United States

Magnetic skyrmions [1] are topologically stabilized, magnetic quasi-particles, which exhibit interesting physical phenomena and are also potential candidates for efficient neuromorphic computation schemes. On the micro-meter scale, they are detectable with Kerr-microscopy, using the magneto-optical Kerr-effect. However, depending on the material stack, temperature, the growth procedure and other influences, those measurement might suffer from noise, low-contrast, intensity gradients or defects, therefore manual data treatment is normally necessary to generate data that can be evaluated easily.
Our approach is to use a convolutional neural network, based on the U-Net [2], to detect the position and shape of the skyrmions in our measurement data. This work was motivated by reports that machine learning has been successfully applied to (micro-)magnetic problems [3]. We are tuning the U-Net with various techniques to optimize the predictions and identify skyrmions and defects fast and with high reliability. A well-trained neural network is shown to minimize manual treatment of data. The approach is also easily extendable to other magnetic structures.&lt;br&gt;

**References:**&lt;br&gt;

[1] Everschor-Sitte et al., Journal of Applied Physics 124, 240901 (2018)&lt;br&gt;
[2] Ronneberger et al., MICCAI 2015. Lecture Notes in Computer Science, vol 9351. Springer, Cham. (2015)&lt;br&gt;
[3] Alexander Kovacs et al., Journal of Magnetism and Magnetic Materials 491, 165548 (2019)&lt;br&gt;

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MMM 2022

Skyrmion detection with U Net

Magnetic skyrmions [1] are topologically stabilized, magnetic quasi-particles, which exhibit interesting physical phenomena and are also potential candidates for efficient neuromorphic computation schemes. On the micro-meter scale, they are detectable with Kerr-microscopy, using the magneto-optical Kerr-effect. However, depending on the material stack, temperature, the growth procedure and other influences, those measurement might suffer from noise, low-contrast, intensity gradients or defects, therefore manual data treatment is normally necessary to generate data that can be evaluated easily.
Our approach is to use a convolutional neural network, based on the U-Net [2], to detect the position and shape of the skyrmions in our measurement data. This work was motivated by reports that machine learning has been successfully applied to (micro-)magnetic problems [3]. We are tuning the U-Net with various techniques to optimize the predictions and identify skyrmions and defects fast and with high reliability. A well-trained neural network is shown to minimize manual treatment of data. The approach is also easily extendable to other magnetic structures. 

**References:** 

[1] Everschor-Sitte et al., Journal of Applied Physics 124, 240901 (2018) 
[2] Ronneberger et al., MICCAI 2015. Lecture Notes in Computer Science, vol 9351. Springer, Cham. (2015) 
[3] Alexander Kovacs et al., Journal of Magnetism and Magnetic Materials 491, 165548 (2019) 

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technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a tutorial, and several special sessions. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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Quantum computation and cryogenic electronics have gained considerable importance in this last decade. Currently, a bottleneck for advancing it further is the power consumption of conventional electronic components, which is not adapted to the needs of cryogenic circuits. Perpendicular Spin-Transfer-Torque Magnetic Random Access Memory (p-STT-MRAM) has potential to comply with cryo-electronics requirements of low power. Previous works done on cryogenic temperature switching of STT-MRAM have assessed its characteristics and the Write Error Rate for different device diameters [1]. The conditions to write an STT-MRAM are promising (0.7V at 9K with 200ns pulses, corresponding to a writing energy of 11.2 pJ) [2]. However, the full integration of MRAMs into quantum processors demands a much lower operating voltage (below 0.1V).Therefore, we focused our research on engineering MTJs for low anisotropy to reduce the critical switching voltage VC and consequentially the write energy per bit Ebit. Our approach consists in changing the interface of the storage layer by adding an insertion layer as in Mg+Ox/X/FeCoB/W/Y/W, where X can be wedges of Mg, FeCoB and Y is permalloy (Py). This type of device can show high thermal stability at cryogenic temperatures (i.e.4K), while having no retention at 300K. This strategy allows the reduction of the storage layer anisotropy by at least one order of magnitude.
Figure 1 shows a current pulse phase diagram of a junction with Mg insertion. Upon changing the operation temperature the write current density JC for junctions with different insertion layers is varying as reported in Figure 2. Device diameter, composition and thickness play an important role in modulating the anisotropy. Tuning these parameters it is possible to bring the switching currents close to 20µA for a 30nm diameter device at 10K (red curve), corresponding to Ebit=1.2pJ. This can be further improved by modulating the required current density with composition as shown in the figure 2. 
**References** [1] L. Rehm, G. Wolf, B. Kardasz, M. Pinarbasi, and A. D. Kent, "Sub-nanosecond spin-torque switching of perpendicular magnetic tunnel junction nanopillars at cryogenic temperatures", Appl. Phys. Lett. Vol. 115, p.182404 (2019).
[2] Lili Lang, Yujie Jiang, Fei Lu, Cailu Wang, et al, "A low temperature functioning CoFeB/MgO-based perpendicular magnetic tunnel junction for cryogenic nonvolatile random access memory", Appl. Phys. Lett. Vol. 116, p.022409 (2020) 

