizing inrush current&lt;sup&gt;[1]&lt;/sup&gt;. In order to effectively weaken the residual flux density to reduce the occurrence probability of magnetizing inrush current, it is necessary to measure the magnitude and direction of the residual flux density. In the existing research, the empirical estimation method&lt;sup&gt;[2]&lt;/sup&gt; and the voltage integration method&lt;sup&gt;[3]&lt;/sup&gt; are mainly used to estimate the residual flux density in the core, but these methods have some limitations in the residual flux measurement of large power transformer. Therefore, the accurate measurement of the residual flux density in the core is of great theoretical significance for the efficient operation of the whole power grid. The main purpose of this paper is to study the most effective method to measure the residual flux density of transformer.&lt;br/&gt;II Theoretical analysis of measurement methods&lt;br/&gt;When the transformer core structure is fixed, the excitation inductance is mainly affected by differential permeability. Residual flux will lead to the change of core differential permeability. By using the method of field-circuit coupling, the magnetic field problem with closed magnetic circuit structure is transformed into the circuit problem with equivalent inductance. Based on the electromagnetic transient characteristics of iron core materials, this paper proposes a residual flux density measurement method of externally applied voltage. The residual flux results in different transient current waveforms under positive and reverse voltage applied in the windings. The relation expression between the extreme value of transient current difference and residual flux is derived theoretically. In order to improve the accuracy of residual flux density measurement, modeling and analysis were carried out on the measured square core, and a set of appropriate test circuit parameters were optimized based on the differential permeability characteristics of the core material. It can be seen from Fig.1 that the transient current differential extremum parameter &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt;, Δ &lt;i&gt;I&lt;/i&gt;&lt;sub&gt;max&lt;/sub&gt; change with residual flux changes obviously, but the parameter &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt; is more sensitive to the change of residual flux in the core. Therefore, &lt;i&gt;t&lt;/i&gt;&lt;sub&gt;s&lt;/sub&gt; is selected as the basis for quantitative detection of residual flux.&lt;br/&gt;III Conclusion&lt;br/&gt;By using the finite element method, the effects of different circuit parameters on the transient process can be compared, and some valuable conclusions are obtained, which will provide a theoretical reference for the subsequent application of the measurement method. Finally, experimental verification was carried out on the measured core, and the estimated residual flux in the core was compared with the actual value. As shown in Figure 2, the maximum measurement error did not exceed 5.4%. Therefore, it was considered that the measurement method proposed in this paper was reliable. This method can be used to test the residual flux of large power transformer without any requirement for transformer, which laid a foundation for the quantitative detection of residual flux in transformer core.

**References:**

[1] Y. Wang, Z. Liu and H. Chen, &quot;Research on Residual Flux Prediction of the Transformer&quot;, IEEE Transactions on Magnetics, Vol. 53, no. 6, pp. 1-4, June 2017.&lt;br/&gt;[2] Colombo E, Santagostino G. &quot;Results of the enquiries on actual network conditions when switching magnetizing and small inductive currents and on transformer and shunt reactor saturation characteristics&quot;, Electra, 1984, 94: 35—53.&lt;br/&gt;[3] W. Wei, Y.Liu, S.W.Mei and et al. &quot;Study on Residual Flux Evaluation Method Based on Variable-Regional Integral during the Voltage Attenuation Process,&quot; &lt;i&gt;2019 IEEE Innovative Smart Grid Technologies - Asia (ISGT Asia)&lt;/i&gt;, Chengdu, China, 2019, pp. 954-959.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/ffc6d5c2761c3b560b36db929ce09c40.jpg)
Fig.1 The curves of transient current difference extremum parameters versus &lt;i&gt;B&lt;/i&gt;&lt;sub&gt;r&lt;/sub&gt;

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8fcc1ffc5fecf23644df6c2889571d89.jpg)
Fig.2 The comparison of experimental residual flux density and estimated residual flux density

INTERMAG 2021

Residual Flux Measurement of Power Transformer Based on Transient Current Difference

