United States

We report on the study of the cycloidal antiferromagnetic state in bulk single crystals of the multiferroic bismuth ferrite using a combination of real-space and reciprocal magnetic imaging techniques [1]. We first discuss the origin of the magnetic stray field allowing us to image the cycloidal modulation of the antiferromagnetic state. This stray field is produced by the small uncompensated moment arising from the spin density wave which is locked to the cycloid [2]. We then use scanning NV center magnetometry to image the magnetic texture, with additional resonant X-ray diffraction measurements to obtain a larger scale insight. We observe the unexpected coexistence inside a single ferroelectric domain of magnetic domains hosting different cycloid wavevectors. We show that the direction of these wavevectors is not strictly locked to the preferred crystallographic axes as continuous rotations bridge different wavevectors. Making profit of the nanoscale spatial resolution of scanning NV-center magnetometry, we show that topological defects form at the junction between the magnetic domains. These defects are identical to those found in a broad variety of lamellar physical systems with rotational symmetries (liquid crystals, magnetic helix [3], ferromagnetic garnets, copolymers, etc.). The presence of these objects in such a multiferroic antiferromagnet offers new opportunities in terms of robustness and electrical control towards their use in spintronic devices.&lt;br&gt;

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

[1] Finco et al, Phys. Rev. Lett. 128, 187201 (2022)
[2] Ramazanoglu et al, Phys. Rev. Lett. 107, 207206 (2011)
[3] Schönherr et al, Nat. Phys. 14, 465 (2018)


MMM 2022

Topological Defects in a multiferroic Antiferromagnet

We report on the study of the cycloidal antiferromagnetic state in bulk single crystals of the multiferroic bismuth ferrite using a combination of real-space and reciprocal magnetic imaging techniques [1]. We first discuss the origin of the magnetic stray field allowing us to image the cycloidal modulation of the antiferromagnetic state. This stray field is produced by the small uncompensated moment arising from the spin density wave which is locked to the cycloid [2]. We then use scanning NV center magnetometry to image the magnetic texture, with additional resonant X-ray diffraction measurements to obtain a larger scale insight. We observe the unexpected coexistence inside a single ferroelectric domain of magnetic domains hosting different cycloid wavevectors. We show that the direction of these wavevectors is not strictly locked to the preferred crystallographic axes as continuous rotations bridge different wavevectors. Making profit of the nanoscale spatial resolution of scanning NV-center magnetometry, we show that topological defects form at the junction between the magnetic domains. These defects are identical to those found in a broad variety of lamellar physical systems with rotational symmetries (liquid crystals, magnetic helix [3], ferromagnetic garnets, copolymers, etc.). The presence of these objects in such a multiferroic antiferromagnet offers new opportunities in terms of robustness and electrical control towards their use in spintronic devices. 

**References:** 

[1] Finco et al, Phys. Rev. Lett. 128, 187201 (2022)
[2] Ramazanoglu et al, Phys. Rev. Lett. 107, 207206 (2011)
[3] Schönherr et al, Nat. Phys. 14, 465 (2018)

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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Implementation of spin transfer torque magneto-resistive random access memory (STT-MRAM) in memory chips requires that the write margin of the MRAM cell △Vwr, defined as the difference between breakdown voltage Vbd and write voltage Vwr for the specified endurance, write error rate and write speed, is sufficiently large in order to accommodate resistance variations arising from external chip circuitry (transistors, metal lines etc). Optimization of MRAM cell design and process as well as MRAM materials development aims at accomplishing these by either reducing Vwr, enhancing Vbd, or both [1]. In this talk we will show that △Vwr can be increased by optimizing the MgO cap layer that is already present in a perpendicular MRAM cell, whose original intended function has been to increase perpendicular magnetic anisotropy energy of the free storage layer (FL) by adding additional Fe/MgO interface, and thus improve the MRAM retention [2]. By increasing the thickness of the MgO cap layer to make its resistance-area product RA close to that of the main MgO barrier, we show that △Vwr can be increased substantially for the given write speed and endurance, without affecting thermal stability of the cell in a significant way. For example, for MRAM cells with diameters 50 - 60 nm we show that Vwr at 50% switching probability for 50 ns pulse width increases by about 0.28 V for thick cap (see Fig. 1(a)) while Vbd obtained by endurance measurements under bipolar stress at the same pulse width increases by almost 0.5 V, resulting in △Vwr improvement of approximately 0.2 V. We will discuss physical mechanisms underlying this finding and its technological importance. 
**References** [1] D. Apalkov et al., Proc. of IEEE 104, 1796 (2016).
[2] G. Jan et al., APEX 5, 093008 (2012). 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/c0b200dd66c243e8b93306a87bb33853.png)