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Control of Interface Anisotropy for Spin Transfer Torque in Perpendicular Magnetic Tunnel Junctions for Cryogenic Temperature Operation

Magnetic tunnel junctions are a key component in non-volatile memory technologies such as magnetic random access memory (MRAM). Typical two-terminal MRAM write speeds have been limited to the nanosecond regime. Currently, sub-nanosecond switching has been achieved in three-terminal structures relying on spin-orbit torque switching mechanisms. However, using this mechanism increases the footprint and number of transistors needed, ultimately limiting scalability. Here, we demonstrate that it is possible to achieve reliable sub-nanosecond switching in a two-terminal design by utilizing a Double Spin Torque magnetic tunnel junction. In this design, a second reference layer is added to the standard two terminal MTJ. Using a non-magnetic spacer, we are able to do so without sacrificing magnetoresistance like in double MTJ designs. Figure 1 shows the error rates for a single device, plotted using a normal quantile scale (using the absolute value of the standard deviation from the fifty-percent switching current density), measured at -40 C, 25 C, and 85 C, for pulse widths from 225 ps to 10 ns. We demonstrate 100% successful switching for 1e6 write attempts using 225 ps wide write pulses, over the temperature range -40 C to 85 C. Further, we show reliable sub-nanosecond switching across a few hundred devices. 1e10 write-endurance testing on a handful of devices also demonstrates that reliability can be achieved as well. Lastly, we compare our Double Spin Torque magnetic tunnel junction to three-terminal spin-orbit torque MRAM. We find that with our design, a 3-10X reduction in write power consumption can be achieved. 
**References**
 
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Reliable Sub nanosecond MRAM with Double Spin

Magnetic skyrmions are recently attracting attention from the viewpoint of application to next-generation spintronics devices such as ultra-low-power Brownian computers. Skyrmions are expected to function as information carriers in those devices because of their unique features such as Brownian motion at near room temperature, small size, easy detection and easy control (1-4). In order to realize such devices, electrical gating and amplification of the skyrmion signal are indispensable. The primary mechanism of the voltage control technique for skyrmions is the voltage-controlled-magnetic-anisotropy effect (VCMA effect) (5-6). In the previous studies using the VCMA effect, for example, modulation of the diffusion coefficient (2) and creation/annihilation of the skyrmions (3) have been demonstrated. However, “skyrmion gates/transistors” have not been realized experimentally yet. Obstacles might be that the conditions creating skyrmions are easily affected by the local stress introduced from the gate fabrication. Furthermore, a non-negligible energy barrier that appears at the edge of the gate electrode, traps the skyrmions there. In this talk, we will present our attempts to realize a device in which skyrmions are not trapped at the edge of the gate electrode.
A skyrmion film consisting of Ta|Co16Fe64B20|Ta|MgO|SiO2 was deposited on a thermally oxidized silicon substrate by the magnetron sputtering. In order to apply voltage to the magnetic layer, thin Ru gate electrodes with a thickness of 2 [nm] were deposited onto this film, and the MOKE microscope observed the motion of skyrmions. Narrow gate electrodes trapped skyrmion at the edge of the electrodes even though no voltage was applied. The wider Ru electrode enables a free passage of the skyrmions through the edge. The result is one of the fundamentals of realizing the skyrmion transistors. 

