United States

Research into magnetic skyrmions and their spintronics applications has revealed complex chiral spin textures. However, direct characterizations of the structure of skyrmion and related spin textures pose an experimental challenge. To better understand their structure, we use Lorentz transmission electron microscopy (LTEM) to track their evolution from well-studied domain walls (DWs) into skyrmion and biskyrmion phases. Magnetic skyrmions were first predicted as a result of the Dzyaloshinskii-Moriya interaction (DMI) found in materials with broken inversion symmetry&lt;sup&gt;1&lt;/sup&gt;. However, topologically equivalent chiral bubbles, or dipole skyrmions, can be stabilized in achiral thin films by competing long-range dipole and short-range DW energies&lt;sup&gt;2&lt;/sup&gt;.&lt;br/&gt;&lt;br/&gt;Recently, a novel skyrmion phase consisting of bound skyrmion pairs with opposite helicities was reported in achiral Fe/Gd multilayers&lt;sup&gt;3&lt;/sup&gt; (Fig. 1). However, the primary magnetic imaging techniques for thin films are LTEM, which yields projected in-plane magnetic field, and resonant X-ray techniques, which yield projected out-of-plane magnetization. This complicates identification of complex magnetic spin textures, as multiple spin textures can yield qualitatively similar projected magnetic fields, and there has been subsequent debate over the structure of the reported skyrmion phases&lt;sup&gt;4,5&lt;/sup&gt;.&lt;br/&gt;&lt;br/&gt;By tracking the field-dependent evolution of magnetic spin textures from the well-studied magnetic stripes to the novel skyrmion phases, we can identify key components of these spin textures. First, by applying an out-of-plane magnetic field with a small in-plane component, stripe DWs form, alternatingly aligned and anti-aligned with the in-plane component, matching previous results&lt;sup&gt;2&lt;/sup&gt;. As the field is further increased, the stripe DWs split, and the aligned DWs form the center of the novel texture, while the anti-aligned form closure loops (Fig. 2), supporting that the magnetization is a pair of contour-rotating vortices. Fully understanding these textures will require knowledge of the 3D structure, so surface sensitive techniques like SEMPA, SPLEEM, and MFM will be vital moving forward.

![](https://assets.underline.io/uploads/markdown_image/1/image/26875a594ef774ade1f7585132522bfd.jpg)

Fig. 1. The projected in-plane field of the novel texture.

![](https://assets.underline.io/uploads/markdown_image/1/image/c339839e8a22aef9d6e717998b111ef8.jpg)

Fig. 2. Stripe domains breaking into the novel phase.

2022 Joint MMM-INTERMAG

Evolution of Novel Chiral Spin Textures in Fe/Gd Based Multilayers

The 15th Joint MMM-INTERMAG Conference (2022 Joint) 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 plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

For tickets to the event, please register at the following link: https://magnetism.org/register

Please register for the Joint MMM-Intermag conference to join the event.

This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

Research into magnetic skyrmions and their spintronics applications has revealed complex chiral spin textures. However, direct characterizations of the structure of skyrmion and related spin textures pose an experimental challenge. To better understand their structure, we use Lorentz transmission electron microscopy (LTEM) to track their evolution from well-studied domain walls (DWs) into skyrmion and biskyrmion phases. Magnetic skyrmions were first predicted as a result of the Dzyaloshinskii-Moriya interaction (DMI) found in materials with broken inversion symmetry1. However, topologically equivalent chiral bubbles, or dipole skyrmions, can be stabilized in achiral thin films by competing long-range dipole and short-range DW energies2. Recently, a novel skyrmion phase consisting of bound skyrmion pairs with opposite helicities was reported in achiral Fe/Gd multilayers3 (Fig. 1). However, the primary magnetic imaging techniques for thin films are LTEM, which yields projected in-plane magnetic field, and resonant X-ray techniques, which yield projected out-of-plane magnetization. This complicates identification of complex magnetic spin textures, as multiple spin textures can yield qualitatively similar projected magnetic fields, and there has been subsequent debate over the structure of the reported skyrmion phases4,5. By tracking the field-dependent evolution of magnetic spin textures from the well-studied magnetic stripes to the novel skyrmion phases, we can identify key components of these spin textures. First, by applying an out-of-plane magnetic field with a small in-plane component, stripe DWs form, alternatingly aligned and anti-aligned with the in-plane component, matching previous results2. As the field is further increased, the stripe DWs split, and the aligned DWs form the center of the novel texture, while the anti-aligned form closure loops (Fig. 2), supporting that the magnetization is a pair of contour-rotating vortices. Fully understanding these textures will require knowledge of the 3D structure, so surface sensitive techniques like SEMPA, SPLEEM, and MFM will be vital moving forward.

