United States

Fourier transform holography (FTH) is a lensless imaging technique that uses a known reference in the sample to retrieve the object of interest in one single step of calculation (&lt;i&gt;i.e.&lt;/i&gt; it does not require an iterative method), overcoming the phase problem inherent to other techniques such as coherent diffraction imaging and ptychography. In the case of an extended reference, a linear differential filter is applied and the object can simply be obtained by calculating the inverse Fourier transform. This approach is known under the name of HERALDO [1].&lt;br/&gt;&lt;br/&gt;By exploiting the x-ray magnetic circular dichroism effect, this technique has shown to be useful to image magnetic textures by providing a projection (sometimes two) of the magnetization in 2D layers [2-5]. In this work, we go further and use FTH to image the magnetic structure of a 3D object. To be sensitive to all three components of the magnetization (perpendicular as well as in-plane), we use a sample setup with two perpendicular slits as complementary references (Fig. 1). By tilting the sample around the axes defined by the two slits, we obtain a dual set of projections which gives information about the internal configuration of the sample [6].&lt;br/&gt;&lt;br/&gt;We discuss the different problems that can arise in the experiment, such as shadowing effects and a reduced angular range for the tilting of the sample, and how these can be conquered. We test the method in a 1μm thick Fe/Gd multilayer with maze-like magnetic pattern and image a circular window of diameter 5μm. Finally, we use this projection set as input to the tomography algorithm that we developed [7] to reconstruct the vector field structure of the whole object.

![](https://assets.underline.io/uploads/markdown_image/1/image/3d094f6eccc80616b54ad2113433005c.jpg)

Fig. 1: Fourier transform holography: The coherent x-ray beam illuminates the whole sample. A circular window is milled into the gold layer, which masks the magnetic sample, to allow passing through the x-rays. Two slit references are also milled across the mask and the sample. After filtering the diffraction pattern and applying the inverse Fourier transform, the magnetic projection is recovered (magnetic contrast is obtained by x-ray magnetic circular dichroism). Tilting the sample around two axes allows us to probe all three components of the magnetization.

2022 Joint MMM-INTERMAG

Imaging the Magnetization Vector with Fourier Transform Holography

## Dr. Nishikant (Nish) Sonwalkar: Academician, Scientist, Musician

![](https://assets.underline.io/uploads/markdown_image/1/image/0f9b63a0b3deba4a355d98e2c87af68a.png)

Dr. Sonwalkar is regarded as a leading expert in the application of computers in education. He has extensive research and development experience in hypermedia authoring, mobile learning, adaptive learning, and brain-based synaptic learning, advanced scientific visualization, database management systems, and computer simulation.

After receiving doctoral degree from MIT in the area of Molecular Dynamics of Nano-interfaces, he joined MIT as faculty in Mechanical Engineering, but his passion for technology enabled education led him become the founding director of Hypermedia Teaching Facility (Hypermedia Lab) at MIT and later he was appointed as the Principal Educational Architect of MIT.

<iframe width="560" height="315" src="https://www.youtube.com/embed/dgGdFmr9kgs" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

NISH 2021

Fourier transform holography (FTH) is a lensless imaging technique that uses a known reference in the sample to retrieve the object of interest in one single step of calculation (i.e. it does not require an iterative method), overcoming the phase problem inherent to other techniques such as coherent diffraction imaging and ptychography. In the case of an extended reference, a linear differential filter is applied and the object can simply be obtained by calculating the inverse Fourier transform. This approach is known under the name of HERALDO [1]. By exploiting the x-ray magnetic circular dichroism effect, this technique has shown to be useful to image magnetic textures by providing a projection (sometimes two) of the magnetization in 2D layers [2-5]. In this work, we go further and use FTH to image the magnetic structure of a 3D object. To be sensitive to all three components of the magnetization (perpendicular as well as in-plane), we use a sample setup with two perpendicular slits as complementary references (Fig. 1). By tilting the sample around the axes defined by the two slits, we obtain a dual set of projections which gives information about the internal configuration of the sample [6]. We discuss the different problems that can arise in the experiment, such as shadowing effects and a reduced angular range for the tilting of the sample, and how these can be conquered. We test the method in a 1μm thick Fe/Gd multilayer with maze-like magnetic pattern and image a circular window of diameter 5μm. Finally, we use this projection set as input to the tomography algorithm that we developed [7] to reconstruct the vector field structure of the whole object.

