# Nanoscale Magnetic Texture Induced by Exchange Bias: Insights from NV Magnetometry

Léo L. Petitdemange, Sébastien Geiskopf, Grégory Malinowski, Mariana Fino

Caseiro, Myriam Pannetier-Lecoeur, Martin Bowen, Michel Hehn, Daniel

Lacour

► To cite this version:

Léo L. Petitdemange, Sébastien Geiskopf, Grégory Malinowski, Mariana Fino Caseiro, Myriam Pannetier-Lecoeur, et al.. Nanoscale Magnetic Texture Induced by Exchange Bias: Insights from NV Magnetometry. Nano Letters, 2026, 10.1021/acs.nanolett.5c05917. [https://doi.org/10.1021/acs.nanolett.5c05917](https://doi.org/10.1021/acs.nanolett.5c05917)

HAL Id: hal-05504493

https://hal.science/hal-05504493v1

Submitted on 11 Feb 2026

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons CC BY 4.0 - Attribution - International License
# Nanoscale Magnetic Texture Induced by Exchange Bias: Insights from NV Magnetometry

L. Petitdemange<fnref n="1" />, S. Geiskopf<fnref n="1" />, G. Malinowski<fnref n="1" />, M. Finocaseiro<fnref n="2" />, M. Pannetier-Lecoeur<fnref n="2" />, M. Bowen<fnref n="3" />, M. Hehn<fnref n="1" />,
D. Lacour<fnref n="1" />,.*

## AFFILIATIONS

## ABSTRACT

Exchange bias, originating at the interface between ferromagnetic and antiferromagnetic layers, plays a pivotal role in spintronic devices such as magnetic tunnel junctions (MTJs) because it stabilizes the magnetization direction of one electrode, often the reference magnetic layer, enabling controlled switching behavior. In this study, we combine macroscopic magnetometry with nanoscale magnetic imaging using nitrogen-vacancy (NV) centers in diamond to investigate the local magnetic texture induced by exchange bias. NV magnetometry offers high-resolution, non-invasive mapping of stray magnetic fields under ambient conditions. To interpret the experimental data, we perform micromagnetic simulations incorporating a granular anisotropy landscape. This approach successfully reproduces both the hard-axis magnetization loops and the spatial distribution of stray fields observed experimentally. From these results, we extract the dispersion of magnetization angles (ripple angle) and extrapolate the coupling field values between MTJ electrodes, attributed to the observed spin texture.

Today, magnetic tunnel junctions are at the heart of the most advanced devices emerging from spintronics research.<fnref n="1" />⁻<fnref n="3" /> The amplitude of the magnetoresistance signal is linked to their spin-dependent electronic transport properties, while the shape of the resistance versus field loop is determined by the magnetic properties of the ferromagnetic electrodes. A common way to tune these properties involves using the so-called exchange bias effect, which occurs when antiferromagnetic and ferromagnetic layers (AF/F) share an interface properly prepared.⁴⁻⁶ Over the last half-century, the exchange bias effect and its impact on ferromagnetic properties have been widely studied due to its fundamental interest and wide range applications in spintronics (e.g. magnetic sensor, MRAM). Beyond macroscopic characterizations, such as measuring magnetization versus the magnetic field, it quickly became apparent that obtaining local information on a microscopic scale was crucial for advancing the current understanding of the exchange bias effect and related macroscopic response.

AF/F systems are known to host magnetic textures characterized by nanoscale modulations of magnetization, which manifest as periodic wave-like patterns referred to as magnetic ripples.⁷⁻⁹ Following its experimental observation in single ferromagnetic layers, theoretical models describing magnetic ripple textures were established in the 1960s.¹⁰ This

magnetic texture has been then quantitatively characterized, again in individual ferromagnetic films using Lorentz transmission electron microscopy.¹¹ The extracted ripple angle (dispersion of magnetization angles) was later confirmed by micromagnetic simulations.¹² Despite their widespread application in spintronic devices, antiferromagnetic/ferromagnetic (AF/F) bilayers still exhibit poorly characterized features related to their magnetic texture. In particular, studies reporting ripple angles within these structures remain scarce, and the implications of such textural formations on the transfer characteristics of magnetic tunnel junctions are seldom addressed.