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ACL 2021

I Introduction The iron core residual flux density is one of the two reasons that cause the no-load closing of the large power transformer to generate magnetizing inrush current[1]. In order to effectively weaken the residual flux density to reduce the occurrence probability of magnetizing inrush current, it is necessary to measure the magnitude and direction of the residual flux density. In the existing research, the empirical estimation method[2] and the voltage integration method[3] are mainly used to estimate the residual flux density in the core, but these methods have some limitations in the residual flux measurement of large power transformer. Therefore, the accurate measurement of the residual flux density in the core is of great theoretical significance for the efficient operation of the whole power grid. The main purpose of this paper is to study the most effective method to measure the residual flux density of transformer. II Theoretical analysis of measurement methods When the transformer core structure is fixed, the excitation inductance is mainly affected by differential permeability. Residual flux will lead to the change of core differential permeability. By using the method of field-circuit coupling, the magnetic field problem with closed magnetic circuit structure is transformed into the circuit problem with equivalent inductance. Based on the electromagnetic transient characteristics of iron core materials, this paper proposes a residual flux density measurement method of externally applied voltage. The residual flux results in different transient current waveforms under positive and reverse voltage applied in the windings. The relation expression between the extreme value of transient current difference and residual flux is derived theoretically. In order to improve the accuracy of residual flux density measurement, modeling and analysis were carried out on the measured square core, and a set of appropriate test circuit parameters were optimized based on the differential permeability characteristics of the core material. It can be seen from Fig.1 that the transient current differential extremum parameter ts, Δ Imax change with residual flux changes obviously, but the parameter ts is more sensitive to the change of residual flux in the core. Therefore, ts is selected as the basis for quantitative detection of residual flux. III Conclusion By using the finite element method, the effects of different circuit parameters on the transient process can be compared, and some valuable conclusions are obtained, which will provide a theoretical reference for the subsequent application of the measurement method. Finally, experimental verification was carried out on the measured core, and the estimated residual flux in the core was compared with the actual value. As shown in Figure 2, the maximum measurement error did not exceed 5.4%. Therefore, it was considered that the measurement method proposed in this paper was reliable. This method can be used to test the residual flux of large power transformer without any requirement for transformer, which laid a foundation for the quantitative detection of residual flux in transformer core.

**References:**

[1] Y. Wang, Z. Liu and H. Chen, "Research on Residual Flux Prediction of the Transformer", IEEE Transactions on Magnetics, Vol. 53, no. 6, pp. 1-4, June 2017. [2] Colombo E, Santagostino G. "Results of the enquiries on actual network conditions when switching magnetizing and small inductive currents and on transformer and shunt reactor saturation characteristics", Electra, 1984, 94: 35—53. [3] W. Wei, Y.Liu, S.W.Mei and et al. "Study on Residual Flux Evaluation Method Based on Variable-Regional Integral during the Voltage Attenuation Process," 2019 IEEE Innovative Smart Grid Technologies - Asia (ISGT Asia), Chengdu, China, 2019, pp. 954-959.

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/ffc6d5c2761c3b560b36db929ce09c40.jpg)
Fig.1 The curves of transient current difference extremum parameters versus Br

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/8fcc1ffc5fecf23644df6c2889571d89.jpg)
Fig.2 The comparison of experimental residual flux density and estimated residual flux density

technical paper

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://s3.eu-west-1.amazonaws.com/underline.prod/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://s3.eu-west-1.amazonaws.com/underline.prod/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://s3.eu-west-1.amazonaws.com/underline.prod/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://s3.eu-west-1.amazonaws.com/underline.prod/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://s3.eu-west-1.amazonaws.com/underline.prod/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.

Direct observation of vertical Bloch line manipulation via in-plane magnetic fields