![](https://assets.underline.io/uploads/markdown_image/1/image/26875a594ef774ade1f7585132522bfd.jpg)

Fig. 1. The projected in-plane field of the novel texture.

![](https://assets.underline.io/uploads/markdown_image/1/image/c339839e8a22aef9d6e717998b111ef8.jpg)

Fig. 2. Stripe domains breaking into the novel phase.

technical paper

The iron-rich alloy Galfenol (Fe1-x-Gax, 10%&lt;x&lt;30%) has been of significant interest for sensor technologies due to the sizeable magnetostriction coefficient found in single-crystal and polycrystalline films. [1,2] However, it is necessary to improve the magnetic softness of the material for many applications. To do so, we have explored the use of Zr and other glass formers and additives, rapid solidification approaches, and subsequent annealing to produce a nanocrystalline (Fe,Ga)-based alloy with the desired magnetostrictive and structural properties. We report studies on a series of 11 melt-spun and annealed (Fe1-x-Gax)92Zr8 alloy ribbons where the Ga concentration (x) has been varied from 15% to 36%. As illustrated in Fig. 1, in contrast to single-crystal and polycrystalline films, the ribbons exhibit the dominant bcc-like phase for Galfenol over a more extensive concentration range with fewer other ordered phases. Analysis of the x-ray peak locations reveals a deviation in lattice parameter from bulk behavior for alloy with similar x, suggesting that the surrounding amorphous phase matrix for the nanocrystallites within the ribbons is Ga-rich. Beginning at x=26%, x-ray diffraction scans exhibit signs of the formation of the ternary ZrFe6Ga6, consistent with CALPHAD-type database calculations. Magnetization measurements reveal a maximum saturation magnetization for the alloy with x=15% and coercivity values increase rapidly on formation of the ternary intermetallic phase. Fig. 2 illustrates the in-plane magnetostriction coefficient for the series of samples, displaying a peak value for x=24-26% which differs from the values observed in single crystalline sample x=18-20%. Acknowledgment: Prepared by LLNL under Contract DE-AC52-07NA2.

![](https://assets.underline.io/uploads/markdown_image/1/image/d0969bacd21d03b76d13d440d0b95364.jpg)

Fig. 1: X-ray diffraction of (Fe1-x-Gax)92Zr8 alloy ribbons for x=15-36% after annealing for 1 hour at 550 oC. (*) peaks indicate the bcc-like phase, with (+) symbols denoting those associated with ZrFe6Ga6.

![](https://assets.underline.io/uploads/markdown_image/1/image/e33e6f18ac454731289f00a2c1bb0a5e.jpg)

Fig. 2: Magnetostriction coefficient vs composition for annealed (Fe1-x-Gax)92Zr8 alloy ribbons for x=15-36%.

Optimizing Magnetostriction in Fe-Ga-Zr Nanocrystalline Alloys

High temperatures and inert atmospheres are required to produce borides due to the covalent character of their chemical bonds and, consequently, their high melting temperatures. Solid and melt state processing of borides from the primary reactants typically results in dense samples, which are crushed, milled, and sieved laboriously into fine powder for further processing. The size reduction process introduces numerous complications that hinder large-scale powder production. Against this backdrop, Molten Salt Infiltration and Encapsulation Method (MSIEM) is a sustainable energy-efficient process that uses no inert gas, relatively low temperatures, and moderately short reaction times to synthesize powders with uniform chemical composition and high-phase purity. In this study, fine particles of the promising magnetocaloric boride AlFe2B2 were prepared by sintering a green compact composed of the constituent elements Al, Fe, and B encapsulated within a layer of KBr molten salt at 1000 °C for 12 hours in the open air. Results indicate that the Al/Fe loading ratio in the precursor compacts strongly influences the phase purity, structural properties, and magnetofunctional response of the samples. It is observed that Curie temperature (Tc), saturation magnetization (Ms), and magnetic entropy change (ΔSmag) of the powders increase with the decrease in the Al/Fe ratio – a feature attributed to the change in the Al/Fe antisite disorder. Powders of nominal composition Al1.2Fe2B2 were found to be nearly single-phase stoichiometric Fe2AlB2 materials containing only 3% Al2O3 as the impurity phase. These powders exhibit an irregular polyhedral morphology with particle sizes in the range 2-5 m and demonstrate a promising magnetocaloric effect corresponding to a ΔSmag = 4.2 J kg−1K−1 at a magnetic field of μ0Happ = 2 T near room temperature, Figure 1. Research efforts centered on 3D printing magnetocaloric structures using the low-cost feedstock AlFe2B2 powders produced via MISEM will be presented and discussed.