Enhancing write margin of perpendicular MRAM cells using thick MgO cap layer

Spin-transfer torque magnetoresistive random-access memory (STT-MRAM) is a promising non-volatile memory technology for eliminating the classical von Neumann bottleneck to build a high-speed, energy-efficient memory hierarchy.1 One of the challenges that STT-MRAM needs to overcome, notably for automotive applications, is the robust and reliable operation in the temperature range of -40 °C to 150 °C.2 Therefore, it is vital to investigate STT-MRAM device characteristics as a function of temperature.
We investigated thermal stability factor (Δ), tunneling magnetoresistance (TMR) ratio, critical switching current (IC), and the other device parameters of STT-MRAM devices from -25 °C to 150 °C. Four different device wafers (W1-4) with increasing storage layer (SL) thicknesses and three different device diameters D1, D2, and D3 (with D1<D2<D3) were studied. The temperature-dependent behavior of Δ and TMR ratio were analytically modeled to understand their thermal variation. Figure 1 shows the experimental values of Δ, and the fitting of its thermal variation by macrospin and domain-wall model for device D2 in W1-4. Extrapolating the thermal variation of Δ, blocking temperatures (Tb) of different types of memory cells were calculated as shown in Fig. 1. It was observed that the magnetization reversal most likely occurs by domain wall motion at lower temperatures, which changes to multinucleation of domains at larger temperatures making Δ invariable with the diameter (not shown here). Figure 2 shows the thermal variation of practical switching efficiency (κ), calculated by considering Δ at different temperatures and IC at -25 °C. Similar to the variation of IC (not shown here), the κ at -25 °C increases with the thickness of SL. This improvement is believed to be due to the decrease in damping constant. This temperature-dependent investigation is important to understand the retention, writing, and reading performance of STT-MRAM cells for high-temperature applications. 
**References** 1 B. Dieny, I.L. Prejbeanu, K. Garello, P. Gambardella, et al., Nat. Electron. 3, 446 (2020).
2 K. Lee, R. Chao, K. Yamane, V.B. Naik, et al., Tech. Dig. - Int. Electron Devices Meet. IEDM 2018-December, 27.1.1 (2019).
3 X. Feng and P.B. Visscher, J. Appl. Phys. 95, 7043 (2004).
 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/22bcf7f98b6fe62f9a9b383439671b72.png)

Thermal Variation of Thermal Stability Factor and Switching Efficiency of STT MRAM Devices

Ferrimagnets (FIMs) can function as high-frequency antiferromagnets while being easy to detect as ferromagnets, offering unique opportunities for ultrafast device applications. While the physical behavior of FIMs near the compensation point has been widely studied, there lacks a general understanding of FIMs that allows us to freely vary the ratio of sublattice spins between the FM and the AFM limit. Such a generic picture can not only reveal the unique features not visible near the compensation point but also unifies the spin dynamics in FIMs with that in FM and AFM materials. Here we investigate the physical properties of a two-sublattice FIM manipulated by static magnetic fields and current-induced torques. By continuously varying the ratio of sublattice spins, we clarify how the dynamical chiral modes in an FIM are intrinsically connected to their Ferro- and Antiferromagnetic counterparts, which reveals unique features not visible near the compensation point. 
**References** [1]M. Guo, H. Zhang, and R. Cheng, Manipulating Ferrimagnets by Fields and Currents, Phys Rev B 105, 064410 (2022).
[2]C. Kim, S. Lee, H.-G. Kim, J.-H. Park, K.-W. Moon, J. Y. Park, J. M. Yuk, K.-J. Lee, B.-G. Park, S. K. Kim, K.-J. Kim, and C. Hwang, Distinct Handedness of Spin Wave across the Compensation Temperatures of Ferrimagnets, Nat Mater 1 (2020).
[3]J. Barker and G. E. W. Bauer, Thermal Spin Dynamics of Yttrium Iron Garnet, Phys Rev Lett 117, 217201 (2016).
[4]S. K. Kim, K.-J. Lee, and Y. Tserkovnyak, Self-Focusing Skyrmion Racetracks in Ferrimagnets, Phys Rev B 95, 140404 (2017).
 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/c467e329628a87539ed45b05a9c34f85.png)