Acknowledgement: The authors acknowledge to Ono laboratory in Kyoto Univ. This research and development work was supported by ULVAC, Inc., JST CREST Grant number JPMJCR20C1, Japan and JSPS KAKENHI Grant Number JP20H05666. 

**References:** 
(1) J. Zázvorka et al., Nat. Nanotechnol., 14, 658–661 (2019), 
(2) T. Nozaki et al., Appl. Phys. Lett., 114, 012402 (2019), 
(3) M. Schott et al., Nano Letters., 17, 3006-3012 (2017), 
(4) B. W. Walker et al., Appl. Phys. Lett., 118, 192404 (2021), 
(5) M. Weisheit et al., Science 315, 349 (2007), 
(6) T. Maruyama et al., Nature Nanotech., 4, 158 (2009), 
(7) Y. Jibiki et al., Appl. Phys. Lett., 117, 082402 (2020)

Control of the skyrmion passage by a gate electrode

FeRh is an archetypal system for the investigation of ultrafast behaviour in coupled transitions due to its meta-magnetic phase transition occurring around 380 K [1]. In this coupled phase transition, the electronic structure transforms lowering the resistivity by ≈ 33%, the lattice expands isotropically with a volumetric expansion of ≈ 1%, and the magnetic order changes from a G-type antiferromagnet (AF) to a ferromagnet (FM) [1], [2]. Previous x-ray diffraction (XRD) studies have indicated that the lattice expands with first-order dynamics within 10-30 ps [3], with long-range AF order throughout the transition [4]. The sub-ps capabilities of the SACLA free-electron laser allowed for investigation of the ultrafast behaviour of the FeRh lattice upon laser excitation. This shows new dynamics at high fluences which were compared to the quasi-static behaviour of the Bragg peaks as measured using heated XRD. We describe the lattice temperature (see Fig. 1a) and expansion as a function of pump-probe delay. We have observed a perturbation to the expected dynamics above fluences of 5 mJ cm-2 where the lattice initially contracts before finally expanding as predicted. We demonstrate that a model (see Fig. 1b) using a transient lattice state [5] can explain the observed behaviour. Our model suggests that the transient state is paramagnetic, reached by a subset of the phonon bands which are preferentially coupled to the electronic system [6]. A complete description of the FeRh structural dynamics requires consideration of coupling strength variation across the phonon frequencies. 
**References** [1] J. S. Kouvel and C. C. Hartelius, J. Appl. Phys., 33, 1343, (1962).
[2] J. S. Kouvel, J. Appl. Phys., 37, 1257–1258, (1966).
[3] S. O. Mariager, F. Pressacco, G. Ingold, et al., Phys. Rev. Lett., 108, 087201, (2012).
[4] M. Grimes, N. Gurung, H. Ueda, et al., AIP Adv., 12, 035048, (2022).
[5] B. Mansart, M. J. G. Cottet, G. F. Mancini, et al., Phys. Rev. B, 88, 054507, (2013).
[6] M. Grimes, H. Ueda, D. Ozerov, et al., Sci. Rep., 12, 8584 (2022) 
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Determination of sub ps lattice dynamics in FeRh thin films.