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:**

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

Antiferromagnetic thin films attract significant interest for future low-power spintronic devices. They are largely insensitive to external magnetic fields, exhibit negligible cross-talk between neighboring memory cells and they can be switched at THz frequencies [1]. Multiferroics, such as bismuth ferrite BiFeO3, in which antiferromagnetism and ferroelectricity coexist at room temperature, appears as a unique platform for spintronic [2] and magnonic devices [3]. The nanoscale structure of its ferroelectric domains has been widely investigated with piezoresponse force microscopy (PFM), revealing unique domain structures and domain wall functionalities [4, 5], but nanoscale magnetic textures present in BiFeO3 and their potential for spin-based technology remain concealed. Depending on the strain, growth conditions and crystal orientation, the magnetic state of BiFeO3 thin films can either show different types of non-collinear cycloids, canted G-type antiferromagnetic orders, or even a mixture of these [6]. In this report, we present two different antiferromagnetic spin textures in multiferroic BiFeO3 thin films with different epitaxial strains, using a non-invasive scanning Nitrogen-Vacancy magnetometer (Qnami, ProteusQTM) based on a single nitrogen-vacancy (NV) defect in diamond (Qnami, QuantileverTM MX), with a calibrated NV flying height of ~35 nm and proven dc field sensitivity of ~1 μT/√Hz. The two BiFeO3 samples were grown on DyScO3 (110) and SmScO3 (110) substrates using pulsed laser deposition. The striped ferroelectric domains in both samples are first observed by the in-plane PFM as shown in Figs. (a) and (b), respectively. The corresponding scanning NV images in Figs. (c) and (d) confirm the existence of the spin cycloid texture, with zig-zag wiggling angles of 90° and 127°, and the propagation wavelength of λDSO≈64 nm and λSSO≈94 nm, respectively. At the local scale, the combination of PFM and scanning NV magnetometry allows to identify the relative orientation of the ferroelectric polarization and cycloid propagation directions on both sides of a domain wall. For the BiFeO3 grown on DyScO3 (110) substrate, the 90-degree in-plane rotation of the ferroelectric polarization imprints the 90-degree in-plane rotation of the cycloidal propagation direction along k1=[-1 1 0] direction, corresponding to the type-I cycloid as shown in Fig. (c). On the contrary, in the BiFeO3 film grown on SmScO3 (110) substrate, the propagation vectors are found to be along k1’=[-2 1 1] and k2’= [1 -2 1] directions in the neighboring domains separated by the 71° domain wall, cf. Fig. (d). It is worth to mentioned that in the previous report [6], BiFeO3 grown on SmScO3 (110), prepared in another growth chamber, showed G-type antiferromagnetic textures, compared to the observed type-II cycloid here in Fig (d). Our results here shed the light on future potential for reconfigurable nanoscale spin textures on multiferroic systems by strain engineering.

**References:**

 [1] V. Baltz, et al., Rev. Mod. Phys. 90, 015005 (2018). [2] J. T. Heron et al., Nature 516, 370–373 (2014). [3] P. Rovillain et al., Nat. Mater. 9, 975–979 (2010). [4] N. Balke et al., Nat. Phys. 8, 81–88 (2011). [5] G. Catalan, et al., Rev. Mod. Phys. 84, 119–156 (2012). [6] A. Haykal, et al., Nat. Commun. 11, 1704 (2020).

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/b5b38edff0eaadbc038640f26e71f1fc.jpg)
Figure: (a-b) In-plane PFM phase images of BiFeO3 films grown on DyScO3 (110) and SmScO3 (110) substrates with resulted strains of -0.35% and +0.5%, respectively. (c-d) NV magnetometry images corresponding to the ferroelectric domains depicted in (a-b). The dashed lines in (c–d) are guides to the eyes, reflecting a change of the cycloid propagation vector associated to the ferroelectric domain walls.

Quantitative Imaging of Antiferromagnetic Spin Cycloidal Textures on Strain Engineered BiFeO3 Thin Films with a Scanning Nitrogen-Vacancy Magnetometer

I. Introduction As a new type of elevator drive and load-bearing member, the composite steel belt has been used widely. Inside the composite steel belt, there are multiple small-diameter steel wire ropes side by side, and the rope spacing is small. The surface of these side-by-side wire ropes is covered with a special plastic material. So, the composite steel belt has large traction capability and high flexibility, which makes the main engine volume smaller than that of the traditional elevator product mainframe. Furthermore, the composite steel belt has more steel wires than the conventional wire rope, which is more durable and has a longer service life. In additional, the composite steel belt is lighter in weight, and it can effectively reduce the vibration and noise during the operation of the elevator. A number of elevator manufacturers are also gradually adopting and promoting the use of composite steel strips in elevators. However, the surface of the composite steel strip is covered with a wear-resistant plastic material such as polyurethane. In the process of use, if the internal steel wire rope has defects such as warping, breaking, misalignment, and thinning, it cannot be recognized by the naked eye, which affects the safety of the elevator. If the internal wire rope has potential defects at the time of leaving the factory, it is easy to scratch the surface rubber material, which is more likely to cause an accident. Therefore, the damage detection of the composite steel belt plays an important role in the safe operation of the elevator [1]. The rope in the composite steel belt belongs to ferromagnetic component, electromagnetic detection methods is ideal for its non-destructive testing [2]. In addition, the electromagnetic detection method has also been used for fine steel wire rope detection and achieved a good detection effect [3]. The wire ropes inside the composite steel belt are just fine steel wire ropes. Electromagnetic finite element simulation analysis (FEA) can provide magnetic field status reference for electromagnetic detection of wire rope [4]. The application of some magnetic dipole model analysis and related algorithms in electromagnetic detection also provides relevant references for the detection of wire rope defects[5,6]. II. Simulation and Excitation Structure Design The schematic diagram of the common composite steel strip structure is shown in Fig. 1(a), and the excitation structure is established as shown in Fig. 1(b). By selecting the appropriate size of permanent magnet and yoke, the wire ropes in the composite steel belt are excited to near saturation. In the simulation, three defects appear on the first, fifth and ninth wire ropes at the same time. Extract the radial magnetic flux leakage directly above and below each wire rope and above and below both sides of the 1st and 10th wire ropes, as shown in Fig. 1(c) and Fig. 1(d). It can be seen that on the defective wire ropes, the radial magnetic flux leakage is large, and on the wire rope without defects, the magnetic flux leakage is very small. Therefore, magnetic detection sensors (such as hall, anisotropic magneto-resistive, giant magneto-resistive, fluxgate, tunnel magneto-resistive, etc.) can be arranged above and below each wire for picking up the magnetic flux leakage signal, thereby detecting the defect. III. Experimental and Results Since the diameter of the wire rope and the distance between the ropes inside the composite steel belt is small. The hall element having a small volume and high sensitivity is selected as the detecting sensor. The halls are placed above and below each wire rope. For the signal processing, the hall output signals above and below each wire are first summed up. Then the noise and interference signals are filtered out by a bandpass filter. Subsequent use of a comparator to determine the defect. Fig.2a) shows a photograph of a steel belt with three defects, each of which is located on a wire rope inside. Fig.2b) shows the design of the steel wire rope detection device inside the composite steel strip and the detection result when the second defect is detected.

