Quantitative Visualization of Thermally Enhanced
Perpendicular Shape Anisotropy STT-MRAM
Nanopillars

Trevor P. Almeida, Alvaro Palomino, Steven Lequeux, Ricardo C. Sousa,
Olivier Fruchart, Ioan Lucian Prejbeanu, Bernard Diény, Aurélien
Masseboeuf, David Cooper

► To cite this version:

Trevor P. Almeida, Alvaro Palomino, Steven Lequeux, Ricardo C. Sousa, Olivier Fruchart, et al. Quantitative Visualization of Thermally Enhanced Perpendicular Shape Anisotropy STT-MRAM Nanopillars. Nano Letters, 2022, 22 (10), pp.4000. 10.1021/acs.nanolett.2c00597. hal-03553914v2

HAL Id: hal-03553914

https://hal.science/hal-03553914v2

Submitted on 23 May 2022

**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 Attribution 4.0 International License
1

2

Quantitative visualization of thermally-enhanced perpendicular shape anisotropy STT-MRAM nano-pillars

3

4

5

6

7

8

9

10

11

12

Abstract

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

Trevor P. Almeida<sup>1,2*</sup>, Steven Lequeux<sup>3</sup>, Alvaro Palomino<sup>3</sup>, Ricardo C. Sousa<sup>3</sup>, Olivier Fruchart<sup>3</sup>, Ioan Lucian Prejbeanu<sup>3</sup>, Bernard Dieny<sup>3</sup>, Aurélien Masseboeuf<sup>3</sup> and David Cooper<sup>1</sup>

<sup>1</sup>Univ. Grenoble Alpes, CEA, Leti, F-38000 Grenoble, France.

<sup>2</sup>SUPA, School of Physics and Astronomy, University of Glasgow, G12 8QQ, UK.

<sup>3</sup>Univ. Grenoble Alpes, CEA, CNRS, Grenoble INP, SPINTEC, 38000 Grenoble, France.

Perpendicular shape anisotropy (PSA) offers a practical solution to downscale spin-transfer torque Magnetic Random-Access Memory (STT-MRAM) beyond the sub-20 nm technology node whilst retaining thermal stability. However, our understanding of the thermomagnetic behavior of PSA-STT-MRAM is often indirect, relying on magnetoresistance measurements and micromagnetic modelling. Here, the magnetism of a NiFe PSA-STT-MRAM nano-pillar is investigated using off-axis electron holography, providing spatially resolved magnetic information as a function of temperature. Magnetic induction maps reveal the micromagnetic configuration of the NiFe storage layer (~ 60 nm high, ≤ 20 nm diameter), confirming the PSA induced by its 3:1 aspect ratio. *In-situ* heating demonstrates that the PSA of the storage layer is maintained up to at least 250 °C, and direct quantitative measurements reveal a moderate decrease of magnetic induction. Hence, this study shows explicitly that PSA provides significant stability in STT-MRAM applications that require reliable performance over a range of operating temperatures.

Keywords: Perpendicular shape anisotropy STT MRAM; nanomagnetism; off-axis electron holography; thermomagnetic stability

*Corresponding author:

