Observation of Buried Magnetic Domains in Grain-Oriented Electrical Steel

Bulk-sensitive microscopic measurements of buried magnetic domains are reported. Utilizing a new magneto-optical effect in the hard X-ray regime, referred to as X-ray magnetic circularly polarized emission (XMCPE), the internal transverse domains in a grain-oriented (GO) electrical steel sheet are unambiguously observed. This allows the lateral shapes of the transverse domains to be successfully visualized. In addition, we discuss the magnetic domain structure of the supplementary domains below the surface from measurements performed at several pairs of incident and exit angles.


I. INTRODUCTION
C ERTAIN magnetic properties of ferromagnetic materials can be modified by controlling or designing the structure of the magnetic domains, which presents the opportunity to tailor magnetic properties by domain engineering. An early but excellent example is the case of grain-oriented (GO) electrical steel, in which a reduction in energy loss is achieved by decreasing the domain width [1], [2], [3], [4]. Some of the magnetic properties of GO electrical steel are undoubtedly governed by the magnetic domain structure. Hence, elucidation of the structure and motion of the magnetic domains is indispensable for understanding the magnetic properties of these magnetic materials [5].
GO electrical steel is a representative soft magnetic material characterized by high permeability, high saturation magnetization, and low energy loss that is primarily used to fabricate the laminated cores of transformers [6]. GO electrical steel is manufactured by rolling (and recrystallization) to obtain sheets with a thickness ranging from 0.23 to 0.35 mm. From a crystallographic perspective, rather surprisingly, these sheets consist of highly oriented single crystals, where the sheet surface and rolling direction are parallel to the (110) plane and the [001] direction, respectively. This crystallographic character affords a highly anisotropic magnetic domain structure. The basic magnetic domains in the demagnetized state are bar domains alternatingly magnetized along the [001] direction, as depicted in Fig. 1(a). In principle, the magnetization process, and thus the major magnetic properties, such as permeability and coercive force, are governed by the motion of the 180 • domains [5], [7], [8], [9]. Manuscript  In reality, however, some degree of misorientation of the crystal axes with respect to the sheet surface and rolling direction always exists. According to convention, β is defined as the angle between the [001] direction and the closest surface of the steel sheet. When β is sufficiently large (for example, 2 • ), supplementary domains are generated to reduce the stray field energy [10], as shown in Fig. 1(a). For a slightly misoriented (110) surface, it is expected that the supplementary domain consists of a pair of lancet domains connected by a transverse domain [ Fig. 1 [7], [10], [11].
From a practical point of view, the transverse domains in GO electrical steel play a significant role. For example, transverse domains give rise to considerable magnetostriction in electrical steel sheets [10], [11], [12], because their magnetization directions are perpendicular to those of the basic bar domains. In particular, magnetostrictive deformation induced by an alternating magnetic field generates acoustic noise in transformers. Hence, reducing magnetostriction is essential for industrial applications. In addition, the transverse domains may contribute to hysteresis loss, as a part of the supplementary domains [7], [10].
The details of the transverse domains, however, remain ambiguous because they are internal magnetic domains that have not been directly observed. Major techniques for the observation of magnetic domains, such as soft X-ray magnetic circular dichroism (MCD) microscopy [13], [14], [15] and magneto-optical Kerr effect microscopy [16], [17], either are surface sensitive, measure magnetic domains close to the surface, or are suited for thin films with a maximum thickness of approximately a few hundred nanometers. In addition, currently available bulk-sensitive magnetic microscopy techniques are associated with certain drawbacks. For example, an outstanding neutron interferometry technique with a remarkable 0018-9464 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See https://www.ieee.org/publications/rights/index.html for more information. material penetration depth was recently developed for magnetic domain wall observations [18], [19], [20]. However, the spatial resolution of this technique ranges from 35 to 100 μm, which is insufficient for measuring supplementary domains. In contrast, hard X-ray MCD microscopy [21], [22], [23] can achieve a very fine spatial resolution of approximately 100 nm, but the probing depth of approximately 10 μm is not long enough to detect buried transverse domains. 3-D magnetic microstructures have been visualized with a high spatial resolution by means of the Libovický method [24], [25]. However, this technique is applicable only to FeSi alloys with a limited range of Si contents. Very recently, we developed a new bulk-sensitive magnetic microscopy technique that utilizes a new magneto-optical effect in the X-ray region, which we refer to as X-ray magnetic circularly polarized emission (XMCPE) [26]. At present, a lateral resolution down to 10 μm has been achieved and a probing depth of up to 40 μm is expected. In this article, we apply our XMCPE microscope to visualize the buried magnetic domains in a GO electrical steel sheet. Although the probing depth is not long enough to observe the entire transverse domain, several features of the supplementary domain can be extracted from the measurements. In Section II, Fig. 2. Schematic top view of the XMCPE microscope. The incident X-rays are focused by a CRL onto the sample. θ in and θ ex are the incident and exit angles, respectively, measured from the sample surface. The characteristic X-rays emitted from the sample (Fe K α emission) are converted into wellcollimated X-rays by a Montel mirror and then the circular polarization analysis is performed using a diamond phase plate and Ge (400) linear polarization analyzer. The detector is an SDD. A raster scan of the sample is performed using an X Z stage, where the X-and Z -directions are horizontal and vertical, respectively. In the experiment, the electrical steel sample was mounted such that the rolling direction was approximately parallel to the X-direction. the experimental details are described. In Section III, the experimentally obtained magnetic domain images exhibiting the transverse domains are presented and compared with the expected results for a simple model of a supplementary domain. We also discuss the magnetostriction of the electrical steel using the obtained width of the transverse domains. Finally, our concluding remarks are provided in Section IV.