Experimental and computational studies on the stress-dependent magnetic property of silicon steel are on-going. A physical magnetization model, an energy-based
multiscale magnetization model called multi-domain particle model (MDPM) [1], was developed, which successfully predicted the stress-dependent properties of silicon steel without using
measured stress-dependent data.
To avoid measurement under arbitrary combination of stress and magnetization directions, several stress models have been developed. This study examines two of them by comparing with
the MDPM. One is the equivalent stress (ES) theory [2] and the other is the stress decomposition (SD) method [3]. The latter assumes that the stress effect can be decomposed into its
principal directions.
A rotational single sheet tester applied a compressive stress to a non-oriented silicon steel sheet in the rolling direction (RD, φ=0). A magnetic field was applied along φ = 0 or π/4. Fig. 1
shows the measured stress dependence of hysteresis loss wx
in the RD when the amplitude of Bx
is 0.5, 0.7 and 1.0 T, where By has only a small effect on the stress dependence of wx
. It
supports the assumption of stress decomposition.
BH loops under the excitation angle of π/4 were simulated using the MDPM, where the directions of stress and applied magnetic field are denoted by φσ
and φH. Fig. 2 shows BH loops as
below: [reference, blue lines] φH=π/4 and φσ=0 with σ = −40, −80 MPa, [ES theory, green lines] φH=φσ=π/4 with σ = −10, −20 MPa based on the ES theory, [SD, brown lines] synthesized
loops of φH=φσ=0 with σ = −40, −80 MPa and φH=φσ=π/2 with σ = 0, and [modified SD, red lines] synthesized loops of φH=φσ=0 with σ = −40, −80 MPa and φH=φσ=π/2 with σ = +40,
+80 MPa. The ES theory roughly predicts the stress dependent loops along φ = π/4, but fails to predict decomposed loops along φ = 0, π/2. The SD fails to reconstruct loops along φ=π/2
because a compressive stress along φ=0 acts as a tensile stress along φ=π/2. The modified SD roughly predicts the stress dependent loops in all the directions by giving tensile stresses
along φ=π/2. 
**References** [1] T. Matsuo, Y. Takahashi, K. Fujiwara, J. Magn. Magn. Mater., vol. 499, 166303, 2020.
[2] M. Rekik, L. Daniel, O. Hubert, IEEE Trans. Magn., vol. 50, 2001604, 2014.
[3] M. Nakano, et. al, IEEJ Trans. Ind. Appl., vol. 129, pp. 1060–1067, 2009. 

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Comparison of measured loss increase Δwx with φH = 0, π/4 and φσ = 0.
 

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Simulated BH loops along (a) φ = π/4, (b) φ = 0, and (c) φ = π/2.

Computational Validation of Method for Decomposition of Mechanical Stress Effect on Magnetic Property of Silicon Steel Sheet

As microwave-assisted magnetic recording (MAMR) is being employed in commercial hard disk drives, technology challenges remain [1][2]. A key one of them is the need for relatively strong ac field amplitude. Here, we present a novel scheme to substantially enhance the efficiency of the ac field. For a single domain magnetic particle of uniaxial anisotropy, the anisotropy energy is Ean=Ksin2θ where θ is the angle between the magnetic moment of the particle and the easy axis and K is the anisotropy energy density. The effective magnetic field due to this anisotropy is Han=HkcosΘ where Hk = 2K/Ms . Since the anisotropy field is a cosine function of the magnetization angle, the resonance frequency varies during a magnetization reversal. Hence, if the applied ac field frequency can match this resonance frequency variation during a magnetization reversal, the efficiency of the ac field should be significantly enhanced. Figure 1 shows the calculation for a single domain particle of Hk=30kOe. A magnetic field with a 2o angle w.r.t. the easy axis and duration of 1ns is applied opposite to the initial magnetization The ac field is a rotating perpendicular to the easy axis with a during of 1ns. The ac field frequency is either a constant (black), linearly decreases to zero, or follows the function of ω0cos(0.86t/τ) where τ=1ns. The horizontal axis is the initial ac field frequency. The ac field amplitude is set as 1% of the anisotropy field at 300 Oe. In the case of the cosine-varying frequency ac field, the switching field reduction is more than 75% Hk, at 6kOe. The substantially enhanced switching field reduction shows the efficiency gain by having ac field frequency following the resonance frequency reduction during the magnetization reversal. Figure 2 shows the switching field of a particle of Hk=25kOe and the ac field frequency is the cosine-varying case. When the ac field amplitude exceeds 350 Oe, the switching can be achieved without the reversal field applied. 
**References** 
[1] J.-G. Zhu, X. Zhu, and Y. Tang, “Microwave assisted magnetic recording,” IEEE Trans. Magn., vol. 44, no. 1, pp. 125–131, Jan. 2008. 
[2] Akihiko Takeo, et al, "Extended Concept of MAMR and its Performance and Reliability," Paper C1, TMRC 2020, August 2020. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/e05b39ad4289c136f43aa718eda6f9c9.png) 
Fig. 1. Switching field vs the initial frequency of ac fields with the frequency being constant (black), linearly decreasing (blue), or cosine-varying (red). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/ab59ce146174a0a2902158a7d364dcb7.png) 
Fig. 2. Switching field vs initial ac field frequency for a cosine-varying frequency rotating ac field.