Tel: +44 (0) 141 330 4712

Email: trevor.almeida@glasgow.ac.uk
1. Introduction

Magnetoresistive random-access memory (MRAM) is a type of non-volatile memory based on the storage of bits of information by magnetic cells with controllable polarity¹. The discovery of the spin-transfer torque (STT) effect has made MRAM industrially relevant, thanks to the ability to write cells with an electric current²⁻⁵. STT-MRAM can be easily integrated with CMOS technology⁶, has low energy consumption⁷, superior endurance⁷,⁸, and rather high areal density⁹. In practice, STT-MRAM involves the use of a magnetic tunnel junction (MTJ) comprising two perpendicularly-magnetized ferromagnetic plates (one magnetically-pinned reference layer and one switchable storage layer) separated by a thin insulating MgO tunnel barrier (1 – 1.5 nm thick). This design is called p-STT-MRAM, the perpendicular anisotropy resulting from interfacial electronic hybridization effects occurring at the interface between the magnetic electrodes and the oxide tunnel barrier¹⁰. MTJs provide a useful system of readable / writable ‘0’ or ‘1’ binary information, as its electrical resistance changes significantly when the layers are magnetized in parallel and antiparallel states. Increasing the areal bit density of p-STT-MRAM requires to reduce the in-plane size or diameter of the nano-patterned MTJ¹¹. However, below a characteristic magnetic length scale around 20nm, this comes with an excessive decrease of the thermal stability of the magnetic moment of the ultrathin storage layer. Perpendicular shape anisotropy (PSA) offers an innovative solution by increasing the storage layer thickness to larger than its diameter, so that its out-of-plane aspect ratio combined with large volume provides additional thermal stability¹²,¹³. PSA-STT-MRAM has been shown previously to indeed be highly thermally stable, making them a practical solution to downsize scalability of STT-MRAM at sub-20 nm technology nodes¹⁴,¹⁵. However, our knowledge of the thermal stability of these STT-MRAM nano-pillars is often indirect, relying on magnetoresistance measurements and micromagnetic modelling. In order to understand fully their thermomagnetic behavior, it is necessary to examine the effect of temperature directly. The advanced transmission electron microscopy (TEM) technique of off-axis electron holography allows imaging of magnetization within nano-scale materials, with high spatial resolution and sensitivity to induction field components transverse to the electron beam¹⁶. Combining electron holography with in-situ heating within the TEM has already allowed direct imaging of the thermal stability of nano-scale signal carriers and fields of magnetic minerals¹⁷⁻¹⁹, meteorites²⁰ and pre-patterned MTJ conducting pillars²¹.

In this paper, we use electron holography to image the micromagnetic configuration of an individual ≤ 20 nm diameter FeCoB / NiFe STT-MRAM nano-pillar and acquire quantitative
1

2

3

4

5

6

7

measurements of magnetic induction from the high-aspect-ratio FeCoB / NiFe composite free
layer. In addition, we experimentally demonstrate the influence of PSA on its thermal stability
through *in-situ* heating within the TEM to 250 °C. This study provides direct evidence of the
PSA exhibited by the high-aspect-ratio free layer, and its improved thermal stability compared
to standard p-STT-MRAM.

## 2. Experimental

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

An array of FeCoB / NiFe PSA-STT-MRAM nano-pillars was fabricated through sequential e-beam lithography, reactive ion etching and ion beam etching¹². The full stack of PSA MTJs has the following composition: SiO₂ / Pt (25 nm) / SAF / Ta (0.3 nm) / FeCoB (1.1 nm) / MgO (1.2 nm) / FeCoB (1.4 nm) / W (0.2 nm) / NiFe (60 nm) / Ta (1 nm) / Ru (3 nm) / Ta (150 nm), where the thick NiFe layer provides the PSA¹²,¹⁴. SAF stands for a synthetic antiferromagnet, providing a compensated-moment antiferromagnetically-pinned magnetic reference as the bottom layer. A protective layer of organic resin (~ 1 µm) was spin-coated onto the array prior to being inserted into a Thermo Fisher Strata 400S dual-beam focused ion beam (FIB) / secondary electron microscope (SEM) for TEM sample preparation. A protective W layer was deposited over the resin and trenches were FIB irradiated until a ~ 3 µm × ~ 20 µm lamella was prepared and transferred to Omniprobe copper lift-out grids, where it was thinned to a thickness of ~ 300 nm using conventional FIB methods. The protective resist layer was etched away using a plasma cleaner and the remaining W layer was broken off with the micromanipulator. High angle annular dark field (HAADF) scanning TEM (STEM) imaging was performed using a probe-Cs-corrected Thermo Fisher Titan TEM with an accelerating voltage of 200kV. Corresponding chemical analysis was provided by energy dispersive X-ray (EDX) spectroscopy using a Super-X EDX system whose geometry consists of four Bruker silicon drift detectors. A Thermo Fisher Titan TEM equipped with an image-Cs corrector and an electron biprism was used to perform off-axis electron holography. Electron holograms were acquired under field-free conditions in Lorentz mode on a Gatan OneView 4K camera. A voltage of 220 V was applied to the biprism, resulting in an interference fringe spacing of ~ 1.7 nm. Stacks of 8 electron holograms (each acquired for 4s) were aligned and then averaged using the Holoview software²² to improve the signal to noise ratio of the reconstructed phase images. The magnetization states of the nano-pillars were visualized through separation of the magnetic contribution to the phase shift from the mean inner potential (MIP), achieved by tilting to ± 40° and applying the strong field of the objective lens (< 1.5 T) to reverse the magnetic
1