Recently, a new magnetic microscopy technique has emerged, based on nitrogen-vacancy (NV) centers in diamond. NV centers are atomic-scale defects consisting of a substitutional nitrogen atom adjacent to a lattice vacancy, forming a spin 1 system with remarkable quantum properties. Their spin state can be initialized and read out optically via photoluminescence, and manipulated using microwave fields, a process known as optically detected magnetic resonance (ODMR). This enables highly sensitive, non-invasive, detection of local magnetic fields under ambient conditions. NV-based magnetometry offers nanoscale spatial resolution.¹³ These advantages also come with limitations: the technique measures only the absolute value of the field projection onto the NV axis, and too large fields

<footnote n="1">¹ Institut Jean Lamour, UMR 7198 CNRS, Université de Lorraine, Campus Artem, 2 allée André Guinier - BP 50840, 54011 NANCY Cedex, France</footnote>

<footnote n="2">²SPEC, CEA, CNRS, Université Paris-Saclay, CEA Saclay 91191 Gif-sur-Yvette, France</footnote>

<footnote n="3">³ Institut de Physique et Chimie des Matériaux de Strasbourg, UMR 7504 CNRS, Université de Strasbourg 23 Rue du Loess, BP 43, Strasbourg 67034, France</footnote>

<footnote>*Electronic mail: daniel.lacour@univ-lorraine.fr</footnote>
suppress the ODMR contrast, preventing reliable imaging. Despite these drawbacks, this recent technique remains particularly well suited for investigating the magnetic texture induced by exchange bias in ferromagnetic layers, as we shall demonstrate in this letter.

These features make it particularly well suited for
investigating the magnetic texture induced by
exchange bias in ferromagnetic layers, as we shall
demonstrate in this letter.

Half-magnetic tunnel junctions, comprising a bottom exchange-biased electrode and a platinum-capped MgO barrier, were fabricated using ultra-high vacuum physical vapor deposition, with a base pressure below $5.0 \times 10^{-9}$ mbar. The detailed layer structure of the stack is as follows: Si/Ta(3)/Pt(5)/Ir<sub>20</sub>Mn<sub>80</sub>(8)/CoFeB(5)/MgO(1)/Pt(2), where the values in parentheses indicate the individual layer thicknesses in nanometers. This correspond to half of the MTJ studied.<sup>14</sup> Following deposition, the sample was subjected to thermal annealing for 1 hour at 300 °C in the presence of an in plane magnetic field of 60 mT. All experiments reported in this letter were conducted at room temperature.

To verify the effectiveness of the activated exchange effect, we performed vibrating sample magnetometry (VSM), applying the magnetic field in the same direction as during the annealing process (■- on fig. 1.). The resulting hysteresis loop exhibits a shift corresponding to an exchange Bias field ($H_{ex}$) of 13 mT. This is consistent with expectations for this thickness range.<sup>14</sup> A slight curvature is also observed prior to the abrupt magnetization reversal.

To evaluate the magnetic anisotropy present in our stack, we performed VSM measurements with the magnetic field applied in the plane of the sample, perpendicular to the annealing field direction. The corresponding results represented by the open orange squares in Fig. 1 (□-) are characteristic of an M(H) loop performed along an hard axis direction as expected. A field of about 18 mT ($H_{sat}$) is necessary to reach the magnetic saturation in this configuration. Considering an uniform rotation of magnetization and a saturation magnetization value $M_s$ of $1200 \times 10^3$ A.m⁻¹ for our CoFeB layer leads to an anisotropy constant of about $11 \times 10^3$ J.m⁻³ (½ .$H_{sat}$. $M_s$).

We then investigate the local magnetic configuration, by performing ODMR frequency measurements while scanning the sample surface at different flying heights, using a commercial Qzabre microscope with a [100] diamond tip from the same manufacturer. These experiments were carried out in the absence of any externally applied magnetic field, following prior positive-field saturation along the annealing-field direction. Tracking the ODMR frequency enables mapping of the magnetic field modulus projected along the NV center axis (ϑ=

125.25° and φ=270° in spherical coordinate for the
[100] tip as sketched in fig. 2a). Absolute value of the
projected field maps were obtained for four distinct
NV center flying heights, ranging from 60 nm to
180 nm.¹³ The resulting 1µm*1µm scans are
presented in fig. 2a. Spatial fluctuations of stray field
can be observed. As the NV center is brought closer
to the sample surface, the recorded magnetic field
amplitude increases, accompanied by an
enhancement in spatial resolution of the field
fluctuations.