Spin Dynamics of Ferrimagnets Jointing Ferro and Antiferromagnets

We study the Hall response of topological defects, such as merons and antimerons, to spin currents in two-dimensional magnets with in-plane anisotropy in the vicinity of the Berezinskii-Kosterlitz-Thouless (BKT) transition [1]. We use a combination of Monte Carlo and spin dynamics simulations to study the transition from spin superfluidity to conventional spin transport, the universal jump of the spin stiffness, and the exponential growth of the transverse vorticity current. We accompany our results by phenomenological description. We show how the spin and vorticity currents can be modulated by changes in density of free topological defects, e.g., by tuning the in-plane magnet across the BKT transition by changing the exchange interaction, magnetic anisotropy, or temperature. We further show how spin and vorticity currents can be controlled by employing connection between vorticity and spin, e.g., we demonstrate spin diode effect.
This work was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Award No. DE-SC0021019.
 
**References** [1] Edward Schwartz, Bo Li, and Alexey A. Kovalev, Phys. Rev. Research 4, 023236 (2022)

Spin and vorticity transport in two dimensional magnets with easy

Spin current generation lies at the heart of modern spintronics. Pure spin current can be generated via spin pumping, wherein the magnetization precession of ferromagnet produces a spin current into a neighboring non-magnetic layer.[1] So far, the spin pumping has mainly been used as a tool for quantifying magnetic parameters, including the spin Hall angle, spin diffusion length, spin mixing conductance, etc.,[2-4] because the efficiency of spin current generation is not large enough for use in spintronic applications, such as current-induced magnetization switching.[5] In this study, we propose a novel method to generate a large spin current via spin pumping. We utilize a FeRh which undergoes a magnetic phase transition from an antiferromagnet (AFM) to ferromagnet (FM) around 370 K.[6] The magnetic phase transition of FeRh from AFM to FM accompanies the change of total angular momentum from zero to finite. The change of angular momentum generates a spin current into a neighboring non-magnetic layer, and is converted to the charge current through the inverse spin Hall effect (ISHE). We find that the ISHE voltage is generated exclusively during the phase transition. Furthermore, the measured signal is found to depend on the sign of spin Hall angle and the direction of magnetization of FeRh, confirming that the observed signal indeed originates from the phase transition-induced spin pumping and ISHE. The generated spin current density is at least 3 orders of magnitude higher than those in previous spin pumping reports,[7,8] and is comparable to that generated by the spin Hall effect.[5] Our work provides a novel way to generate spin current, which could be utilized in potential spintronics applications.