2

3

4

5

6

7

8

9

10

### 3. Results

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

contribution²³. *In-situ* heating up to 250°C was performed using a Gatan heating holder under field-free magnetic conditions, allowing 30 minutes to stabilize from thermal drift at each temperature interval. The heating was repeated and the magnetic reversal was performed at each temperature interval to isolate the MIP, and subtracted from the first heating to reconstruct the thermomagnetic behavior of the nano-pillars¹⁸,¹⁹. For the construction of magnetic induction maps, the cosine of the magnetic contribution to the phase shift was amplified (× 150) to produce magnetic phase contours and arrows were added to show the direction of the projected induction.
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Overview of the morphology, chemical composition and structural properties of the **nano-pillar.** (a) HAADF STEM image of the nano-pillar; and (b) associated EDX chemical maps showing the elemental distribution of iron, nickel, ruthenium, tantalum and oxygen. (c) EDX chemical map highlighting the iron / nickel-rich center and oxygen-rich surface of the nano-pillar. (d,e) Precession electron diffraction acquired from the boxed region (red) in (c), showing the (d) amorphous surface; and (e) crystalline core. The colored scale bar denotes the normalized electron intensity between zero and maximum intensity. (f) Elemental line profile acquired along the red arrow in (c) and averaged vertically over ~ 15 nm, displaying the cross-section of normalized x-rays % for iron, nickel and oxygen content.</figcaption></figure>

Figure 2 presents phase information reconstructed from electron holography of the nano-pillar, including quantification of magnetic induction and associated magnetization. The electron hologram of Fig. 2a shows the morphology of the nano-pillar at the same magnification as the associated projected magnetic induction map (Fig. 2b), which clearly demonstrates the existence of a magnetic dipole within the nano-pillar. This is emphasized by superimposing the associated magnetic induction over the EDX chemical map (Fig. 2c), where the magnetic contours flow along the major axis of the NiFe section. A line profile of the magnetic phase contribution ($\phi_m$) acquired along the white arrow in Fig. 2c (averaged vertically over ~15 nm) is overlaid over the chemical profile from the same region (Fig. 2d). The magnetic phase shift $\Delta\phi_m$ in the pillar can be used to quantify the integrated in-plane magnetic induction related to the nano-pillar, where the minimum and maximum $\phi_m$ values [Fig. 2c, dotted vertical lines (pink)] coincide with the full width half maximum of the Ni / Fe chemical profiles. Extracting quantitative calculations of magnetization from such local observations must be handled with care as it displays integrated information (see Supplementary materials for details on the calculations summarized below). At first approximation, the nano-pillar can be treated as a
uniformly-magnetized infinite cylinder of radius $r$. The magnetic induction transverse to the
electron beam direction is considered to arise from magnetization only (neglecting dipolar
fields, i.e., stray field and internal demagnetizing field) and can be estimated with the
Aharonov-Bohm effect using a radius of ~ 8.6 nm (obtained from Fig. 2d). A first value of $\mu_0 M_s$
$= 0.82 \pm 0.06$ T is extracted with the standard deviation determined from the noise of free space.
To better quantify this important parameter, we can estimate the associated demagnetizing field
of such a structure with the $F_{ijk}$ functions from Hubert's formalism using a prism approach$^{24}$, at
the exact same location of the measurement of the integrated magnetic flux obtained with the
phase slope. We then obtain a better estimation of $\mu_0 M_s = 1.19 \pm 0.08$ T with the removal of
the integrated demagnetizing and stray field globally antiparallel to magnetization, which
lowered our first approximation. Subsequently, to overcome the geometrical approximation for
the integrated demagnetizing field estimation with a prismatic geometry, we performed a
tomographic reconstruction through inverse Abel transformation$^{25}$ to extract the magnetic flux
density in the core vicinity of the cylinder. The resulting value was finally adjusted with the
local estimation of demagnetizing field through $F_{ijk}$ functions, as the tomography method helps
to deconvolve the B field but not the internal $H_d$. Our final extraction leads to a value for the
spontaneous magnetization induction of the NiFe nano-pillar of $\mu_0 M_s = 1.14 \pm 0.01$ T.
Considering the geometric approximation for the pillar is only estimated at one position of the
structure, this value is substantially more precise and is in reasonable agreement with the
spontaneous induction for a Ni$_{81}$Fe$_{19}$ chemical composition, expected to reach 1.05 T$^{26}$. We
ascribe the difference to uncertainties related to the exact value of the composition of the alloy
the diameter of the PSA, and the sharpness of its outer surface. Due the small size of the nano-
pillar, the position along the nano-pillar axis of direct $\phi_m$ measurement can also have a marked
effect on the magnitude of the stray field, as shown in larger Co and Fe nanowires$^{27}$. Being
systematic, these errors are expected to have no impact on the thermomagnetic measurements
reported in the following section. More details in our analysis of this quantification are given
in the supplementary materials.