Efficiency Enhanced Magnetic Resonance Switching of Single Domain Particle with Uniaxial Anisotropy

Arrays of magnetic nanowires (NWs) are an attractive platform with tremendous potential for developing novel magnetic applications, e.g., next-generation information technologies or sensors [1]. The synthesis of NWs by electrochemistry shows multiple degrees of freedom allowing for tailoring the composition, crystallographic structure and, consequently, magnetic properties [2,3]. Herein, FeNi NWs were grown by electrodeposition into anodized aluminum oxide (AAO) membranes (Fig. 1a). The broad range of electrolytes and voltages used, allowed us to study the anomalous FeNi co-deposition by a compositional analysis, being explained within a modified Bocris-Drazic-Despic (BDD) model [4]. X-ray diffraction patterns showed a change from bcc crystallographic structure for Fe-rich NWs to fcc structure at mid and low Fe content, with biphasic bcc-fcc phase for equiatomic NWs. Tuning the synthesis conditions led to FeNi NWs with a range of magnetic hardness, observing an increase in coercivity (from 0.2 kOe to 1 kOe) for a decreased Fe content (Fig. 1b). Coercivity angular measurements showed that the magnetization reversal is dominated by transverse domain wall reversal and indicated a decrease in magnetostatic interactions among NWs as the source of the coercivity rise. First-order reversal curves (FORCs) highlighted the limited role of the magnetic interactions in the arrays, except for Fe0.80Ni0.20 NWs which showed a FORC diagram for magnetically interacting NWs (Fig. 1c). This study shows how the magnetic properties of the NWs can be tailored through an optimized control of the synthesis conditions and adapted to the requirements of the final application. Fig. 1: (a) SEM image of NWs grown inside the AAO template, (b) Hysteresis loops for FeNi NWs with different compositions, and (c) FORC diagram for Fe0.80Ni0.20 NWs. Acknowledgements Authors acknowledge support from EU M-ERA.NET and MICINN through COSMAG (PCI2020-112143) and NEXUS (PID2020-11521RB-C21). A.J.C.-H. and E.M.P. acknowledge support from "La Caixaâ€ Foundation (ID 100010434) through the Doctoral INPhINIT Incoming program (LCF/BQ/DI20/1178002) and AEI (JdC-I program, IJC2020-043011-I/MCIN/AEI/10.13039/501100011033) and EU by NextGenerationEU/PRTR, respectively.

Analysis of the Magnetic Interactions in FeNi Nanowire Arrays through FORC and Angular Coercivity Measurements

The need to measure high-frequency magnetic permeability has increased due to the 5th generation mobile communication system. We developed a microstrip line-type
probe and demonstrated comprehensive bandwidth permeability measurement up to 67 GHz [1]. For the permeability measurement of the thick magnetic sample, the demagnetizing effect
caused the measurement error and the shift of the ferromagnetic resonance (FMR) [2-3]. In this study, a microstrip conductor with slits has been developed to enhance the current
uniformity and reduce the demagnetizing effect in the thick magnetic material, as shown in Fig. 1 (a). This in-plane excitation decreased the demagnetizing effect. Fig. 1(b) shows the
photograph of the microstrip line type probe with slits. The probe consists of a microstrip conductor (1.3 mm in total width) on a glass substrate and a ground plane. The 15 μm wide copper
conductors (2 μm in thickness) and 15 μm wide gap were fabricated by lift-off process and rf sputtering. Also, the SMA connectors were connected with both input and output terminals.
First, S21 is calibrated by applying a strong DC field (2 T) in the vertical direction of the high-frequency field to saturate the sample. Secondly, S21 is measured without a strong DC field.
The complex permeability was optimized by the complex impedance and FEM analysis [2]. Fig. 2 shows the relative permeability of the NiZn ferrite sheet (3 mm x 1 mm, 100 μm thick).
Measured permeability agreed well with the value of the Nicolson-Ross-Weir method [4]. The measurement point was 201 from 0.1 GHz to 20 GHz. 96% of the whole real part was within
±15%, and 92% of the entire imaginary part was within ±15%. We have demonstrated that this microstrip line type probe with slits can accurately evaluate thick magnetic material because
the uniform current inside the microstrip conductor prevents the measurement error caused by the demagnetizing effect. 