Generation of Large Spin Current Burst during Magnetic Phase Transition of FeRh

Strain-induced modification of magnetic properties in hybrid piezoelectric/ferromagnetic heterostructures is being intensively investigated due to its potential for low-power
spintronics applications based on magnetic domain wall (DW) motion ([1], [2]).
In this study, we present PMN-PT(011)/Ta/CoFeB/MgO-based devices where both out-of-plane and in-plane strain configurations have been exploited to control DW dynamics. In PMNPT (011), the application of a gate voltage along the out-of-plane (OOP) direction of the sample leads to a non-volatile polarisation state which can be reverted back to the un-poled state by
annealing at temperatures above the Curie temperature ([3]), which was confirmed in our system by piezoresponse force microscopy. In this configuration, we observe a non-volatile
increase in the coercivity in 10µm wires in the poled state of about 90% with respect to the unpoled state. This response can be linked not only to a strain-control of magnetic anisotropy but
also to a strain-controlled change in the homogeneity of the magnetic landscape. The multiple polarisation directions of the domains in the un-poled state of the PMN-PT can translate into
a wider anisotropy distribution in the magnetic system, compared to the poled state. This can significantly affect DW nucleation/depinning fields, which opens the door to using strain to
control magnetic disorder. We also combine this non-volatile effect with local, volatile, in-plane control of DW dynamics, dominated by strain-induced changes in magnetic anisotropy.
In conclusion, we present a multifunctional strain-controlled device where both disorder and anisotropy can be manipulated. We show that multiple strain configurations in
piezoelectric/ferromagnetic hybrid structures can open new opportunities for the electrical
manipulation of DW dynamics. 
**References** [1] Na Lei, Thibaut Devolder, Guillaume Agnus, et al., Nature Communications, 4, 1-4 (2013)
[2] P. M. Shepley, A. W. Rushforth, M. Wang, et al., Scientific Reports, 5, 1-5 (2015)
[3] V.S. Kathavate, B. Praveen Kumar, I. Singh, et al., Ceramics International, 46, 12876-12883 (2020)

Exploring multiple strain geometries in PMN PT/Ta/CoFeB/MgO magneto

Ferrimagnetic (FiM) alloys as GdFeCo, formed by rare-earth (RE:Gd) and transition-metal (TM:FeCo) sublattices antiferromagnetically coupled, constitute the most promising platform to develop the next generation for ultrafast spintronics devices. These alloys combine the advantages of ferromagnetic and antiferromagnetic materials, and their properties can be easily manipulated by tunning the relative composition of the RE and TM. For instance, except at the magnetization compensation point, they present a finite magnetization which can be detected with the same techniques as done in ferromagnets. At the same time, FiM are almost insensitive to external magnetic fields and their negligible magnetostatic interaction makes them ideal candidates to store information with high density. They have recently raised strong interest owing to their ultrafast magneto-optical switching properties [1], and the possibility to drive series of domain-walls (DWs) with high speed under current pulses due to spin-orbit torques (SOTs) [2]. We have developed an advanced micromagnetic model (mM) to explore both the local all-optical switching (AOS) under ultrashort laser pulses with duration of a few fs, and the subsequent domain and DW dynamics by injection of current pulses along a heavy metal (HM) underneath the FiM. The scheme is shown in Fig. 1(a). Starting with a uniform state where both sublattices are anti-parallel aligned along the z-axis, a laser pulse is applied. A proper selection of the fluence and duration of the laser pulse [3] results in a reversed domain flanked by two homochiral DWs, which are subsequently driven along the FiM strip upon injection of the current pulses along the HM [4]. Fig 1(b)-(c) shows an example of the laser-induced writing and current-driven shifting of a sequence magnetic domains (bits). In the talk, we will describe the details of the mM and how it can be used to infer the potential of these FiM/HM stacks to develop DW-based memory devices. 
**References** 
[1] See for instance T. A. Ostler et al. Nat. Commun. 3, 1666 (2012). 
[2] L. Caretta et al. Nature Nanotechnology. 13, 1154 (2018). 
[3] V. Raposo et al. Phys. Rev. B 105, 104432 (2022). 
[4] E. Martinez at al. J. Magn. Magn. Mater. 491, 165545 (2019). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/b0094215f4561838a4b53be007b025e2.png) 
Fig.1. (a) Scheme of the HM/FiM stack with the laser. (b) Temporal sequence of laser (top) and current (bottom) pulses to write a 01101000 bit sequence. (c) Snapshots of the resulting bit
sequence.

All optical writing and current driven shifting of bits in ferrimagnetic strips: a micromagnetic study