![](https://assets.underline.io/uploads/markdown_image/1/image/3d094f6eccc80616b54ad2113433005c.jpg)

Fig. 1: Fourier transform holography: The coherent x-ray beam illuminates the whole sample. A circular window is milled into the gold layer, which masks the magnetic sample, to allow passing through the x-rays. Two slit references are also milled across the mask and the sample. After filtering the diffraction pattern and applying the inverse Fourier transform, the magnetic projection is recovered (magnetic contrast is obtained by x-ray magnetic circular dichroism). Tilting the sample around two axes allows us to probe all three components of the magnetization.

technical paper

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

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

The aerospace industry has become increasingly reliant on carbon fibre composite (CFC) as a structural component in aircraft, due to its strength to weight ratio. One of the disadvantages of CFC are their vulnerability to impact damage and external environment changes during flight, which causes barely visible damage to the structure. One solution to this is structural health monitoring (SHM), which monitors the composite structure to provide early detection for damage. Previous work has found that magnetostrictive ribbons [1] and inkjet printed copper coils used as actuator-sensor pairs have good resolution to detect damage to CFC [2]. This research has focused on inkjet printing magnetic sensors, which can be directly attached to the surface of the composite. JetLab IV (by MicroFab) with piezoelectric print head (60um diameter orifice) was used. The sensor designs were printed using Magnetite (20% in DMF, IPA and water) and nickel (2% in NMP and water) nanoparticle dispersion inks, manufactured by Nanoshel LLC on photo paper (25x25mm) (fig 1). A MPMS3-SQUID magnetometer was used to characterise the ink’s magnetisation (fig 2). Magnetite and nickel has saturation magnetisation values of 78 and 27 emu/g respectively. Different designs and printer parameters were explored and their magnetic performance evaluated the magnetic performance of the printed designs using simple mechanical testing such as 3-point bending test and impact testing.

![](https://assets.underline.io/uploads/markdown_image/1/image/93225e2ded45120b9d7b64a6504b9660.jpg)

Fig 1. Magnetite printed design on photo paper

![](https://assets.underline.io/uploads/markdown_image/1/image/b678abbf59eac3de5f65db1d82d9bf3b.jpg)

Fig.2 Hysteresis loop of magnetite and nickel ink

Printing magnetostrictive materials for structural health monitoring of carbon fibre composite

The giant magnetoresistance (GMR) devices are attractive as cost-efficient gradiometers due to a larger magnetoresistance (ΔR/R) in a simple structure [1]. Many studies showed that NiFeCr seed layers promote a strong 111 crystallographic texture of GMR films that gives rise to a large ΔR/R [2-4]. However, the effect of NiFeCr composition on GMR has not been reported. In this work, we made a systematic study on the structure and GMR effect of NixFeyCrz /Fe16Co66Ni18 /[Cu /Fe16Co66Ni18]5 /Ru films deposited on SiOx substrate. NiFeCr and FeCoNi layers were deposited by co-sputtering (Ni, Fe, Cr) and (Co80Fe20, Ni), respectively. Figure 1 shows a contour of ΔR/R for various NixFeyCrz compositions, with a typical ΔR/R vs μ0H curve corresponding to Ni55Cr45 seed layer. The maximum ΔR/R ~ 35±2.5% (sensitivity ~ 0.25 %/mT) is observed for the seed layers (Ni0.55Cr0.45)100-yFey with 0 ≤ y ≤ 47, indicating that Ni:Cr = 55:45 ratio is critical for large ΔR/R. The estimated bilinear (J1) and biquadratic (J2) interlayer exchange coupling in this region show stronger antiparallel coupling (J1/J2 ≥ 1). On the other hand, for Ni:Cr ≥ 62:38 or Ni:Cr ≤ 48:52, ΔR/R reduces to &lt; 22% as antiparallel coupling reduced (J1/J2 &lt; 1). XRD θ-2θ profiles confirm that [FeCoNi/Cu] multilayer has fcc 111 texture with the diffraction peaks (2θ111) located between 43.70 and 43.96°. We found a clear correlation between 2θ111 and ΔR/R; i.e. films with high ΔR/R ~ 35±2.5% (i.e. on seed layers (Ni0.55Cr0.45)100-yFey with 0 ≤ y ≤ 47) show 43.88° ≤ 2θ111 ≤ 43.96°, whereas films with ΔR/R ≤ 25% show 2θ111&lt; 43.82°. We also calculated the sheet resistance of GMR films at parallel magnetization (RP in Ω/■). Figure 2 consists a contour of ΔR/R plotted for corresponding values of 2θ111 and RP, which clearly shows that films with high ΔR/R consists 43.88°≤ 2θ111≤ 43.96° and lower RP. As lower RP associates to larger grain size [5], these observations indicate that the seed layers of (Ni0.55Cr0.45)100-yFey with 0 ≤ y ≤ 47 induce large gain size in the [FeCoNi/Cu] multilayer, thus realizes the large ΔR/R and sensitivity.

