France



Modern MRAM technology relies on the magnetic tunnel junction (MTJ) consisting of the state-of-the-art CoFeB/MgO heterostructure. Although current studies support the importance of this heterostructure to the technology, the concern of MgO dielectric breakdown limits MRAM lifetime. We found that inserting an ultra-thin Mg (0.4nm) layer between CoFeB and MgO could promote lifetime and change polarity dependence on applied voltage (Fig.1). However, it traded off the perpendicular magnetic anisotropy and tunneling magneto-resistance. In this work we visualized the modified CoFeB/MgO with Mg insertion against dielectric breakdown by using an in-situ x-ray absorption spectroscopy technique. We find this technique very helpful to understand the origin of interface reconstruction in association with the changes of energy barrier-height and electronic occupation, which are invisible but essential to the MTJ’s performance. This is due to the uniqueness of the element-/orbital specificity and the real-time design of the setup. We established a bridge correlating the heterostructure’ microscopic and macroscopic properties, by cross-utilizing the x-ray technique with spin transport measurements and atomistic magnetic simulation (Vampire). This thus offers us comprehensive insights which may improve contact engineering of the MTJ technology.

**References:**

[1] Van Beek, Simon, et al. &quot;Impact of processing and stack optimization on the reliability of perpendicular STT-MRAM.&quot; &lt;i&gt;2017 IEEE International Reliability Physics Symposium (IRPS)&lt;/i&gt;. IEEE (2017).&lt;br/&gt;[2] Van Beek, Simon, et al. &quot;Understanding and empirical fitting the breakdown of MgO in end-of-line annealed MTJs.&quot; &lt;i&gt;2020 IEEE International Reliability Physics Symposium (IRPS)&lt;/i&gt;. IEEE (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/706c071b51b55198e8156662bc6a6fd7.jpg)
Fig. 1: Welbull distribution versus breakdown voltage for the pMTJ stack consisting of (a) SAF/CoFeB(8Å)/MgO(10Å)/CoFeB(11.5Å)/Ta(3Å) (referred to w/o Mg sample), (b) SAF/CoFeB(8Å)/MgO(10Å)/Mg(4Å)/CoFeB(11.5Å)/Ta(3Å) (referred to with Mg sample). Blue and red data correspond to positive and negative voltages applied to the MTJ, respectively. SAF refers to synthetic antiferromagnetic layer which consists of [Co(4Å)/Pt(3Å)]&lt;sub&gt;7&lt;/sub&gt;/Co(6Å)/Ru(8Å)/[Co(4Å)/Pt(3Å)]&lt;sub&gt;3&lt;/sub&gt;/Co(4Å). &lt;i&gt;β&lt;/i&gt; and &lt;i&gt;η &lt;/i&gt;refer to slope parameter and extrapolated breakdown voltage, respectively.



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Virtualizing CoFeB/MgO Reconstruction Effects on the STT-pMTJ&#39;s Performance

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Modern MRAM technology relies on the magnetic tunnel junction (MTJ) consisting of the state-of-the-art CoFeB/MgO heterostructure. Although current studies support the importance of this heterostructure to the technology, the concern of MgO dielectric breakdown limits MRAM lifetime. We found that inserting an ultra-thin Mg (0.4nm) layer between CoFeB and MgO could promote lifetime and change polarity dependence on applied voltage (Fig.1). However, it traded off the perpendicular magnetic anisotropy and tunneling magneto-resistance. In this work we visualized the modified CoFeB/MgO with Mg insertion against dielectric breakdown by using an in-situ x-ray absorption spectroscopy technique. We find this technique very helpful to understand the origin of interface reconstruction in association with the changes of energy barrier-height and electronic occupation, which are invisible but essential to the MTJ’s performance. This is due to the uniqueness of the element-/orbital specificity and the real-time design of the setup. We established a bridge correlating the heterostructure’ microscopic and macroscopic properties, by cross-utilizing the x-ray technique with spin transport measurements and atomistic magnetic simulation (Vampire). This thus offers us comprehensive insights which may improve contact engineering of the MTJ technology.