28

29

30

31
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Overview of the magnetic induction associated with the nano-pillar and its quantification. (a) Electron hologram of the nano-pillar; and (b) reconstructed magnetic contribution to the total phase, revealing the PSA along its major axis. (c) Combined EDX / magnetic induction map showing magnetic contours flowing along the major axis of the NiFe section. The contour spacing is 0.042 rad (cosine amplified by 150 times). (d) Line profile acquired along the white arrow in (c) and averaged vertically over ~ 15 nm around the mid-height of the PSA free layer, superimposing the cross-section of magnetic phase over the chemical profile.</figcaption></figure>

Figure 3 presents the thermomagnetic behavior of the nano-pillar during in-situ heating from room temperature to 250 °C. The initial combined EDX / magnetic induction map of Fig. 3a displays the nano-pillar at 20 °C, with the magnetization pointing from the bottom to the top of the NiFe free layer and confirming its PSA. The associated magnetic induction maps of Figs 3b-h display the same nano-pillar during heating from 100 °C to 250 °C at 25 °C intervals. It is evident that the NiFe section retains its upward direction of magnetization at all temperatures up to 250 °C. The thermomagnetic stability of the NiFe section in the nano-pillar is supported by Figure 4, which presents corresponding quantitative measurements of magnetic induction at each temperature interval. The $\Delta\phi_m$ was measured from the same area presented in Fig. 2c,d and $\vec{B}$ calculated using equation S2 (Supplementary information), which is proportional to magnetization. The average value of $\vec{B}$ is ~ 0.8 ± 0.06T and the trend-line exhibits a decrease of ~0.08T between 20 °C and 250 °C, which is in good agreement with a ~ 0.09T decrease over the same temperature range in bulk permalloy (Ni₈₀Fe₂₀)²⁸,²⁹. If heated to higher temperatures, the nano-pillar would be expected to follow the same bulk properties and become paramagnetic at a Curie temperature around ~ 575 °C²⁸,²⁹. As the contribution of the dipolar field to the measured induction field is proportional to magnetization for PSA, we expected that Fig.4 is representative of the thermal decay of magnetization in the PSA.
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Visualization of the thermomagnetic stability within the nano-pillar. (a-h) Combined EDX / magnetic induction maps showing the PSA in the NiFe section of the nano-pillar acquired at (a) 20 °C; or during *in-situ* heating at 25 °C intervals from (b) 100 °C to (h) 250 °C. The contour spacing is 0.042 rad for all the magnetic induction maps (cosine multiplied by 150 times) and the magnetization direction is shown using arrows.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Magnetic induction associated to the nano-pillar as a function of temperature. Calculated magnetic induction transverse to the electron beam using the direct measurement of magnetic contribution to the phase from the NiFe section shown in Figure 3 with temperature, i.e., including a contribution from the demagnetizing and stray fields globally opposite to magnetization in the pillar, from 20 °C to 250 °C.</figcaption></figure>
1 **4. Discussion**