![](https://assets.underline.io/uploads/markdown_image/1/image/4346a8190fe3318f3b32ca88c88cdf33.jpg)

Fig.1: Contour of ΔR/R for various NixFeyCrz seed layers, with a typical ΔR/R vs μ0H.

![](https://assets.underline.io/uploads/markdown_image/1/image/86da0d555064a39961ce21673bf3bcf0.jpg)

Fig.2: Contour map of ΔR/R plotted against 2θ111 and RP.

The compositional dependence of NiFeCr seed layer on the giant magnetoresistance of [FeCoNi/Cu] multilayers

Because emerging wide-bandgap devices enable higher frequency switching, modeling of high-frequency magnetic components becomes increasingly important in designing a high-density switching mode power supply. In such difficult situations, the power electronics circuit designers can be helped with obtaining customized and non-linear models for the magnetic components with measurements to reduce their development time and cost [1-5]. Recent studies indicate that the accurate prediction for the model relies on rectangular-voltage-excited measurements [6]. Especially, the double-pulse-test (DPT) is the preferred test method to measure the switching parameters and evaluate the dynamic behaviors of power devices. On the other hand, image classification using deep learning (DL) technology has already been shown to produce results with very high accuracy, in some cases even surpassing human capabilities [7]. Therefore, we propose a large-signal power magnetic components analysis technique combining DPT and DL shown in Fig. 1 for the classification, the non-linear modeling, and the loss estimation. The unique point of the proposed technique is using the measured waveform image data of DPT. The multi-dimension waveform images include the individual characteristics of the measured magnetic components. The project goal is that the power electronics designer can easily have the large-signal characteristics of the magnetic components on their own. In this presentation, the experimental and analysis results applying for the classification of magnetics components with the proposed technique are discussed as our first step for this project. For example, the classification of three different materials and component styles using commonly available inductor whose nominal inductance value is indicated as 100uH. The results are summarized in the table in Fig. 2. And all of the indexes show perfect results, which means the classification is completed. Thus, the results reveal that the large-signal waveforms include very important information for the magnetic characterization, and the image recognition with DL helps the analysis of the waveforms.

![](https://assets.underline.io/uploads/markdown_image/1/image/ad3acfdc6698b51ca477999c19a60f9e.jpg)

Fig. 1 Proposed Analysis System

![](https://assets.underline.io/uploads/markdown_image/1/image/6f0df08734decb06c4beb137cc4cba4d.jpg)

Fig. 2 Evaluated Process and The Results

Large-Signal Characterization Technique for Power Electronics Magnetic Components by Deep Learning with Double Pulse Test Measurement Image

The strong demand for 3D packaging technology has accelerated the miniaturization of passive devices, and inductors are facing challenges because the inductance value will be sacrificed when the size is shrinking. The magnetic core is one of the solutions due to its enhancement of inductance density but it will also add complexity to the fabrication process. Previous research [1-3] shows that the performance enhancement brought by the integration of magnetic will be shadowed by the process complexity. A novel method to fabricate the magnetic core inductors on flexible substrates is proposed in this work. The inductor has a stacking structure of three layers: the Cu trace layer, and the two layers of magnetic core (under and above the Cu). The Cu trace is patterned by the wet etch process on the flexible PCB, and the upper layer magnetic core is directly sputtered on the Cu trace layer with the polyimide layer being planarized on the Cu surface as insulation. A polyimide layer on the carrier wafer is prepared as the substrate for the lower magnetic core layer and the pattern is also created by the liftoff process. Then, the two finished layers are aligned and bonded with a flip-chip bonder with high precision and efficiency. The whole process is shown in Fig.1. Before the whole fabrication process, the device patterns are designed and optimized by the finite element analysis software to extract the parameters for comparison. And finally, the finished devices (shown in Fig.2) are measured with the radiofrequency probe station. The result shows that the inductance density and the quality factor of the magnetic core inductor could be 3.61 nH/mm2 and 6.22, respectively, with the device size being only 0.95 mm2. Compare with the air core inductor with the same Cu trace pattern, the magnetic core inductor elevates the inductance by 10% and still keeps the same low profile, of which the thickness of the whole device is within 100 um. These parameters are measured and extracted at 100 MHz and this is the widely used frequency for the power delivery applications such as the in-chip integrated voltage regulators.