**References:** 

[1]S. Yabukami et. al., IEEE Transactions on Magnetics, Vol. 57, No. 2, 6100405 (2021). 
[2]S. Yabukami et al., IEEE Transactions on Magnetics, vol. 58, No. 2, 6100305 (2022). 
[3]K. Takagi et. al., Journal of Magnetic of Japan, vol. 46 (2022, in press). 
[4]A. M. Nicolson et. al., Transactions on Instrumentation and Measurement, vol. 19, no. 4, pp. 377-382 (1970). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/cefd07059a335bcf9db54bfe87161218.png)

Thin Film Microstrip Line Type Probe with Slits and Permeability Measurement of Thick Magnetic Material

In the fields of magnetism and spintronics, magnetic multilayers continue to thrive as pivotal structures to functionalize magnetic interactions, including the interfacial Dzyaloshinskii-Moriya interaction (DMI), and to engineer complex non-trivial spin textures [1-3]. However, previous research has focused almost exclusively on 2D structures. The challenge in studying 3D textures is in obtaining the necessary spatial resolution and sensitivity to resolve them. Here we show that this challenge can be met by reference-aided coherent diffractive x-ray imaging combining the robust Fourier Transform Holography with phase retrieval algorithms [4,5]. Based on this amplified wide-angle scattering, we achieve 5 nm spatial resolution for spin textures in Pt/Co/Cu magnetic multilayers, which allows us to clearly resolve fine domain walls (Fig.1c). Surprisingly, while conventional low-resolution images only show the well-known stripe domain state characteristic of such multilayers, our high-resolution images additionally reveal several small, mostly circular features of much weaker contrast (Fig. 1a,b), indicating a reduced net magnetization in the out-of-plane direction. Interestingly, while these features are clearly magnetic in nature and interact with the domain walls, they do not annihilate at the largest fields available in our system (220 mT). We associate the features to a localized increased surface roughness, leading to a local loss of perpendicular magnetic anisotropy promoting in-plane spin alignment and of 3D magnetic textures.

Revealing 3D Magnetic Textures in [Pt/Co/Cu]15 Multilayers by Coherent X ray Imaging with 5 nm Resolution

The frustrated interactions in nanomagnetic arrays can lead to the emergence of complex behaviour. Here we consider nanomagnets with dimensions on the crossover from single ferromagnetic domain (macrospin) and vortex states [1-3], in both ordered and disordered array geometries. Magnetic force microscopy reveals that there is a ratchet-like transformation of macrospins into vortices, during minor loop magnetic reversals. Simulations show that interactions with neighbouring magnets play an important role, giving cooperative growth of macrospin and vortex chains. This gradual evolution of linkages is neuromorphic in character, and interesting for both neurally-inspired computation [1] and self-assembly of magnonic circuits[3]. 

**References:** 

[1]Gartside, Jack C., et al. "Reconfigurable Training and Reservoir Computing via Spin-Wave Fingerprinting in an Artificial Spin-Vortex Ice." Nature Nanotechnology (2022)
[2]Gartside, Jack C., et al. "Reconfigurable magnonic mode-hybridisation and spectral control in a bicomponent artificial spin ice." Nature Communications 12.1 (2021): 1-9.
[3]Stenning, Kilian D., et al. "Magnonic bending, phase shifting and interferometry in a 2d reconfigurable nanodisk crystal." ACS nano 15.1 (2020): 674-685.

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Control of Interface Anisotropy for Spin Transfer Torque in Perpendicular Magnetic Tunnel Junctions for Cryogenic Temperature Operation

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