**References:**

[1] Van Beek, Simon, et al. "Impact of processing and stack optimization on the reliability of perpendicular STT-MRAM." 2017 IEEE International Reliability Physics Symposium (IRPS). IEEE (2017). [2] Van Beek, Simon, et al. "Understanding and empirical fitting the breakdown of MgO in end-of-line annealed MTJs." 2020 IEEE International Reliability Physics Symposium (IRPS). IEEE (2020).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/706c071b51b55198e8156662bc6a6fd7.jpg)
Fig. 1: Welbull distribution versus breakdown voltage for the pMTJ stack consisting of (a) SAF/CoFeB(8Å)/MgO(10Å)/CoFeB(11.5Å)/Ta(3Å) (referred to w/o Mg sample), (b) SAF/CoFeB(8Å)/MgO(10Å)/Mg(4Å)/CoFeB(11.5Å)/Ta(3Å) (referred to with Mg sample). Blue and red data correspond to positive and negative voltages applied to the MTJ, respectively. SAF refers to synthetic antiferromagnetic layer which consists of [Co(4Å)/Pt(3Å)]7/Co(6Å)/Ru(8Å)/[Co(4Å)/Pt(3Å)]3/Co(4Å). β and η refer to slope parameter and extrapolated breakdown voltage, respectively.

Virtualizing CoFeB/MgO Reconstruction Effects on the STT-pMTJ's Performance

technical paper

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

**References:**

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

**Images:**

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

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

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

**References:**

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

**Images:**

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

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

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://assets.underline.io/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://assets.underline.io/uploads/markdown_image/1/image/71c400da15890673ef973c968b06563d.jpg)

![](https://assets.underline.io/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://assets.underline.io/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://assets.underline.io/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.

Anisotropic Magnetoresistance Zero-Field Domain Wall Depinning in Cylindrical Nanowires

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://assets.underline.io/uploads/markdown_image/1/image/ffc6d5c2761c3b560b36db929ce09c40.jpg)
Fig.1 The curves of transient current difference extremum parameters versus Br

![](https://assets.underline.io/uploads/markdown_image/1/image/8fcc1ffc5fecf23644df6c2889571d89.jpg)
Fig.2 The comparison of experimental residual flux density and estimated residual flux density

Residual Flux Measurement of Power Transformer Based on Transient Current Difference

Spin transfer torque magnetic random-access memory (STT-MRAM) is one of the promising non-volatile memory (NVM) technology resolving scalability issue, current consumption, and current leakages of traditional transistor-based memories. Due to the intrinsic STT-switching stochasticity and thermal fluctuation dependance of MRAM technology, potential transitions and retention faults may happen during chip operating life [1]. Consequently, each bit writing and reading should be tested many times (&gt; 106 iterations) to quantify the fault event occurrence, and validate that each fault is well detected and addressed by the error correction code (ECC) algorithms. For large memory arrays (&gt;MB), non-persistent faults with ppm occurrences are difficult to test. Extrapolating the transition faults of large array in 10 years operation within few microseconds is challenging and does require the use of faults acceleration factors to limit the testing time [2], as well as the use of on-chip BIST (Built In-Self-Test) circuitry with algorithms optimized for testing MRAM arrays at higher speed than with external electrical tester. The MRAM switching behavior dependance with temperature is usually used to compress the retention time through application of weak but long disturb current [1,4], and application of temperature while testing [3]. Although these approaches are helping in reducing the retention testing time for each bit cell of the array, it is still very problematic for addressing full testing of large arrays. As example, the testing of each bit using different proposed algorithms leads to test time of 0.5 to 3 sec per bit cell, which is way too long for large array testing [1-4]. To further improve testing time, it is interesting to apply a magnetic field as an additional acceleration factor, as applying an offset field in opposite direction to the anisotropic field of free layer will help in further compressing the retention [2]. Importantly, testing MRAM arrays under magnetic field also allows to evaluate the immunity of the bit cells to parasitic external field [5]. The difficulty for testing MRAM arrays at wafer level for such purpose is the need of using an external magnetic field, perpendicular to the wafer and covering the entire array surface area in the range of 1 to 10mm2 while testing electrically at high temperature. It requires both a good field strength and uniformity on the covered area. In this presentation, we propose a new magnetic head designed for the testing of large arrays, aiming in both optimizing the identification of non-persistent faults related to STT-switching stochasticity and reducing retention testing time. The system can also be used for evaluating bit cells persistence to magnetic interference through magnetic disturbance test. The proposed magnetic test head system is integrating a new 5-poles design from Hprobe proprietary 3D magnetic generator. In test operation, the magnetic head is docked on the head plate of 300mm wafer probing station (figure 1) with the probe card placed underneath. The system is driven by external software interface or operating with triggered signals enabling field application synchronized with electrical measurements. The test head integrates two robotic systems enabling three modes of operations. (i) Field calibration mode to generate and optimize the field patterns to be used in testing; (ii) testing mode for electrical probing and under static or variable magnetic field; and (iii) field monitoring mode to verify that the field stimulus is under the specification limits required by application. A hexapod robot is handling the electro-magnet with six degrees of freedom (X, Y, Z, roll, pitch and yaw). Other two axis system is used for controlling the position of the 3D hall sensor used to sense the magnetic field, scanning the entire area of the array in 3D with step resolution of less than 10µm. The system enables to work with standard probe cards having hundreds of needles and is designed to do the field calibration at the exact DUT position above the chuck. STT-MRAM anisotropy is oriented perpendicular to the wafer, and compression scheme for non-persistent fault testing requires magnetic field strength at the upper range of the free layer switching field (100-400mT). The proposed system can generate a perpendicular field up to 700mT (Fig.1) and is sufficient for time acceleration testing of bit cell switching and retention, as well as for field immunity testing. The last would be beneficial to be made also by applying disturbance field in the planar direction to the wafer, the system can generate 3D fields and a maximum planar field amplitude of 100mT is obtained. The achieved non-uniformity is less than 5% over an area above 5mm2 (Fig.2), which is enough to cover arrays of &gt;64Mb considering an average density of &lt; 0.08 mm2/Mb [6].