![](https://assets.underline.io/uploads/markdown_image/1/image/9d73279a565e56c01aa0293d4f0c5845.jpg)

The Fabrication process.

![](https://assets.underline.io/uploads/markdown_image/1/image/0fc585fb76a9a86add06825af359c037.jpg)

The finished device with the magnetic core on the top and bottom layers.

A Low-cost Novel Method to Fabricate Integrated Magnetic Core Inductor Embedded in Organic Substrate

Magnetic nanocomposites have applications in power electronics, where properties such as high permeability, high thickness, high operating frequency, and low loss are desired. Recent work shows that electroinfiltration, where a magnetic composite is formed by electroplating a metal through a deposited nanoparticle layer, produces magnetic composites with high permeabilities and low losses [1]. However, electroinfiltration has a thickness limitation of &lt;4 μm. Attempts to overcome this by fabricating multiple composite layers have been demonstrated, but reveal a trade-off between composite thickness and maximum operating frequency [2]. This trade-off is due to dimensional resonance, caused by the formation of standing waves in the material cross-section. Laminations can be used to overcome this effect, as the resulting laminated layers have smaller cross-sections that increase the frequency at which standing waves begin to form [3]. This work demonstrates a process to create thick magnetic composites by laminating layers of infiltrated magnetic composite with insulating layers of parylene to reduce dimensional resonance effects, as seen in Figure 1. For the magnetic layer, composites made from iron-oxide nanoparticles infiltrated with nickel-metal are used. Four samples are made, containing 1, 2, 3, and 5 layers of magnetic composite, separated from each other by approximately 1-2.5 μm of parylene. Structural characterization of these samples was done using SEM with EDS capabilities, showing that the desired laminated structures were achieved. Next, dc magnetic characterization showed that the magnetic properties of the laminated composites remain nearly constant with the increase in thicknesses. Finally, ac magnetic measurements reveal that these laminated composites have a constant dimensional resonance of ~350 MHz irrespective of an increase in the number of layers, as seen in Figure 2. In conclusion, it is evident that laminating the nanocomposites reduces the effects of dimensional resonance, and a fabrication process for implementing laminations into electroinfiltrated composites has been demonstrated.

![](https://assets.underline.io/uploads/markdown_image/1/image/5ea576300cbef4d9bd7faac9c6149a5f.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/a047796add6514afab8b783c426ceed4.jpg)

Fabrication of thick, laminated, electroinfiltrated magnetic nanocomposites to reduce dimensional resonance effects

Fabrication of thick, laminated, electroinfiltrated magnetic nanocomposites to reduce dimensional resonance effects

Power electronics is attracting strong attention as one of the key technologies for realizing the carbon neutral society. A higher switching frequency in a power module is sought for making it more compact. However, inductors hinder it because the loss in the magnetic core rapidly increases. Thus, it is crucial to study and eventually suppress the magnetic loss in MF, HF and VHF bands (300 kHz – 300 MHz). Conventional RF permeameters measure mutual or self inductance of the coil wound around the magnetic sample. This method has the following problems, 1) it requires the sample to be the final toroidal shape, and 2) it cannot apply an external magnetic field. It is desirable to measure the RF permeability of a single particle in the powder stage as a function of magnetic field to gain more insight. For this purpose, we developed the transformer coupled permeameter (TC-Perm), and successfully measured a single Sendust particle used in noise suppression sheet over 10 MHz – 20 GHz1). Then we modified it to further expand the bandwidth. In the initial configuration of TC-Perm, the lower bandwidth limit is set by the vector network analyzer (VNA). We replaced it with another VNA covering 100 kHz – 44 GHz. The S21 parameter of the jig is proportional to frequency at low frequencies because the two CPWs are inductively coupled. This causes the signal level becoming smaller than the noise floor level of the VNA below a few 10 MHz, making it impossible to measure at low frequencies. We modified the TC-Perm as shown in Fig. 1 to avoid this problem. A low noise amplifier (LNA) with noise figure of 2.4 dB is inserted between the jig and VNA below 100 MHz. Above 100 MHz, the LNA is bypassed by two semiconductor RF analog switches. The Permalloy calibration sample used in Ref. 1 was measured using this system under a bias field of 200 mT. The modified TC-Perm showed approximately 40 times smaller noise level at low frequencies than before modification, which allows it to seamlessly measure the permeability over 300 kHz – 44 GHz. Acknowledgement - This work is supported by MIC SCOPE JP195003002.