<figure><img src="image_2.png" /><figcaption>**Figure 1:** Magnetization vs Field loops. Vibrating sample magnetometer measurements were performed in two configurations. ■-: The magnetic field is applied along the annealing field direction. □-: The magnetic field is applied perpendicularly to the annealing field direction in the sample plan. ⌒: Micromagnetic simulation.</figcaption></figure>

A more quantitative evaluation of the experimental configurations is obtained by extracting the field distribution histograms from the experimental images. This approach eliminates spatial variations and allows us to focus solely on the distribution of field intensity. Figure 2.b displays the histograms derived from the acquired images in the form of bar plots. A Gaussian like behavior is observed in the field distributions, with the full width at half maximum (FWHM) increasing from 0.45 mT to 1.8 mT as the flying heights decrease from 180 nm to 60 nm (see ⊕ points on fig. 2b inset). Although imaging at shorter distances would have increased the spatial resolution, this was not possible due to the loss of ODMR contrast caused by the stronger magnetic fields encountered at lower flight heights.

To gain deeper insight into the magnetic properties
underlying the measured stray fields, we conducted
micromagnetic simulations using the GPU-
accelerated software package MuMax3 ¹⁵. To
eliminate edge effects, periodic boundary conditions
were used within the two directions of the sample
plane. The spatial distribution of the experimentally
measured stray fields being strongly indicative of
magnetization inhomogeneity (i.e. region with non-
zero divergence within the magnetization vector field),
we reasonably decided to introduce a grainy
structure within the simulated sample. The slight
curvature observed in the VSM loop along the
exchange bias direction further supports this
assumption, indicating that magnetization undergoes
rotation before complete reversal¹⁶.

The interface exchange interaction with the
antiferromagnetic layer is effectively accounted for
through an induced inhomogeneous magnetic

anisotropy within the ferromagnetic layer. Any
intrinsic homogenous magnetic anisotropy was
attributed to the CoFeB layer, as it is negligibly small
compared to the anisotropy induced by exchange
bias.

<figure><img src="image_3.png" /><figcaption>**Figure 2a.** Experimental map of the magnetic stray field. The 1µm² ODMR images were recorded at NV center flying heights of 180, 130, 90, and 60 nm. **2b Comparison between the histogram distributions of the experimental & simulated magnetic stray fields.** 2b Inset: Full Width at Half Maximum of Gaussian fits for experiments (⊕) and simulations (IPPING) vs. Flying Heights. The same set of micromagnetic parameters was maintained for all NV center flying heights. **2c Simulated images.** The simulated images display the absolute value of the magnetic stray fields projected along the central axis. These stray fields were computed based on the magnetic texture obtained from a micromagnetic simulation.</figcaption></figure>

Thus, each grain was assigned a specific anisotropy
magnitude and orientation, thereby introducing
localized variations in magnetic behavior across the
sample. Fig. 3a shows the simulated sample
subdivision into grains for an angular dispersion of 35°

<figure><img src="image_4.png" /><figcaption>**Figure 3a: Subdivision of the sample into grains with varying anisotropy directions.** The color code indicates the orientation of the anisotropy relative to the Y-axis. **3b Distribution of anisotropy angle.**</figcaption></figure>

(Full Width at Half Maximum) distributed in the film plane. Each region is characterized by a distinct anisotropy orientation (color-coded). The associated Gaussian distribution is presented just beside it (fig. 3b). After a few iterations to optimize the simulation parameters (as shown in Section S2 of the Supplementary Material for grain-size optimization). It appears that many pairs of anisotropy value / angular dispersion reproduce successfully the hard-axis VSM loops (see Fig. 4a). Higher values of anisotropy and angular dispersion promote the formation of 360° domain walls, as reported in other systems¹⁷,¹⁸, but this behavior is not observed in the cases considered here.