**References:**

[1] H.M. Lei, G.Y. Tian, “Broken wire detection in coated steel belts using the magnetic flux leakage method,” Insight, vol. 55, no. 3, pp.126-31, 2013. [2] H. R. Weischedel, R. P. Ramsey, “Electromagnetic testing, a reliable method for the inspection of wire ropes in service,” NDT&E Int., vol. 22, no. 3, pp.155-161, 1989. [3] X. L. Yan, D. L. Zhang, and S. M. Pan, “Online nondestructive testing for fine steel wire rope in electromagnetic interference environment”, NDT E Int., no. 92, pp. 75–81, 2017. [4] R. H. Priewald, C. Magele, and P. D. Ledger, et al. “Fast magnetic flux leakage signal inversion for the reconstruction of arbitrary defect profiles in steel using finite elements”. IEEE Trans. Magn., vol. 9, no. 1, pp. 506-516, 2013. [5] Li E, Kang Y, Tang J. et al. “Analysis on Spatial Spectrum of Magnetic Flux Leakage Using Fourier Transform”. IEEE Trans. Magn., vol. 54, no. 8, pp. 6201810, 2018. [6] Hosseingholizadeh S, Filleter T, Sinclair A. “Evaluation of a Magnetic Dipole Model in a DC Magnetic Flux Leakage System”. IEEE Trans. Magn., vol. 55, no. 4, pp. 6200407, 2019.

**Images:**
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/71c400da15890673ef973c968b06563d.jpg)

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/245708bac6cfce5ff30346c106e13afb.jpg)

Electromagnetic Non-destructive Testing of Wire Rope Inside Composite Steel Belts