![](https://assets.underline.io/uploads/markdown_image/1/image/fec082390465e6e7aae541daa230f473.jpg)

Block diagram of TC-Perm after modification.

![](https://assets.underline.io/uploads/markdown_image/1/image/b6d1d01fc1c45c4be7f0f8a32ce8f82f.jpg)

Measurement result of a Py sample with and without LNA.

Modification of transformer coupled permeameter (TC-Perm) for wider bandwidth

The welds of steel structures, used in the bridges and roadway steel decks, are stressed areas where fatigue cracks are prone to occur. Once a fatigue crack occurs in a weld, it spreads and becomes larger, increasing the risk of collapse of the structure. Therefore, it is important to detect fatigue cracks in welds at an early stage. However, the surfaces of the structures are coated to protect the structure itself and the landscape. This makes it difficult to detect cracks using the conventional methods of visual inspection and magnetic particle inspection. In this study, a sensor probe adapted to the weld shape of the structure was developed for detecting cracks with the surface coating using the unsaturated AC magnetic flux leakage (USAC-MFL). This method utilizes a small AC magnetic field in the unsaturated region of the initial magnetization for steel and measures the magnetic flux leakage due to the crack. We have previously reported that the crack detection of steel plates was realized with low power and high sensitivity using the USAC-MFL [1]. To evaluate the performance of the developed sensor probe, 20 samples of welded joints with an average coating thickness of 125 and 250 μm were prepared. The slits were located in three positions: in the rib, the weld, and the base (Fig. 1). A total of 70 slits, ranging from 1 mm to 5 mm depth, were measured. The differential signals from the two sensors were recorded and analyzed. The same measurements were performed in the non-slit areas to compare the signals of the slits. Figure 2 shows the result measured at the slits positioned in the weld. The correlation coefficient of slit depth and differential intensity was 0.89, indicating a strong correlation. The same tendency was obtained for the slits in the rib and base. The differential signal intensity of the slit was larger than that of the non-slit area, even 1 mm depth. These results suggest that the USAC-MFL and the developed sensor probe can be used to detect cracks in the welds of steel structures at an early stage with the surface coating.

![](https://assets.underline.io/uploads/markdown_image/1/image/0d1693854f1cfd481032ccf0b4002494.jpg)

Fig. 1 Welded joint sample with surface coating and the sensor probe.

![](https://assets.underline.io/uploads/markdown_image/1/image/0bd665c2474845ff0803bb88336e9692.jpg)

Fig. 2 Dependence of differential signal intensity and slit depth measured in the weld.

Crack detection for welded joint with surface coating using unsaturated AC magnetic flux leakage

This work presents a novel system to image formation permeability of the reservoir in situ downhole. Colloidal magnetite fluid with high magnetic permeability is injected from the surface into the subsurface formation. The magnetic fluid permeates through the formation some radial distance ΔR over a given period of time, which is directly related to the formation permeability. A sensor array which measures the radial distribution of magnetic permeability surrounding the tool is deployed downhole during this injection process. By comparing the magnetic permeability radial distribution surrounding the sensor before/during/after fluid injection, the system is able to directly measure phase permeability of the surrounding formation in situ. The sensor array measures the radial magnetic permeability distribution of the formation via mutual inductance between pairs of solenoid coils axially distributed along a downhole tool. As the magnetic permeability of the material surrounding the solenoid coils increases, the mutual inductance between coils increases. Eddy current effects on mutual inductance measurements can be minimized by reducing the interrogation frequency of the measurement such that electrical conductivity and permittivity changes have no effect on the measurement of interest, e.g. the measurement is insensitive to the movement of brine and hydrocarbon and sensitive only to the movement of the magnetic permeability doped fluid. Measuring mutual inductance across the array of solenoid coils distributed along the tool enables the system to map the radial distribution of magnetic permeability surrounding the sensor. A laboratory prototype of this sensor system was built and evaluated for its sensitivity to changes in magnetic permeability distributions surrounding the tool. Results from these laboratory tests are compared to analytical predictions of the tool response. Magnetic permeability doped fluid of various concentrations are measured with the sensor array, and measurement results are compared to the predicted magnetic permeability of the various concentrations of doped fluid.