Fitting the hard-axis VSM loop alone is thus not
sufficient to discriminate between the possible
magnetic properties. In order to identify a unique set
<figure><img src="image_5.png" /><figcaption>**Figure 4a.** Comparison between VSM measurements and micromagnetic simulations. The normalized M(H) loop (□) is superimposed on simulation results obtained for six different combinations of anisotropy constant (K) and angular dispersion. **4b. Histogram of stray field distribution.** The experimentally obtained histogram from the ODMR image at a flying height of 60 nm (in gray) is superimposed on stray field histograms extracted from micromagnetic simulations performed for six different combinations of anisotropy constant (K) and angular dispersion.</figcaption></figure>

of parameters, we extended the comparison between experimental data and simulations to the magnetic stray field distribution histograms. Figure 4b shows a comparison between histograms simulated for various anisotropy/angular dispersion pairs and the one obtained through NV center imaging at a flight height of 60 nm. Lower values of these parameters result in simulated histograms with more pronounced peaks near the zero-field region. This behavior reflects the fact that reduced anisotropy and angular dispersion diminish spatial fluctuations in magnetization, thereby lowering the resulting magnetic stray field. This analysis allows us to identify a unique parameter set: $K = 20*10^3$ J.m$^{-3}$, and Angular dispersion = 35° that fits both the hard-axis VSM loop and the experimentally obtained histogram (exp.: Gray bar graph & sim.: - in fig 4b). The anisotropy value derived from this simulations batch is approximately twice that inferred from VSM measurements, under the assumption of a coherent macro-spin reversal mechanism. This outcome is expected, as a reduction in dispersion leads to an increase in the saturation field. The anisotropy

parameter is thus elevated to compensate for the otherwise reduced $H_{sat}$.

At that stage, we established a set of simulation parameters (summarized in Table 1) which we used to reproduce the experimental results. Using this same set of parameters, both the spatial distribution and the amplitude of the magnetic field fluctuations were accurately captured across all explored flying heights (see fig. 2c). In addition, Figure 2b presents a comparison between the experimentally acquired field histograms and those derived from simulation. The consistent agreement across all flying heights provides further confirmation of the simulation's high fidelity. The micromagnetic simulation is characterized by a root mean square (RMS) angular deviation of 7.7° in the magnetization vector, known as the ripple angle.

<table><caption>**Table 1: Simulation parameters**</caption><tr><td>M<sub>s</sub></td><td>1200 * 10<sup>3</sup> A.m<sup>-1</sup></td></tr><tr><td>Cell size (x,y,z)</td><td>2* 2* 5* [10<sup>-9</sup> m]<sup>3</sup></td></tr><tr><td>Grain size</td><td>50 * 10<sup>-9</sup> m</td></tr><tr><td>K</td><td>20 * 10<sup>3</sup> J.m<sup>-3</sup></td></tr><tr><td>value disp.</td><td>20%</td></tr><tr><td>angular disp.</td><td>35°</td></tr><tr><td>A<sub>exch</sub></td><td>17 * 10<sup>-12</sup> J.m</td></tr><tr><td>grain bond.</td><td>-10%</td></tr><tr><td>α</td><td>3</td></tr></table>

Magnetic tunnel junctions frequently exhibit magnetic coupling between their ferromagnetic electrodes, and minimizing (or at least controlling) this coupling is essential for reliable device performance in practical applications. Unwanted coupling can lead to poorly defined antiparallel states, offsets in the transfer function of magnetic field sensors, and excessive power consumption. This coupling can originate from various sources, including interfacial roughness<sup>19,20</sup>, edge effects<sup>21</sup>, electronic interactions<sup>22,23</sup>, and magnetic texture<sup>24,25</sup>.

The modeling presented in this letter enables extrapolation of the magnetic coupling field originating from the magnetic texture induced by exchange bias, which influences the free layer of a magnetic tunnel junction. To achieve this, we extracted the magnetic field component parallel to the exchange bias direction at distances of 5, 10, and 15 nm from the simulated ferromagnetic layer. The corresponding field distributions are shown in Figure 5. As the distance decreases, the histograms exhibit a progressive shift away from the zero-field baseline. The data points ⊕ represent field values associated with the highest occurrence. In the inset of Figure 5, these values are shown as a function of distance. To estimate the coupling field in the range pertinent to magnetic tunnel junctions, we employed a previously established model incorporating magnetic periodic inhomogeneity effects<sup>25</sup>:
$$H = \frac{\pi^2}{\sqrt{2}} \left(\frac{h^2}{\lambda\lambda_F}\right) \mu_0 M_s \exp\left(-\frac{2\pi\sqrt{2d}}{\lambda}\right) \quad (1),$$