II. EXPERIMENTAL
The XMCPE is a phenomenon in which the characteristic X-rays emitted from a magnetized specimen are circularly polarized [27]. The degree of circular polarization in the energy-resolved characteristic X-rays of a magnetic element is proportional to the element-selective magnetization in the emitting region parallel to the emission direction. Therefore, by measuring the degree of circular polarization of the emitted X-rays, the magnetization of the emitting position projected onto the emission direction can be estimated.
A key advantage of XMCPE is the large dichroic effect for the K α emissions of 3d transition-metal elements in the hard X-ray region (25% for the Fe K α 1 emission). Furthermore, because the energy of the excitation photons is arbitrary, high-energy incident X-rays, which have a high penetration length, can be used. Consequently, magnetic domains up to 40 μm below the surface are expected to be measurable for iron.
A schematic view of the microscope is presented in Fig. 2. Because highly brilliant X-rays are required as the excitation source for XMCPE experiments, similar to other photon-hungry inelastic X-ray scattering spectroscopic techniques, the experiments were conducted using a synchrotron radiation beam on beamline BL11XU at SPring-8. The incident X-ray energy was set to 26 keV using a Si(111) doublecrystal monochromator, and higher harmonics were reduced by detuning the second crystal of the monochromator. The incident polarization was linear and horizontal. The monochromatized X-rays were then focused onto the sample using a compound refractive lens (CRL). The focal spot size was determined to be 6 × 8 μm 2 (vertical × horizontal) by scanning a gold wire. The sample was a commercial GO electrical steel sheet of 300 μm thickness coated with a 3 μm insulating layer (JIS:30P105), which was mounted on an X Z stage to perform a raster scan, where both the X (horizontal) and Z (vertical) directions were parallel to the sheet surface. The only magnetic element in the sample was Fe. Hence, we measured the Fe K α emission. The incident angle θ in and exit angle θ ex were measured with respect to the sample surface.
The characteristic X-rays divergently emitted from the sample were collected and converted into a well-collimated beam by a Montel mirror, the center of which was positioned 200 mm downstream of the sample, followed by a phase plate and a linear polarization analyzer to evaluate the degree of circular polarization. The phase plate was a 0.5-mm-thick single-crystal diamond plate with (100) surface orientation and operated near the 220 reflection. This functioned as a quarter-wave plate to convert the right-and left-handed circularly polarized X-rays into vertically linearly polarized X-rays by introducing phase shifts of +(π/2) and −(π/2), respectively. The linear polarization analyzer was a Ge (400) single crystal, which was operated near the scattering angle of 2θ A 90 • such that the vertically linear component of the X-rays was mainly reflected. The X-ray detector was a silicon drift detector (Amptek XR-100SDD). The linear polarization analyzer also played the role of an energy analyzer. The measurement energy was selected to be 6.405 keV, corresponding to the region of maximum circular polarization in the emission spectrum.
The degree of circular polarization is equal to the flipping ratio (I + − I − )/(I + + I − ) [27], where I + and I − denote the detected intensities for phase shifts of +(π/2) and −(π/2), respectively. Hence, the magnetization of the emitting position projected onto the emission direction can be obtained by measuring the flipping ratio. The flipping ratio was calculated at each sample position by measuring the intensities in the sequence I + I − I − I + by rocking the phase plate. The anomalous absorption of the phase plate (the Borrmann effect) [28] was corrected by multiplying I − by 1.04. Finally, 2-D magnetization images were acquired by scanning the sample with a 10 μm step using the X Z stage. The details of the XMCPE microscope are presented in Sugawara et al. [26]. We obtained magnetic domain images at three pairs of θ in and θ ex values, namely, 90 • and 70 • , 70 • and 90 • , and 50 • and 110 • , respectively.