![](https://assets.underline.io/uploads/markdown_image/1/image/a8837a4474972e06f1721268e9344f16.jpg)

Magnetic Permeability Sensor Array Prototype To Evaluate Reservoir Phase Permeability in-Situ Downhole

Effect of individual magnetic nanoparticle on magnetization reversal of ferromagnetic layers is well know [1,2 ]. Here we present effect of ferromagnetic surface of the magnetoresistive sensor on magnetic susceptibility of nanoparticles (NPs), deposited on the sensor surface. Deposition of CoFe2O4 nanoparticles on CoFeB/Ta/CoFeB platform, containing two ferromagnetic nanolayers, changes blocking temperature of the NPs. Magnetic dipole interaction between the NPs and the platform effects frequency and field dependences of the blocking temperature of the NPs. Effective barrier of magnetization reversal and blocking temperature of NP, coupled with ferromagnetic platform, are higher, than in NP deposited on diamagnetic substrate. We observed feedback of magnetic susceptibility of cobalt ferrite cubic nanoparticles on magnetic dipole interaction between NPs and ferromagnetic bilaere CoFeB/Ta/CoFeB platform. The main magnetic characteristics of dynamical magnetization reversal in NPs are changed, when they are deposited on the surface of the ferromagnetic platform. Change of the blocking temperature of NPs under the magnetic dipole interaction with platform is caused by increase of the constant of effective magnetic anisotropy of the NPs up to 15-20%. Micromagnetic modeling predicts change of platform magnetization under individual NP up to 10 % that is similar with changes of the blocking temperature, effective magnetic anisotropy and other phenomenological parameters directly determined in experiments (Fig.1).The variations of the magnetizations of the two ferromagnetic layers under alternative magnetic field were visualized by micromagnetic modeling. Obtained results have principal importance for correct data collecting in lab-on-chip devices, where concentration of the NPs or magnetically labeled biology objects should be measured. Change of the AC susceptibility of NPs caused by their magnetic dipole interaction with the platform can valuably affect estimated number of nanoparticles in real devices.

![](https://assets.underline.io/uploads/markdown_image/1/image/654e8026a3211609a42279c3b16cd777.jpg)

Fig.1. Calculated orientations of local magnetization in top and bottom layers of the CoFeB/Ta/CoFeB platform in presence of ferromagnetic NP on its surface in external magnetic field.

Feedback of magnetic nanoparticles susceptibility to their magnetic dipole interaction with ferromagnetic GMR sensor

The linear magneto-optic Kerr effect (LinMOKE) as well as the quadratic MOKE (QMOKE) are important magneto-optic effects of fundamental physics but also powerful tools for thin-film sample characterization, e.g., to analyze magnetocrystalline anisotropies via vectorial magnetometry [1] or to sense the crystallographic ordering in Heusler compounds [2]. In order to separate and study the dependencies of LinMOKE and QMOKE on the crystallographic direction, the so-called eight-directional method can be used [3]. For each crystallographic in-plane direction, a magnetic field is applied in eight in-plane directions (every 45°) and the responses are added up or subtracted depending on the odd and even nature of LinMOKE and QMOKE with respect to the magnetization. So far,this method or similar ones have been utilized to characterize (001)-and (011)-oriented thin films of cubic crystal structure [4,5]. In addition, new setups for QMOKE spectroscopy have been realized for (001)-oriented thin films [6]. Within this contribution, we apply the eight-directional method to sputter-deposited Ni(111) thin films and report on a strong three-fold anisotropy in longitudinal MOKE (LMOKE), see Fig. 1. This anisotropy can be explained by theory as an optical interplay of elements in the permittivity tensors of first and second order in M, effectively creating cubic MOKE contributions, i.e., MOKE of third order in M. Furthermore, we studied Ni(111) thin films with and without several multiple (111) phases of 60° in-plane rotation (twinning) which have been characterized by off-specular x-ray diffraction texture maps. We observed substantial reduction of QMOKE oscillations in a twinned sample compared to a thin film with almost no twinning. This indicates that the LMOKE anisotropy truly is of crystallographic origin in the ferromagnetic layer and is not due to other, e.g., interface effects.

![](https://assets.underline.io/uploads/markdown_image/1/image/ee68c6112eec764f164a4c5214b5abe1.jpg)

QMOKE anisotropy measurement of a 20-nm thick Ni film on MgO(111) at a wavelength of 406 nm. The threefold anisotropy of longitudinal MOKE (∝ ML in black), transverse MOKE (∝ MT in green) and QMOKE (∝ MLMT in blue, as well as ∝ MT2-ML2 in red) are clearly visible.

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