where $t_F$ denotes the thickness of the ferromagnetic layer, d the separation distance (flying height), $\lambda$ the period of the ripple texture and h is an effective parameter correlated to the thickness of the ferromagnetic layer. In the inset of Figure 5, the red line corresponds to a fit obtained using the equation (1). The results show good agreement, with a ripple periodicity of 64 nm, which is comparable to the grain size. Extrapolation yields ferromagnetic coupling field values in the range of 1.1 to 1.3 mT for distances between 2 and 1 nm, consistent with the typical order of magnitude observed experimentally in magnetic tunnel junctions.

<figure><img src="image_6.png" /><figcaption>Figure 5: Distribution of the magnetic field component parallel to the bias direction. Histograms of the field distribution were calculated for planes positioned at distances of 15, 10, and 5 nm from the simulated layer. Inset: Highest frequency fields vs. height. The red line represents a fit using equation (1).</figcaption></figure>

In this work, we combined macroscopic magnetometry with nanoscale NV-based magnetic imaging to investigate a magnetic texture induced by exchange-biased. Incorporating a granular anisotropy landscape into our micromagnetic simulations allows to achieve quantitative agreement with both the hard-axis VSM loops and the stray field maps obtained via NV center microscopy. This dual-scale approach underscores the system sensitivity to magnetic inhomogeneities.

Moreover, by analyzing the spatial distribution of the magnetic field component parallel to the bias direction, we extrapolated coupling field for nanometric separations. These findings suggest that magnetic texture induced by exchange bias can significantly contribute to interlayer coupling, with implications for device performance and design.

Looking ahead, future investigations may focus on the impact of annealing protocols on anisotropy dispersion, enabling controlled engineering of magnetic texture and improved performance of spintronic devices. Furthermore, the robustness of the micromagnetic simulations established in this letter should facilitate the exploration of thermally induced local magnetization fluctuations in the time domain. This could lead to a deeper understanding of

the magnetic-origin noise observed in magnetic tunnel junctions.

## SUPPORTING INFORMATION

S1. Example of the code used for the simulations

S2. Micromagnetic simulations varying the grain size

## ACKNOWLEDGMENTS

This work was supported partly by France 2030 government investment plan managed by the French National Research Agency under grant references Equipex e-DIAMANT ANR-21-ESRE-0031 and Initiative d'Excellence Lorraine (LUE) ANR-15-IDEX-04-LUE. L. Petitdemange and M. Caseiro respectively acknowledge the program Lorraine Université d'Excellence (LUE) and the PEPR SPIN-ADAGE ANR-22-EXSP-0006 for founding their Phds. Partial support also comes from ANR-21-CE50-0039 (ANR SpinElec).

## REFERENCES

(1) Peng, S. z.; Zhang, Y.; Wang, M. x.; Zhang, Y. g.; Zhao, W. Magnetic Tunnel Junctions for Spintronics: Principles and Applications. In *Wiley Encyclopedia of Electrical and Electronics Engineering*; John Wiley & Sons, Ltd, 2014; pp 1–16. https://doi.org/10.1002/047134608X.W8231.

(2) Maciel, N.; Marques, E.; Naviner, L.; Zhou, Y.; Cai, H. Magnetic Tunnel Junction Applications. *Sensors* **2020**, *20* (1), 121. https://doi.org/10.3390/s20010121.

(3) Zink, B. R.; Lv, Y.; Wang, J.-P. Review of Magnetic Tunnel Junctions for Stochastic Computing. *IEEE Journal on Exploratory Solid-State Computational Devices and Circuits* **2022**, *8* (2), 173–184. https://doi.org/10.1109/JXCDC.2022.3227062.

(4) Parkin, S. S. P.; Roche, K. P.; Samant, M. G.; Rice, P. M.; Beyers, R. B.; Scheuerlein, R. E.; O'Sullivan, E. J.; Brown, S. L.; Bucchigano, J.; Abraham, D. W.; Lu, Y.; Rooks, M.; Trouilloud, P. L.; Wanner, R. A.; Gallagher, W. J. Exchange-Biased Magnetic Tunnel Junctions and Application to Nonvolatile Magnetic Random Access Memory (Invited). *Journal of Applied Physics* **1999**, *85* (8), 5828–5833. https://doi.org/10.1063/1.369932.