The magnetostriction of the same GO electrical steel used in the X-ray experiments was also measured. The measurement system consisted of a horizontal double-yoke singlesheet tester and a laser displacement meter. The specimen dimensions were 400 × 100 mm 2 and the rolling direction was parallel to the long axis of the specimen. The measurements were performed at maximum magnetic flux densities of 1.5, 1.7, and 1.9 T and a frequency of 50 Hz with sine wave excitation.

III. RESULTS AND DISCUSSION
We first present a wide-view image of the magnetic domains near the surface of the GO electrical steel sheet in Fig. 3. The experimental conditions were slightly different from those described in Section II. The incident energy was 17.3 keV and the detector was a Pilatus 100 K. The incident angle θ in and exit angle θ ex were 90 • and 60 • , respectively. The step size was 30 μm in both the X-and Z -directions. The basic bar domains and lancet domains can be clearly observed. At this incident energy, the average probing depth is approximately 10 μm. Hence, it is plausible that only the bar and lancet domains near the surface are observed. Although the measurements are sufficiently sensitive with respect to the magnetization component perpendicular to the sheet plane, because θ ex was 60 • , it is considered that the magnetizations in this domain image are (nearly) parallel to the sheet plane. The magnetization in the red and blue regions is oriented toward the left and right, respectively.
We next focus our attention on visualizing the buried transverse domains. We measured the area approximately indicated by the black rectangle in Fig. 3. Magnetic domain images measured at an incident energy of 26 keV are shown in Fig. 4. The exit angles are 70 • , 90 • , and 110 • for Fig. 4(a)-(c), respectively. At first glance, Fig. 4(a) appears to show only the bar and lancet domains. However, careful examination of the domain image reveals that the regions adjacent to the rightmost side of the lancet domains possess a deeper color, indicating enhanced contrast for the magnetization component perpendicular to the sheet plane. This tendency is readily apparent from Fig. 4(b), in which only the magnetization component perpendicular to the sheet plane is observed by setting θ ex = 90 • . Therefore, the spot-like domains observed in Fig. 4(b) must possess substantial magnetization perpendicular to the sheet plane. Hence, we can conclude that they are transverse domains. Note that the observed transverse domains show complicated shapes, in contrast to a simple rod-like domain, as shown in the left panel of Fig. 1(b). We will discuss this point later. In this domain image, it is also interesting to note that the small but finite β gives rise to a weak contrast for the magnetic domains, which is helpful  for confirming the positions of the bar and lancet domains. Upon further increasing θ ex to 110 • to obtain Fig. 4(c), the red and blue contrast is reversed with respect to that in Fig. 4(a), while the color of the transverse domains remains unchanged. A comparison of all three images reveals that the transverse domains are also clearly observed in Fig. 4(c), although they are merged into the lancet domains.
Subsequently, to determine whether these measurements can capture the characteristic features of supplementary domains, we prepared a model structure of a supplementary domain and calculated the flipping ratios by convoluting the model structure with the instrumental resolutions obtained from raytrace calculations, as described in the supplementary material. In the ray-trace calculations, a source, a Montel mirror, and a Ge (400) analyzer crystal were taken into account. The observed and calculated results are presented in Fig. 5 The supplementary domain model is presented in Fig. 6. We assume that β is 1 • , the thickness of the lancet domain T lan is 43 μm, the angle between the transverse domain and the surface R tra is 60 • , and the width of the transverse domain T tra is 70 μm. The scale factor of the ordinate is the flipping ratio for the full moment and is chosen to be 0.2. The origins of the X-axis are set to 2.23 and 2.17 mm for the upper and lower panels of Fig. 5, respectively. The magnetization of the transverse domain is also assumed to be parallel to the [100] direction. As seen in Fig. 5, the agreement is remarkably good, although it is not perfect. For Fig. 5(a), (b), (d), and (e), almost all of the features are very well reproduced, except small deviations along the X-direction in Fig. 5(a) and (d). In contrast, it seems that there are obvious discrepancies in Fig. 5(c) and (f), where the peak or valley structures stemming from a transverse domain are not experimentally observed. This can presumably be ascribed to the incompleteness of the model used in the calculations. The slight disagreement along the X-direction in Fig. 5(a) and (d) is ascribed to an experimental issue, namely, that the center of sample rotation was not identical to the emission point.