**References:**

[1] H. Naeimi et al., “STTRAM scaling and retention failure,”Intel Technology Journal, vol. 17, 2013, https://www.intel.com/ content/dam/www/public/us/en/documents/research/2013-vol17-iss-1n-intel-technology-journal.pdf#page=54. [2] Wu, Lizhou & Taouil, M. & Rao, Siddharth & Marinissen, Erik & Hamdioui, Said. (2020). Survey on STT-MRAM Testing: Failure Mechanisms, Fault Models, and Tests. (https://arxiv.org/abs/2001.05463) [3] A. Iyengar, S. Ghosh, and S. Srinivasan, “Retention testing methodology for STTRAM,” IEEE Design & Test, vol. 33, pp. 7–15, 2016, doi:10.1109/MDAT.2016.2591554. [4] I. Yoon and A. Raychowdhury, “Test challenges in embedded STTMRAM arrays,” in Int. Symp. Quality Electronic Design, Mar. 2017, doi:10.1109/ISQED.2017.7918289. [5] Y. Chih et al., "13.3 A 22nm 32Mb Embedded STT-MRAM with 10ns Read Speed, 1M Cycle Write Endurance, 10 Years Retention at 150°C and High Immunity to Magnetic Field Interference," 2020 IEEE International Solid- State Circuits Conference - (ISSCC), San Francisco, CA, USA, 2020, pp. 222-224, doi: 10.1109/ISSCC19947.2020.906295 [6] S.H. Han et al, “28-nm 0.08 mm2/Mb Embedded MRAM for Frame Buffer Memory”, in International Electron Device Meeting 2020

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/67ac20f6011a1a46800ed12d99483a54.jpg)
Fig. 1 – Perpendicular field versus the gap between 3D generator and DUT and an illustration of the test head mounted on wafer probing station

![](https://assets.underline.io/uploads/markdown_image/1/image/fde7b8a2d8ec18f3f26560cab9038494.jpg)
Fig. 2 – Field area uniformity (at 4mm gap) of perpendicular field

System for testing non-persistent switching and retention faults of STT-MRAM arrays