![](https://assets.underline.io/uploads/markdown_image/1/image/b241cd2e4bc44d322718a4b672be8b39.jpg)

Fig 1. Magnetic entropy change curves of powders of composition Al1.2Fe2B2 synthesized via MISEM using KBr salt. Inset shows the morphology of the sintered powders.

Low-cost Processing of AlFe2B2 Feedstock Powders for Additive Manufacturing of Magnetocaloric Structures

Gas liquefaction is an essential aspect for gas storage and transport and its demand will significantly increase as the use of gases such as natural gas as well as H2, He, N2, and O2 become prominent in the development of new technologies (e.g. hydrogen based ones). Systems based on the magnetocaloric effect (MCE) are attracting the interest of the scientific community as they can overcome some of the issues of conventional liquefaction systems [1, 2]. In this work, we studied a series of rare-earth rich RE6Co2Ga (RE = Ho, Dy or Gd) compounds, which shows excellent MCE in the range of H2 and N2 liquefaction temperatures [3]. All the samples crystallize in the Ho6Co2Ga-type crystal structure (Immm space group) without significant presence of impurity phases. The nature of the thermomagnetic transition depends on the rare-earth element, showing metamagnetic anti-to-paramagnetic (AF to PM) transitions for Ho and Dy while a ferro-to-paramagnetic (FM to PM) transition is obtained for Gd. Novel MCE field dependence method [4] and conventional Banerjee's criterion have been used for distinguishing the order of the transition: samples with Ho and Dy are found to undergo first-order phase transition whereas a second order phase transition is observed for the one with Gd. Fig.1 depicts the temperature dependence of the isothermal entropy change (ΔSiso) for a magnetic field change of 0-5 T for Ho and Gd samples. The two compounds show significant values of 10.1 and 9.1 J kg-1 K-1 at 26 and 75 K, close to the liquefaction temperatures of H2 and N2, respectively.

![](https://assets.underline.io/uploads/markdown_image/1/image/f4b22391b23280e34c4bc60b9a3ec65c.jpg)

The temperature dependence of isothermal entropy change for Ho6Co2Ga and Gd6Co2Ga compounds whose crystal structures belong to Ho6Co2Ga-type.

Cryogenic magnetocaloric effect and thermomagnetic transitions in RE6Co2Ga (RE = Ho, Dy or Gd) compounds

Materials for magnetocaloric refrigeration near room temperature attract main attention, but compounds exhibiting large magnetocaloric effects (MCE) in the cryogenic regime are also of importance.1,2 In particular, MCE materials that can support liquefaction of certain gases, from hydrogen (boils at 20 K) to natural gas (~110 K), are of interest for diversification of energy supplies.2 Here we report a large MCE in GdNi1-xCox series in the temperature range between 70 and 115 K that can be controlled by varying x(Co) between 0 and 0.15. The compounds undergo second-order magneto-elastic transformations where the transitions from paramagnetic to ferromagnetic states are coupled with anisotropic changes in lattice parameters without significant changes in phase volume.3,4 Lattice symmetry also remains unperturbed across the transitions.3,4 While the transition temperatures increase nearly linearly with x(Co), doping with Co slightly reduces the maximum magnetic entropy changes: from -14 J/ Kg K at 71 K when x(Co) = 0 to -10 J/Kg K at 115 K when x(Co) = 0.15 (all values are quoted for a 50 kOe magnetic field change). The calculated temperature-averaged-entropy changes (TECs), one of the important figures of merit for assessing the potential of magnetic refrigerants,5 are comparable with the best known potential magnetocaloric materials exhibiting second-order phase transition. Our detailed analysis of the magnetic field dependence of the magnetic entropy changes along with critical exponent analysis explore the role of magneto-elastic coupling on the magnetocaloric properties of GdNi1-xCox alloys. Acknowledgement: This work was performed at Ames Laboratory and was supported by the Division of Materials Science and Engineering of the Office of Basic Energy Sciences of the U.S. Department of Energy (DOE). Ames Laboratory is operated for the U.S. DOE by Iowa State University under Contract No. DE-AC02-07CH11358.

Large cryogenic magnetocaloric effect in GdNi1-xCox (0 ≤ x ≤ 0.15)

Long-range ferromagnetic order in the single-layer limit appears to be possible in several chromium-based chalcogenides and halides with layered structure. Ab initio calculations based on the density functional theory of different Cr-based chalcogenides are analyzed approaching the twodimensional limit. The focus will be on magneto-crystalline anisotropy and how to obtain an out-of-plane magnetic polarization that would help circumvent the restrictions of the Mermin-Wagner theorem. This will be studied through various means like strain, pressure, the stability of charge density waves (CDW)[1], stoichiometry and other different structural details. The electronic structure of these compounds will be discussed as an approach to the understanding of the magnetic properties of the transition metal chalcogenide family in general.