Kagome-lattice magnets RMn6Sn6 recently emerged as a new platform to exploit the interplay between magnetism and topological electronic states [1]. Some of the most exciting features of this family are the dramatic dependence of the easy magnetization direction on the rare-earth specie, despite other magnetic and electronic properties being essentially unchanged, and the Kagome geometry of the Mn planes that in principle can generate flat bands and Dirac points; gapping of the Dirac points by spin-orbit coupling has been suggested recently to be responsible for the observed anomalous Hall response in the member TbMn6Sn6. In this work [2], we address both issues with density functional calculations and are able to explain, with full quantitative agreement, the evolution of magnetic anisotropy, including a complete reversal upon adding an $f$-electron with zero magnetic orbital quantum number when going from Ho to Er. We also show the microscopic origin of this computational result using a simple and physically transparent analytical model. We analyze in detail the topological properties of Mn-dominated bands and demonstrate how they emerge from the multiorbital planar Kagome model. We further show that, despite this fact, most of the topological features at the Brillouin zone corner K are strongly 3D, and therefore cannot explain the observed quasi-2D AHE, while those few that show a quasi-2D dispersion are too far removed from the Fermi level. We conclude that, contrary to previous claims, Kagome-derived topological band features bear little relevance to transport in RMn6Sn6, albeit they may possibly be brought to focus by electron or hole doping. 
**References:** [1] J.-X. Yin, S. S. Zhang, H. Li, K. Jiang, G. Chang, B. Zhang, B. Lian, C. Xiang, I. Belopolski, H. Zheng, T. A. Cochran, S.-Y. Xu, G. Bian, K. Liu, T.-R. Chang, H. Lin, Z.-Y. Lu, Z. Wang, S. Jia, W. Wang, and M. Z. Hasan, Giant and anisotropic many-body spin-orbit tunability in a strongly correlated kagome magnet, Nature 562, 91 (2018) 
[2] Y. Lee, R. Skomski, X. Wang, P. P. Orth, A. K. Pathak, B. N. Harmon, R. J. McQueeney, I. I. Mazin, and L. Ke, Interplay between magnetism and band topology in Kagome magnets RMn6Sn6, arXiv 2201, 11265 (2022), https://arxiv.org/abs/2201.11265 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/0f783c20cf93a9b8838fc51289261234.png) 
Fig. 1 Variation of magnetic energy (in meV/f.u.) as a function of spin-axis rotation in RMn6Sn6, with R = Gd, Tb, Dy, Ho, and Er, calculated (a) with and (b) without R-4f contributions. $\theta$ is the angle between the spin direction and the out-of-plane direction. The experimental easy directions for each compound are denoted by arrows in panel (a). The lines are just guides for the eye. 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/6b36d3bf48826bb00709ef58034f99e5.png) 
Fig. 2 Band structures projected on surface BZ calculated without (blue) and with (red) SOC in TbMn6Sn6. The k-dependent DOS are integrated along kz and are calculated in DFT.

Interplay between magnetism and band topology in Kagome magnets RMn6Sn6

Ferromagnetic thin films with perpendicular magnetic anisotropy (PMA) provide an excellent support to develop media for high-density magnetic recording. To optimize
the density of magnetic domains and control the magnetic response of the magnetic film to an applied magnetic field, further understanding of the domain pattern formation and evolution
throughout the magnetization process is necessary. Here we study the in-situ morphology of magnetic domains in [Co/Pt]N multilayered thin films with PMA via magnetic force
microscopy (MFM). We found that the domain pattern evolves between three distinct topologies: bubble pattern, short stripe pattern, and maze pattern. Previous studies1-4 have
demonstrated that the morphology of these patterns at remanence depends on the number of bilayer repeats, layer thickness, and maximum of the previously applied field. Here we extend
the remanence study to explore the evolution of the domain patterns under in-situ magnetic field. Domain density and interdomain distance are key metrics for quantifying morphological
changes in the domain patterns, as illustrated in Figure 1. Using MFM, we mapped the domain density and interdomain distance in response to the in-situ and maximum applied magnetic
field up to 7.2 kOe. We completed these studies for layer repeats of N from 20 down to 10 and Co thicknesses from 30 Å down to 10 Å. We found three main types of in-situ phase
transitions, which result in the previously observed remanent phase transitions Additionally, we found that the domain density is maximized with in-situ applied field when N = 20 with Co
thicknesses of 30 Å. 