Magnetic susceptibility methods particularly, AC susceptibility measurement have shown high potential to provide a fast characterization and standardization technique of magnetic nanoparticles (MNPs) [1]–[4]. Depending on the applications, AC magnetometers have been developed to measure magnetic responses from MNPs where Neel and Brown relaxation parameters are mostly characterized and utilized in these applications. From the acquired Brownian and Neel relaxation, physical and magnetic properties of the MNPs can be estimated such as the hydrodynamic size and magnetic anisotropy energy ratio. However, the characterization frequency range of the Neel and Brownian relaxations plays an important role where a wider frequency range may reveal further information on the MNP properties. In this study, to realize a simple, wideband, and sensitive AC magnetometer for bio-sensing applications and characterization of magnetic nanoparticles (MNPs), we report the improvements in the detection unit of our previously developed induction-based AC magnetometer [5] for achieving a larger usable range of the detection frequency. In order to obtain a linear sensitivity response, the induction coil is typically operated below its self-resonance frequency where its inductive property becomes dominant and not affected by the parasitic capacitance. This self-resonance frequency is governed by the coil’s inductance and parasitic impedance, and increasing the self-resonance frequency by reducing the coil’s inductance will extend the usable frequency range of the coil. However, it should be noted that there is a trade-off between the coil’s usable frequency range and sensitivity where an increase of the self-resonance frequency may reduce the coil’s sensitivity at the low-frequency region. In the attempt to achieve a wide frequency range yet sufficiently sensitive pickup coil, we compared the sensitivity and usable frequency range of 6 different designs of pickup coils by investigating the effect of inductance and parasitic capacitance. The number of turns and coil section separation were varied from 400 to 200 turns, and 1 to 4 sections, respectively. We found that the usable frequency range was greatly affected by the pickup coil’s inductance due to the self-resonance phenomena compared to parasitic capacitance. A low noise amplification circuit was designed based on two AD8429 instrument amplifiers and fabricated on a 2-layer printed circuit board as shown in Fig. 1 (a). For the field excitation unit, the excitation coil was designed to produce a field uniformity of more than 90% and constructed using a Litz wire with 60 strands of 0.1-mm Cu wire. The acquisition of the magnetization signal was realized by implementing a generalized Goertzel algorithm to achieve fast signal and phase extractions [6] in comparison to the conventional use of Fast Fourier Transform and lock-in amplifier techniques. As a result, the developed magnetometer showed a sensitivity of 10-8 Am2/sqrt(Hz) at 6 Hz and a frequency range of up to 158 kHz. We then demonstrated the developed AC magnetometer by evaluating the effect of viscosity on the frequency response of thermally blocked, single-core nanoparticles (SHP30, Ocean Nanotech, USA). The viscosity of the carrier liquid was varied by different weights of glycerol mixed in a constant volume of purified water and the Fe-concentration was fixed at 0.5 mg/mL. The excitation frequency was swept from 5 Hz to 158 kHz at a maximum field of 0.55 mTpp to obtain discrete 51 measurement points within the acquisition time of 5 minutes. As a result, the peak for the imaginary part was observed to be shifted towards lower frequency values when the wt/V% of the glycerol solution was increased. From the real and imaginary magnetization curves, the hydrodynamic size and the average anisotropy energy ratio s were estimated to be 60.6 nm and 25, respectively. It can be expected that the developed AC magnetometer can be a valuable tool in providing a simple, fast, and reliable assessment of MNPs for bio-sensing applications. Acknowledgments This work was supported by the Ministry of Higher Education of Malaysia under the grant number of FRGS/1/2019/TK04/UMP/02/4 (RDU1901154), the Research Management Center of Universiti Malaysia Pahang under the grant number of RDU1903100, and the “Strategic Promotion of Innovative R&D” of the Japan Science and Technology Agency (JST).

**References:**

[1] J. Wells et al., “Standardisation of magnetic nanoparticles in liquid suspension,” J. Phys. D. Appl. Phys., vol. 50, no. 38, p. 383003, Sep. 2017, doi: 10.1088/1361-6463/aa7fa5. [2] P. Schier et al., “European Research on Magnetic Nanoparticles for Biomedical Applications: Standardisation Aspects,” Curr. Trends Biomed. Eng. Bioimages Anal. PCBEE 2019. Adv. Intell. Syst. Comput., vol. 1033, no. May, pp. 316–326, 2020, doi: 10.1007/978-3-030-29885-2_29. [3] M. M. Saari et al., “Influence of Viscosity on Dynamic Magnetization of Thermally Blocked Iron Oxide Nanoparticles Characterized by a Sensitive AC Magnetometer,” J. Supercond. Nov. Magn., vol. 32, no. 9, pp. 2765–2772, Sep. 2019, doi: 10.1007/s10948-019-5031-6. [4] S. Ota et al., “Effects of size and anisotropy of magnetic nanoparticles associated with dynamics of easy axis for magnetic particle imaging,” J. Magn. Magn. Mater., vol. 474, no. September 2018, pp. 311–318, 2019, doi: 10.1016/j.jmmm.2018.11.043. [5] M. M. Saari, N. S. Suhaimi, N. A. C. Lah, K. Sakai, T. Kiwa, and K. Tsukada, “A Sensitive AC Magnetometer using A Resonant Excitation Coil for Magnetic Fluid Characterization in Nonlinear Magnetization Region,” in 2018 IEEE International Magnetics Conference (INTERMAG), Apr. 2018, pp. 1–4, doi: 10.1109/INTMAG.2018.8508784. [6] P. Sysel and P. Rajmic, “Goertzel algorithm generalized to non-integer multiples of fundamental frequency,” EURASIP J. Adv. Signal Process., vol. 2012, no. 1, p. 56, Dec. 2012, doi: 10.1186/1687-6180-2012-56.