(5) Lacour, D.; Jaffrès, H.; Nguyen Van Dau, F.; Petroff, F.; Vaurès, A.; Humbert, J. Field Sensing Using the Magnetoresistance of IrMn Exchange-Biased Tunnel Junctions. *J. Appl. Phys.* **2002**, *91* (7), 4655–4658. https://doi.org/10.1063/1.1450050.

(6) Negulescu, B.; Lacour, D.; Montaigne, F.; Gerken, A.; Paul, J.; Spetter, V.; Marien, J.; Duret, C.; Hehn, M. Wide Range and Tunable Linear Magnetic Tunnel Junction Sensor Using Two Exchange Pinned Electrodes. *Applied Physics Letters* **2009**, *95* (11), 112502. https://doi.org/10.1063/1.3226676.

(7) Wiśniowski, P.; Stobiecki, T.; Kanak, J.; Reiss, G.; Brückl, H. Influence of Buffer Layer Texture on Magnetic and Electrical Properties of IrMn Spin Valve Magnetic Tunnel Junctions. *Journal of Applied Physics* **2006**, *100* (1), 013906. https://doi.org/10.1063/1.2209180.

(8) Ali, M.; Marrows, C. H.; Hickey, B. J.; Offi, F.; Wang, J.; Chelaru, L. I.; Kotsugi, M.; Kuch, W. Suppression of Magnetization Ripple by Exchange Bias. *Phys. Rev. B* **2009**, *79* (6), 064415. https://doi.org/10.1103/PhysRevB.79.064415.

(9) De Haas, O.; Schäfer, R.; Schultz, L.; Barholz, K.-U.; Mattheis, R. Rotational Magnetization Processes in Exchange Biased Ni81Fe19/Fe50Mn50 Bilayers. *Journal of Magnetism and Magnetic Materials* **2003**, *260* (3), 380–385. https://doi.org/10.1016/S0304-8853(02)01344-6.

(10) Hoffmann, H. Quantitative Calculation of the Magnetic Ripple of Uniaxial Thin Permalloy Films. *Journal of Applied Physics* **1964**, *35* (6), 1790–1798. https://doi.org/10.1063/1.1713743.

(11) Cowan, A.; McNeill, K.; Janjua, M. B.; McVitie, S. Characterisation of Magnetisation Ripple Using Lorentz Microscopy: Effect of Ultra-Thin Ni79Fe21 Seed Layers on Magnetic Properties of Ni45Fe55. *Journal of Magnetism and Magnetic Materials* **2021**, *535*, 168094. https://doi.org/10.1016/j.jmmm.2021.168094.

(12) Yuan, L.; Jiang, J.; Di, Y.; Bie, S.; He, H. Micromagnetic Simulation of the Magnetic Dispersion Angle and Effective Damping Factor for the Single-Phase Soft Magnetic Films. *Journal of Magnetism and Magnetic Materials* **2008**, *320* (7), 1393–1397. https://doi.org/10.1016/j.jmmm.2007.11.025.

(13) Rondin, L.; Tetienne, J.-P.; Hingant, T.; Roch, J.-F.; Maletinsky, P.; Jacques, V. Magnetometry with Nitrogen-Vacancy Defects in Diamond. *Rep. Prog. Phys.* **2014**, *77* (5), 056503. https://doi.org/10.1088/0034-4885/77/5/056503.
(14) Geiskopf, S.; Igarashi, J.; Malinowski, G.; Lin, J.-X.; Gorchon, J.; Mangin, S.; Hohlfeld, J.; Lacour, D.; Hehn, M. Single-Shot All-Optical Magnetization Switching in in-Plane Magnetized Magnetic Tunnel Junction. Applied Physics Letters 2025, 126 (15), 152405.
https://doi.org/10.1063/5.0254042.

(15) Vansteenkiste, A.; Leliaert, J.; Dvornik, M.; Helsen, M.; Garcia-Sanchez, F.; Van Waeyenberge, B. The Design and Verification of MuMax3. AIP Advances 2014, 4 (10), 107133. https://doi.org/10.1063/1.4899186.