2 The main reason to fabricate STT-MRAM nano-pillars with PSA is to stabilize and preserve
3 the magnetic configuration of the free FeCoB / NiFe composite layer in response to temperature
4 fluctuations during operation. It is evident from the *in-situ* heating TEM experiment that the
5 dipolar magnetic orientation along the major axis of the NiFe section (bottom to top) is retained
6 at all temperature intervals up to at least 250 °C. In addition, the associated direct measurements
7 of $\vec{B}$ (average ≈ 0.8T ± 0.06T) did not vary sufficiently to suggest a change in magnetic
8 orientation, nor magnetization. The slight decreasing trend in magnitude of $\vec{B}$ is attributed to an
9 expected reduction in spontaneous magnetization when heating towards the Curie
10 temperature³⁰, as would be observed in the same bulk material. As the shape-anisotropy energy
11 barrier of the nano-pillar scales linearly with $M_S^2$, this confirms that the energy barrier of
12 switching between parallel and anti-parallel states has not been exceeded up to at least 250 °C,
13 and the PSA has provided significant thermal stability compared to standard p-STT-MRAM
14 stacks based on ultrathin films¹²⁻¹⁵. In standard p-STT-MRAM, the spontaneous magnetization
15 may indeed decrease by a few tens of percent at 250°C due to enhanced fluctuations in low-
16 dimensions for the ultrathin films involved, and the energy barrier associated with
17 perpendicular anisotropy may decrease even more as it relies on interfacial magnetic
18 anisotropy, which suffers from enhanced thermal decay due to its two-dimensional nature³¹⁻³³.
19 Further, the maximum temperature of *in-situ* heating used (250 °C) far exceeds the operating
20 temperatures for a range of STT-MRAM device applications, including commercial (70 °C),
21 industrial (85 °C), automotive (125 °C) and military (150 °C)³⁴. It is also comparable to the
22 temperature of reflow soldering used to attach chips to a printed circuit board (260 °C)³⁵. This
23 thermal stability is crucial for many FLASH-replacement applications in which the program
24 code is loaded in the chip prior to reflow soldering.

25 In conclusion, this electron holography study has provided explicit evidence of the PSA in
26 ≤ 20 nm diameter p-STT-MRAM nano-pillar; previously only measured indirectly by
27 magnetoresistance measurements and micromagnetic modelling. The enhanced thermal
28 stability of PSA-STT-MRAM, compared with standard p-STT MRAM based on these films,
29 has been confirmed by both imaging and quantitative measurements from their magnetic
30 configuration during *in-situ* heating. This supports the use of PSA-STT-MRAM in a variety of
31 applications that require reliable performance over a range of operating temperatures.
32
33

32

33
## 5. Supporting Information

2 Dipolar field calculation (S1) and quantitative phase analysis (S2).

## 6. References

1. B. Dieny, et al., Opportunities and challenges for spintronics in microelectronics industry, *Nat. Electron.* 2020, **3**, 446-459.

2. S. Bhatti, et al., Spintronics based random access memory: a review, *Mater. Today.* 2017, **20**, 530-548.

3. S. Ikeda, et al., A perpendicular-anisotropy CoFeB-MgO magnetic tunnel junction, *Nat. Mater.*, 2010, **9**, 721.

4. A. D. Kent, Spintronics: Perpendicular all the way, *Nat. Mater.*, 2010, **9**, 699.

5. T. Liu, Y. Zhang, J. W. Cai and H. Y. Pan, Thermally robust Mo/CoFeB/MgO trilayers with strong perpendicular magnetic anisotropy, *Sci. Rep.*, 2015, **4**, 5895.

6. D. McGrath, Intel says FinFET-based embedded MRAM is production-ready. EE Times (20 February 2019); https://go.nature.com/3gQyWzf.

7. Apalkov, D., Dieny, B. & Slaughter, J. M. Magnetoresistive random access memory. *Proc. IEEE*, 2016, **104**, 1796-1830.

8. Khvalkovskiy, A. V. et al. Basic principles of STT-MRAM cell operation in memory arrays. *J. Phys. D.* 2013, **46**, 074001.

9. S.-W. Chung, T. Kishi, J. W. Park, M. Yoshikawa, K. S. Park, T. Nagase, K. Sunouchi, H. Kanaya, G. C. Kim, K. Noma, M. S. Lee, A. Yamamoto, K. M. Rho, K. Tsuchida, S. J. Chung, J. Y. Yi, H. S. Kim, Y. S. Chun, H. Oyamatsu and S. J. Hong, *Proceedings of the 2016 IEDM conference*, 2016, 27.1.

10. B. Dieny and M. Chshiev, Perpendicular magnetic anisotropy at transition metal/oxide interfaces and applications. *Rev. Mod. Phys.*, 2017, **89**, 025008.