Investigations the current-driven domain wall (DW) motion in cylindrical nanowires (CNWs) are more valuable if performed at zero applied external field for their use in prospective electronic devices. Here, we present an all-magnetoelectrical method to pin DWs in multi-segmented CNWs, maintain them pinned at zero field and de-pin them using current pulses. We test this in compositionally modulated nickel/cobalt (~ [10/14] μm) and nickel/cobalt/nickel (~ [3/7/3] μm) CNWs of c.a. 150 - 190 nm diameter where DWs can be pinned in a predictable and reproducible way and their soft/hard magnetic texture has been fairly studied [1]–[3]. Furthermore, we perform micromagnetic simulations to interpret and study the behavior of the magnetoresistance as a function of segment length. The method is based on the anisotropic magneto-resistance (AMR) measurement of a CNW with a pinned DW [4] for which we show the relevant range of one branch in Figure 1 (solid line). This branch starts from a saturated magnetization state in the “right” direction (3000 Oe, not shown) and moves to a saturated state in the “left” direction (-3000 Oe, not shown), as indicated by the arrow at the bottom. The CNW’s long axis is parallel to the applied field. Simplifying, AMR gives an overall measure of the portion of the CNW’s magnetization that is not along the direction of the applied electrical current: at ±3000 Oe, most of the CNW’s magnetization is in the same direction as the electrical current, i.e., along the CNW’s long axis, resulting in a saturated high resistance state. As the field decreases, magnetization vortexes appear at the ends of the CNW, driving magnetization away from the axial direction and resulting in a low resistance state. When the field is ramped in the opposite direction, a DW propagates from one of the ends and is pinned at some point within the nickel segment [1], increasing the axial component of the magnetization as indicated by the rapid increase in resistance in Figure 1 (“Domain wall pinning”). Finally, when the field is further increased, the DW de-pins and propagates to the opposite end from where it was initially nucleated leaving most of the magnetization in the axial direction, as indicated by the second resistance change in Figure 1 (“Domain wall de-pinning”). Note that pinned DWs and vortexes at the ends of the CNW lower the resistance as they are mainly composed of magnetization textures out of axis. To test current-driven DW motion at zero field, a DW has to be pinned first by saturating the magnetization to +3000 Oe, decreasing the field, inverting it and increasing it only until the first resistance jump is reached (red, open squares in Figure 1). After this, the field is reduced to 0 (blue, open triangles in Figure 1), at which point current pulses are applied. To verify whether the DW is still pinned after reducing the field to zero and/or that a current pulse has de-pinned it, the field is ramped up again in the negative direction (towards -3000 Oe). If the DW had de-pinned as a consequence of reducing the field, the CNW’s magnetization would return to a “right” state and the domain wall pinning resistance jump would be registered again, which we never observed. If the DW remained pinned, even after the application of a pulse, only the DW de-pinning resistance jump was observed, as seen in Figure 2 (solid red squares), where a current pulse of 9.21x1011 A/m2 and 10 ns width was applied. On the other hand, if a current pulse de-pinned the DW, neither of the resistance jumps would be observed, as seen in Figure 2 (solid blue triangles), where a pulse of 1.38x1012 A/m2 and 20 ns width was used. This method resembles recent ones in the sense that the state of the CNW is known after the current pulse is sent, for example using MFM [5] or TEM [6]. As the DW is de-pinned at high enough current densities, the width of the pulse can be used to estimate the DW speed by successively reducing the pulse width until no de-pining event is found. With this, the velocity is estimated as the length of the cobalt segment over the current pulse width. We find that the de-pinning event is dependent on the direction of the applied current and that the magnetoresistance value for pinned domain walls increases as the length of the segments increases, which is consistent with our simplified view of AMR. This suggests that, for long enough CNWs, the DW width remains constant as the segment length increases, which we also confirmed with micromagnetic simulations. We believe this method can be used to study current-induced DW de-pinning at zero applied field in soft/hard magnetic CNWs with known magnetic configurations.

**References:**

[1] Y. P. Ivanov, et al, ACS Nano, vol. 10, no. 5, pp. 5326–5332 (2016) [2] S. Lopatin, Y. P. Ivanov, J. Kosel, and A. Chuvilin, Ultramicroscopy, vol. 162, pp. 74–81 (2016) [3] C. Bran et al., ACS Nano, vol. 14, no. 10, pp. 12819–12827, (2020) [4] H. Mohammed, E. V. Vidal, Y. P. Ivanov, and J. Kosel, IEEE Trans. Magn., vol. 52, no. 7 (2016) [5] M. Schöbitz et al., Phys. Rev. Lett., vol. 123, no. 21, pp. 1–5 (2019) [6] Y. P. Ivanov, et al, ACS Appl. Mater. Interfaces, vol. 9, no. 20, pp. 16741–16744 (2017)

**Images:**

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/58702b89496d700156b28fb30ad38e88.jpg)
Figure 1. Anisotropic magneto-resistance measurement of a cylindrical nanowire with a pinned domain wall rescaled to the domain wall pinning and de-pinning field range and the subsequent reduction of external field to zero where nanosecond square current pulses are applied.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/fbc20f594c582e2ebe95d27127378af1.jpg)
Figure 2. Magnetoresistance profile after two different current pulses are applied at zero field: 9.21x1011 A/m2, 10 ns width (red squares), the de-pinning resistance jump indicates the domain wall was not de-pinned; 1.38x1012 A/m2, 20 ns (blue triangles) results in the de-pinning of the DW as the depinning resistance jump is not observed.

Residual Flux Measurement of Power Transformer Based on Transient Current Difference

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Residual Flux Measurement of Power Transformer Based on Transient Current Difference

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