The validity of the simulation parameters is evaluated as follows. A scale factor of 0.2 is confirmed by the agreement between experiment and simulation at both sides of Fig. 5(a) and (d). β = 1 • is also verified from the agreement of the baselines at both sides of Fig. 5(b) and (e). We performed calculations for T tra = 40, 60, 70, 80, and 100 μm at T lan = 43 μm. The calculations at T tra = 40 and 100 μm display apparent disagreement. Hence, we consider that T tra lies between 60 and 80 μm. Similarly, we also performed calculations for T lan = 25, 34, 43, 52, and 60 μm at T tra = 70 μm. At T lan = 25 and 60 μm, the calculated curves deviate to some extent from the observed data. Therefore, we estimate that T lan = 43 ± 9 μm. It should be noted that T tra and T lan correlate with each other. Hence, for an accurate estimation of these parameters, a more sophisticated model of a supplementary domain and reliable estimation of the instrumental resolution are necessary. It should also be noted that the parameters may differ between supplementary domains. However, because of the ambiguity in the supplementary domain model and instrumental resolutions, we used the same parameters for both supplementary domains in the simulations.
Using the obtained width of the transverse domains, we can discuss the magnetostriction of the electrical steel. We measured the magnetostriction of the same electrical steel at 50 Hz up to 1.9 T and found that it increased by approximately 7 × 10 −7 with respect to the demagnetized state. On the other hand, we counted the number of supplementary domains in a representative area (12 × 9.5 mm 2 ) using a garnet indicator film and found this value to be 57. Assuming that all transverse domains possess the same shape (a width of 120 μm along the transverse direction (TD) and a width of 70 μm along the rolling direction), we estimate the volume ratio of the transverse domains to be 0.42%. Therefore, the expected magnetostriction in the saturated state ((3/2)λ 100 × volume ratio) is only 1.6 × 10 −7 , where λ 100 = 2.6 × 10 −5 . This large discrepancy cannot be ascribed solely to the assumption that all of the transverse domains have the same volume. Thus, we infer that there exist other contributions to the magnetostriction. For instance, small supplementary domains that cannot be observed using an indicator film may exist.
We would also like to point out that the supplementary domains observed in these measurements are neither isolated supplementary domains, as shown on the left side of Fig. 1(b), nor successively connected supplementary domains, referred to as lancet combs, as shown on the right side of Fig. 1(b). (See Fig. S2 in the supplementary material.) It is considered that the width of an ideal lancet domain of length L lan is equal to 2L lan sin β [11], which corresponds to 70 μm for L lan = 2 mm (see Fig. 4(a) in Sugawara et al. [26]), whereas the observed width is approximately 120 μm. Therefore, it is probable that two or more lancet domains joined to afford the observed large lancet domain. If the 90 • domain wall in the transverse domains is not easy to move, it is likely that the transverse domains remain unconnected to each other. It is also interesting to consider that the transverse domain at approximately Z = −4.06 is elongated along one direction. It is known that lancets join to form combs when β is relatively large. Simultaneously, it is supposed that transverse domains connect with each other in a line to afford a plate [right side of Fig. 1(b)]. The observed elongated domain may be a short variation of such a transverse plate. In fact, the angle between the [001] direction and the elongated direction is approximately 47 • , which is close to the ideal angle of 55 • .
At the end of this section, we would like to remark that the observation of buried magnetic domains does not require the magnetization component to be perpendicular to the surface. In these measurements, we certainly enhance the sensitivity for the component parallel to the normal direction (ND). However, by enhancing the sensitivity parallel to the TD, the transverse domains would be distinctly observed owing to the large [110] component. In general, the observation of internal magnetic domains is conducted by increasing the sensitivity parallel to the direction along which the difference in magnetization with respect to neighboring domains is substantially large. An internal magnetic domain whose magnetization lies antiparallel to those of the surrounding domains would be most clearly observed.
IV. CONCLUSION In this experimental study, we successfully visualized the buried magnetic domains in a GO electrical steel sheet by XMCPE microscopy in the hard X-ray region using high-energy incident X-rays to enhance the bulk sensitivity. The internal transverse domains are unambiguously and directly observed and the width of the transverse domains is estimated to be 70 μm through simulations. The shapes of the transverse domains are considerably different from those expected, thus demonstrating the importance of direct experimental observations. Because XMCPE experiments can be conducted under a magnetic field, we next intend to measure the field evolution of the lancet and transverse domains. We also plan to develop a procedure for performing depthresolved XMCPE microscopy measurements to enable the 3-D visualization of the lancet and transverse domains in the near future.
SUPPLEMENTARY MATERIAL See supplementary material for the calculated instrumental resolutions of the XMCPE microscope and a magnified view of Fig. 4(b).