11. V. D. Nguyen, P. Sabon, J. Chatterjee, L. Tille, P. Veloso Coelho, S. Auffret, R. Sousa, L. Prejbeanu, E. Gautier, L. Vila and B. Dieny, Novel approach for nano-patterning magnetic tunnel junctions stacks at narrow pitch: A route towards high density STT-MRAM applications, *2017 IEEE International Electron Devices Meeting (IEDM)*, 2017, DOI: 10.1109/IEDM.2017.8268517.

12. N. Perrissin, S. Lequeux, N. Strelkov, A. Chavent, L. Vila, L. D. Buda-Prejbeanu, S. Auffret, R. C. Sousa, I. L. Prejbeanu and B. Dieny, A highly thermally stable sub-20 nm magnetic random-access memory based on perpendicular shape anisotropy, *Nanoscale*, 2018, **10**, 12187.
1

2

13. K. Watanabe, B. Jinnai, S. Fukami, H. Sato and H. Ohno, Shape anisotropy revisited in single-digit nanometer magnetic tunnel junctions, *Nat. Commun.* 2018, **9**, 663.

3

4

5

6

14. N. Perrissin, N. Caçoilo, G. Gregoire, S. Lequeux, L. Tillie, N. Strelkov, A. Chavent, S. Auffret, L. D. Buda-Prejbeanu, R. C. Sousa, L. Vila, I. L. Prejbeanu and B. Dieny, Perpendicular shape anisotropy spin transfer torque magnetic random-access memory: towards sub-10 nm devices. *J. Phys. D: Appl. Phys.*, 2019, **52**, 505005.

7

8

9

10

15. S. Lequeux, N. Perrissin, G. Grégoire, L. Tillie, A. Chavent, N. Strelkov, L. Vila, L. D. Buda-Prejbeanu, S. Auffret, R. C. Sousa, I. L. Prejbeanu, E. Di Russo, E. Gautier, A. P. Conlan, D. Cooper and B. Dieny, Thermal robustness of magnetic tunnel junctions with perpendicular shape anisotropy, *Nanoscale*, 2020, **12**, 6378.

11

12

13

14

16. V. Boureau, M. Stano, J-L. Rouviére, J-C. Toussaint, O. Fruchart and D. Cooper, High-sensitivity mapping of magnetic induction fields with nanometer-scale resolution: comparison of off-axis electron holography and PDPC, *J. Phys. D: Appl. Phys.* 2021, **54**, 085001.

15

16

17

17. T. P. Almeida, T. Kasama, A. R. Muxworthy, W. Williams, and R. E. Dunin-Borkowski, Observing thermomagnetic stability of non-ideal magnetite particles: Good paleomagnetic recorders? *Geophys. Res. Lett.* 2014, **41**, 7041.

18

19

20

18. T. P. Almeida, A. R. Muxworthy, A. Kovács, W. Williams, P. D. Brown, and R. E. Dunin-Borkowski, Direct visualization of the thermomagnetic behavior of pseudo-single-domain magnetite particles, *Sci. Adv.* 2016, **2**, e1501801.

21

22

23

24

19. T. P. Almeida, A. R. Muxworthy, A. Kovács, W. Williams, L. Nagy, P. Ó Conbhuí, C. Frandsen, R. Supakulopas, and R. E. Dunin-Borkowski, Direct observation of the thermal demagnetization of a vortex structure held by a non-ideal magnetite recorder, *Geophys. Res. Lett.* 2016, **43**, 8426.

25

26

27

28

20. J. Shah, W. Williams, T. P. Almeida, L. Nagy, A. R. Muxworthy, A. Kovács, M. A. Valdez-Grijalva, K. Fabian, S. S. Russell, M. J. Genge and R. E. Dunin-Borkowski, The oldest magnetic record in our solar system identified using nanometric imaging and numerical modeling, *Nat. Commun.* 2018, **9**, 1173.

29

30

31

32

21. V. Boureau, V. D. Nguyen, A. Masseboeuf, A. Palomino, E. Gautier, J. Chatterjee, S. Lequeux, S. Auffret, L. Vila, R. Sousa, L. Prejbeanu, D. Cooper and B. Dieny, An electron holography study of perpendicular magnetic tunnel junctions nanostructured by deposition on pre-patterned conducting pillars, *Nanoscale*, 2020, **12**, 17312.
1

2

3

22. V. Boureau, R. McLeod, B. Mayall and D. Cooper, Off-axis electron holography combining summation of hologram series with double-exposure phase-shifting: Theory and application, *Ultramicroscopy*, 2018, **193**, 52-63.