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/31298569e8861862e56ebd7954d7d29b.jpg)
Fig. 1. a) Diagram of the developed AC magnetometer. b) The arrangement and configuration of the excitation coil with respect to the sample and pickup coil.

![](https://assets.underline.io/uploads/markdown_image/1/image/250b9fca4d1de27aa2318159dbd55abe.jpg)
Fig. 2. (a) The normalized real and imaginary susceptibilities of the SHP30 particles at different glycerol wt/V % in the solutions with respect to the frequency. (b) The ratio between the imaginary and real susceptibilities of the SHP30 solutions with respect to the frequency normalized by each Brownian frequency fB.

Towards A Wideband Induction-Based AC Magnetometer for A Fast Characterization of Magnetic Nanoparticles.

Magnetic nanoparticles are powerful tools in biomedical applications, where they are employed in both diagnosis and therapy. A prerequisite for the efficiency of these applications are precisely characterized particles. To this end, several magnetic measurement techniques are established. They all have in common that they measure the magnetic response of the particles exposed to an externally applied magnetic field, which may change the aggregation state of the particles [1]. To overcome this limitation, the method of Thermal Noise Magnetometry (TNM) has been developed to characterize magnetic nanoparticle ensembles without the use of an external magnetic excitation [2]. Amplitude variations in the net magnetic moment of the sample are measured, which are caused by thermal fluctuations in the system. Rather than measuring the dissipation or impedance in the system as a result of the application of the external field, the thermal fluctuations are studied in the absence of the external excitation. The dissipation-fluctuation theorem describes the accordance between the conventional dissipation characterization techniques such as Magnetorelaxometry (MRX) or AC-Susceptibility (ACS) measurements [4, 5], and the fluctuation-based TNM technique. The total switching rate of the magnetic moments depends on volume, anisotropy, aggregation of the particles and the viscosity and temperature of the suspension. TNM measurements have been proven to be feasible, and complementary to other characterization techniques due to its diminutive impact on the sample [2, 5]. In this contribution we present a numerical framework which we use to mirror our TNM measurements, in order to further establish this characterization method. First, we numerically investigate and explain the dependence of the stochastic TNM signal on basic parameters such as the number of particles and their volume. The linear dependence on the number of particles is experimentally verified. Next, we designed a sample holder geometry by solving an optimization problem, maximizing the noise power in our setup (see Fig. 1). Its performance is compared to that of a cylindrical sample holder, typically used for MRX measurements. This was done by measuring the noise power as a function of the sample distance from the detector (i.e. the depth profile of the experimental setup), both computationally and experimentally (Fig. 2). We obtained an increase in noise signal by a factor of 3.5 for the optimized sample holder, while the volume of the sample decreased by more than half. The superior signal amplitude of our optimized sample holder and the match between computed and measured depth profile demonstrate the accuracy and importance of our TNM simulations. The theoretical framework allows us to study aspects of TNM which are hard to accomplish experimentally, making it possible to visualize them and gain insight in the experiment. Our results therefore contribute to the further establishment of TNM as a magnetic nanoparticle characterization method.

**References:**

[1] Myrovali, E. et al., Sci. reports, Vol. 6, p. 37934 (2016) [2] Leliaert, J. et al., Appl. Phys. Lett., Vol. 107, p. 222401 (2015) [3] Wiekhorst, F., Steinhoff, U., Eberbeck, D. & Trahms, L., Pharm. Res., Vol. 29, p. 1189 (2012) [4] Ludwig, F., Guillaume, A., Schilling, M., Frickel, N. & Schmidt, A. M., J. Appl. Phys., Vol. 108, p. 33918 (2010) [5] Leliaert, J. et al., J. Phys. D: Appl. Phys., Vol. 50, p. 085004 (2017)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/7ea209e345c17a0e6c8b74d2e36a0635.jpg)
The geometry for the regular cylindrical and the optimized 200 µl sample in the experimental setup

![](https://assets.underline.io/uploads/markdown_image/1/image/a05936f4f0f2c5859de5571080a6414a.jpg)
The measured and simulated noise power as a function of the depth in the warm bore of both sample geometries

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