(16) Granular anisotropy landscapes are commonly observed in many ferromagnetic systems, and they can give rise to ripple textures. However, this is not the case for a 5 nm CoFeB ferromagnetic film. This alloy, widely employed in spintronic applications, is characterized by square M(H) loops and very low switching fields. Within this thickness range, and in the absence of a direct interface with an antiferromagnetic layer, it does not exhibit any magnetic ripple texture. See for instance: Lin, J.-X.; Le Guen, Y.; Hohlfeld, J.; Igarashi, J.; Remy, Q.; Gorchon, J.; Malinowski, G.; Mangin, S.; Hauet, T.; Hehn, M. Femtosecond-Laser-Induced Reversal in in-Plane-Magnetized Spin Valves. Phys. Rev. Appl. 2024, 22 (4), 044051.
https://doi.org/10.1103/PhysRevApplied.22.044051.

(17) Dean, J.; Kohn, A.; Kovács, A.; Zeltser, A.; Carey, M. J.; Hrkac, G.; Allwood, D. A.; Schrefl, T. The Formation Mechanism of 360° Domain Walls in Exchange-Biased Polycrystalline Ferromagnetic Films. Journal of Applied Physics 2011, 110 (7), 073901.
https://doi.org/10.1063/1.3642982.

(18) O'Shea, K. J.; Rode, K.; Kurt, H.; McGrouther, D.; MacLaren, D. A. Concentric 360° Domain Wall Nesting in Magnetic Tunnel Junction Films: A Lorentz TEM Study. J. Phys. D: Appl. Phys. 2015, 48 (5), 055001. https://doi.org/10.1088/0022-3727/48/5/055001.

(19) Schrag, B. D.; Anguelouch, A.; Ingvarsson, S.; Xiao, G.; Lu, Y.; Trouilloud, P. L.; Gupta, A.; Wanner, R. A.; Gallagher, W. J.; Rice, P. M.; Parkin, S. S. P. Néel "Orange-Peel" Coupling in Magnetic Tunneling Junction Devices. Applied Physics Letters 2000, 77 (15), 2373-2375.
https://doi.org/10.1063/1.1315633.

(20) Néel, L. Sur Un Nouveau Mode de Couplage Entre Les Aimantations de Deux Couches Minces Ferromagnétiques. Comptes Rendus Hebdomadaires Des Seances De L Academie Des Sciences 1962, 255 (15), 1676-1681.

(21) Anguelouch, A.; Schrag, B. D.; Xiao, G.; Lu, Y.; Trouilloud, P. L.; Wanner, R. A.; Gallagher, W. J.; Parkin, S. S. P. Two-Dimensional Magnetic Switching of Micron-Size Films in Magnetic Tunnel Junctions. Applied Physics Letters 2000, 76 (5), 622-624.
https://doi.org/10.1063/1.125838.

(22) Slonczewski, J. C. Conductance and Exchange Coupling of Two Ferromagnets Separated by a Tunneling Barrier. Phys. Rev. B 1989, 39 (10), 6995-7002. https://doi.org/10.1103/PhysRevB.39.6995.

(23) Faure-Vincent, J.; Tiusan, C.; Bellouard, C.; Popova, E.; Hehn, M.; Montaigne, F.; Schuhl, A. Interlayer Magnetic Coupling Interactions of Two Ferromagnetic Layers by Spin Polarized Tunneling. Phys. Rev. Lett. 2002, 89 (10), 107206.
https://doi.org/10.1103/PhysRevLett.89.107206.

(24) Dimopoulos, T.; Tiusan, C.; Henry, Y.; Da Costa, V.; Ounadjela, K.; Van Den Berg, H. A. M. Compensation of Magnetostatic Interactions in Magnetic Tunnel Junctions with Artificial Antiferromagnets. Journal of Magnetism and Magnetic Materials 2002, 242-245, 512-514.
https://doi.org/10.1016/S0304-8853(01)01088-5.

(25) Tiusan, C.; Hehn, M.; Ounadjela, K. Magnetic-Roughness-Induced Magnetostatic Interactions in Magnetic Tunnel Junctions. Eur. Phys. J. B 2002, 26 (4), 431-434. https://doi.org/10.1140/epjb/e20020110.

<figure><img src="image_7.png" /><figcaption>TOC Graphic</figcaption></figure>