**References:** 

1. A. S. Westover, K. Chesnel, K. Hatch, P. Salter and O. Hellwig, Journal of Magnetism and Magnetic Materials 399, 164-169 (2016). 
2. K. Chesnel, A. S. Westover, C. Richards, B. Newbold, M. Healey, L. Hindman, B. Dodson, K. Cardon, D. Montealegre, J. Metzner, T. Schneider, B. Böhm, F. Samad, L. Fallarino and
O. Hellwig, Physical Review B 98 (22), 224404 (2018). 
3. Fallarino, A. Oelschlägel, J. A. Arregi, A. Bashkatov, F. Samad, B. Böhm, K. Chesnel and O. Hellwig, Physical Review B 99 (2), 024431 (2019). 
4. A. Gentillon, C. Richards, L. A. Ortiz-Flores, J. Metzner, D. Montealegre, M. Healey, K. Cardon, A. Westover, O. Hellwig and K. Chesnel, AIP Advances 11 (1), 015339 (2021). 


![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/3c9444db7ca08250e56aea7951c4926c.png)

 
Fig. 1 Domain density plot for [Co(10 Å)/Pt(7 Å)]20 as a response to the in-situ applied magnetic field, Hin-situ, and for a maximum applied magnetic field of 6.4 kOe. "Reversed domains"
refers to domains where the magnetization is anti-aligned with the applied field while "parallel domains" refers to domains where the magnetization is aligned with the applied field.
ROB-08

Mapping In situ Morphological Phase Transitions of Magnetic Domains in [Co/Pt]N under applied magnetic field

Magnetic skyrmions are topologically nontrivial spin textures with envisioned applications in energy-efficient magnetic information storage [1,2]. Toggling the presence of magnetic skyrmions via writing/deleting processes is essential for spintronics applications, which usually requires a magnetic field, current injection, electric field, laser pulse, or thermal excitation [3,4]. A key challenge is to directly image such ultrasmall spin textures in order to confirm their topological character. 

Using spin-polarized low-energy electron microscopy (SPLEEM), we have demonstrated a new, field-free method to write/delete magnetic skyrmions at room temperature, via hydrogen chemisorption/desorption cycles on Ni/Co/Pd/W(110) [5]. The spin structures of the written skyrmions are resolved to be hedgehog Néel-type via magnetization vector mapping using SPLEEM (Fig. 1). Supported by Monte-Carlo simulations, the skyrmion creation/annihilation is attributed to the hydrogen-induced magnetic anisotropy change on ferromagnetic surfaces. The roles of hydrogen and oxygen on magnetic anisotropy and skyrmion deletion on other magnetic surfaces are also demonstrated. 

In another study, we focus on the interfacial Dzyaloshinskii-Moriya interaction (DMI), which stabilizes magnetic chirality with preferred handedness. Experimentally, controlling the handedness is crucial to tune the efficiency of current-induced manipulation of spin texture. This is conventionally achieved by stacking asymmetric multilayers where the thickness of each layer is at least a few monolayers. We observed an ultrasensitive chirality switching in (Ni/Co)n multilayer induced by capping only 0.22 monolayer of Pd [6]. Using SPLEEM, we monitor the gradual evolution of domain walls from left-handed to right-handed Néel walls and quantify the DMI induced by the Pd capping layer (Fig. 2). We also observe the chiral evolution of a skyrmion during the DMI switching, where no significant topological protection is found as the skyrmion winding number varies. This corresponds to a minimum energy cost of < 1 attojoule during the skyrmion chirality switching. 

These results open up new opportunities for designing energy-efficient skyrmionic and magneto-ionic devices. They also illustrate the effectiveness of SPLEEM in resolving magnetization vector in chiral spin textures with high spatial resolution.

This work has been supported in part by the NSF (DMR-2005108), SRC/NIST SMART Center and US DOE. 

References [1] R. Wiesendanger, Nat. Rev. Mater. 1, 16044 (2016).
[2] A. Fert, et al. Nat. Rev. Mater. 2, 17031 (2017).
[3] W. Jiang, et al. Phys. Rep. 704, 1-49 (2017).
[4] X. Zhang, et al. J. Phys.: Condens. Matter 32, 143001 (2020).
[5] G. Chen, et al. Nat. Commun. 13, 1350 (2022).
[6] G. Chen, et al. Nano Lett., in press; arXiv: 2206.12069.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/e3d647dc58c4efce282d51103355d0ce.png)

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