4

5

6

7

23. T. P. Almeida, T. Kasama, A. R. Muxworthy, W. Williams, L. Nagy, T. W. Hansen, P. D. Brown and R. E. Dunin-Borkowski, Visualized effect of oxidation on magnetic recording fidelity in pseudo-single-domain magnetite particles, *Nat. Commun.* 2014, **5**, 5154.

8

9

24. A. Hubert and R. Schafer, *Magnetic Domains. The Analysis of Magnetic Microstructures*, Springer-Verlag, Berlin, Heidelberg, New York, 1998.

10

11

12

25. C. Phatak, L. de Knoop, F. Houdellier, C. Gatel, M. J. Hštch and A. Masseboeuf, Quantitative 3D electromagnetic field determination of 1D nanostructures from single projection, *Ultramicroscopy*, 2016, **164**, 24-30.

13

14

26. R. D. Tikhonov and A. A. Cheremisinov, Magnetization of Permalloy Films, *Russian Microelectronics*, 2017, **46 (2)**, 95-104.

15

16

17

27. K. Chai, Z. Li, W. Huang, G. Richter, R. Liu, B. Zou, J. Caron, A. Kovács, R. E. Dunin-Borkowski and J. Li, Magnetic quantification of single-crystalline Fe and Co nanowires via off-axis electron holography, J. Chem. Phys. 2020, 152, 114202.

18

19

20

28. A. B. Johnston, J. N. Chapman, B. Khamsehpour and C. D. W. Wilkinson, *In situ* studies of the properties of micrometre-sized magnetic elements by coherent Foucault imaging, *J. Phys. D: Appl. Phys.* 1996, **29**, 1419-1427.

21

29. R. M. Bozorth, 1964 Ferromagnetism (New York: Van Nostrand) p 112.

22

23

24

30. X. Zhang, Y. Lao, J. Sklenar, N. S. Bingham, J. T. Batley, J. D. Watts, C. Nisoli, C. Leighton and P. Schiffer, Understanding thermal annealing of artificial spin ice, *APL Mater.* 2019, **7**, 111112.

25

26

27

28

31. H. Sato, E. C. I. Enobio, M. Yamanouchi, S. Ikeda, S. Fukami, S. Kanai, F. Matsukura and H. Ohno, Properties of magnetic tunnel junctions with a MgO/CoFeB/Ta/CoFeB/MgO recording structure down to junction diameter of 11 nm, *Appl. Phys. Lett.*, 2014, **105**, 062403.

29

30

32. H. Sato, S. Ikeda and H. Ohno, Magnetic tunnel junctions with perpendicular easy axis at junction diameter of less than 20 nm, *Jpn. J. Appl. Phys.*, **2017**, 56, 0802A6.

31

32

33

33. L. Thomas, G. Jan, J. Zhu, H. Liu, Y.-J. Lee, S. Le, R.-Y. Tong, K. Pi, Y.-J. Wang, D. Shen, R. He, J. Haq, J. Teng, V. Lam, K. Huang, T. Zhong, T. Torng and P.-K. Wang, Perpendicular spin transfer torque magnetic random access memories with high spin
1

torque efficiency and thermal stability for embedded applications (invited), *J. Appl.*

2

*Phys.*, 2014, **115**, 172615.

3

34. J. M. Iwata-Harms, G. Jan, H. Liu, S. Serrano-Guisan, J. Zhu, L. Thomas, R-Y. Tong, V. Sundar and P-K. Wang, High-temperature thermal stability driven by magnetization dilution in CoFeB free layers for spin-transfer torque magnetic random access memory, *Sci. Rep.* 2018, **8**, 14409.

5

6

7

35. Meng-Chun Shih et al., "Reliability study of perpendicular STT-MRAM as emerging embedded memory qualified for reflow soldering at 260°C," *2016 IEEE Symposium on VLSI Technology*, 2016, pp. 1-2, doi: 10.1109/VLSIT.2016.7573411.

8

9

10

## Funding

11

CEA-Leti is a Carnot Institute. This work was supported by the French ANR via Carnot funding and the European Research Council (ERC MAGICAL, 669204).

12

13