Two-dimensional Magnetic Order in Cr-based Transition Metal Chalcogenides

Spin-orbit torque enables electrical control of the magnetic state of ferromagnets or antiferromagnets. The quintessential system exhibiting spin-orbit torque is a bilayer composed of a heavy metal and a ferromagnet. The heterostructure bilayer geometry breaks the inversion symmetry and allows the spin-orbit torque arising from the spin current flow from the heavy metal layer to the ferromagnetic layer. In this work, we consider the intrinsic spin-orbit torque generated in inversion symmetry breaking magnetic materials directly without stacking with other materials. In the first example of ferromagnetic monolayer Fe3GeTe2, we calculate the intrinsic spin-orbit torque which arises due to the global inversion symmetry breaking. In addition, spin-orbit torque in Fe3GeTe2 has the unique property that the lowest order contribution is fieldlike and time-reversal even because of the C3z rotation symmetry. This is in contrast to the conventional case in which the lowest order is time-reversal odd and fieldlike and the next lowest-order is time-reversal even and dampinglike. We next show that the next lowest-order spin-orbit torque in Fe3GeTe2 is time-reversal odd and dampinglike which can play a more important role in switching the magnetization in the ensuring dynamics, as described by the Landau-Lifshitz-Gilbert equation. In the second example of antiferromagnetic bilayer CrI3, we find staggered dampinglike (time-reversal even) torque and uniform fieldlike (time-reversal odd) torque due to local inversion symmetry breaking and global inversion plus time-reversal symmetry. This is similar to the previous studies of CuMnAs and Mn2Au, where the Neel order switching is demonstrated using uniform fieldlike torque. However, CrI3 has a unique property in that the anisotropy energies and exchange energies are similar in magnitude. This leads to qualitatively different results in the switching dynamics: the staggered dampinglike torque is the dominant switching mechanism. The primary role of staggered dampinglike torque applies to other antiferromagnets in which the product of Gilbert damping and exchange field is smaller than the anisotropy field.

Intrinsic spin-orbit torque in van der Waals magnetic materials

Due to the long spin diffusion length and the high mobility, monolayer graphene is an intriguing material element for spintronic applications [1]. For example, if a monolayer graphene can be magnetized, Dirac electrons and holes will carry opposite spins, leading to a good spin filter or a convenient generator of pure spin currents. However, a prestine monolayer graphene does not have net magnetization. Previous experiments have demonstrated that when a monolayer graphene is transferred to the surface of a magnet, the p orbitals on the carbon atoms can overlap with the magnetic atoms in the adjacent layer, leading to an induced magnetization in the graphene layer [2]. This is known as the proximity effect, and has been reported in different types of ferromagnetic heterostructures. Compared to ferromagnets, antiferromagents are better candidates to magnetize graphene. Due to the zero net magnetization, an antiferromagnet does not respond to external magnetic noise, and therefore devices using antiferromagnetic heterostructures have good scalbility and stability. Also, antiferromagents can switch almost three orders of magnitude faster than conventional ferromagnets, which may lead to high-speed information processing. Here, we show that a monolayer graphene can indeed be magnetized through the proximity effect provided by a thin film of hexagonal chromium selenide (Fig. 1), a semiconducting antiferromagnet [3]. The induced spin splitting energy is experimentally measured to be 134meV at 2K. Such exchange splitting is experimentally confirmed by the shift of quantum oscillations in the graphene layer. The magnitude of the splitting energy is obtained by its modulation through field cooling, with the exchange splitting energy increasing driven by positive cooling fields and decreasing by negative cooling fields (Fig. 2). The magnitude of the exchange coupling and the Laudau-level indices are confirmed by a machine-learning search for the best fit in a large parameter space. Such spin splitting is also supported by polarized neutron reflectometry and magneto-optic Kerr measurements. Acknowledgements: The transport measurement and theoretical modelling in this work were supported by Spins and Heat in Nanoscale Electronic Systems (SHINES), an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under award #SC0012670. We are also grateful for support from the National Science Foundation (NSF) (DMR-1411085 and DMR-1810163) and the ARO programme (contract no. W911NF-15-1-10561). Research was performed in part at the NIST Center for Nanoscale Science and Technology. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant no. OCI-1053575. Specifically, it used the Bridges system (supported by NSF award no.ACI-1445606) at the Pittsburgh Supercomputing Center (PSC). Certain commercial equipment, instruments or materials are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

![](https://assets.underline.io/uploads/markdown_image/1/image/17681d6778d9ccff54b5964943012fc1.jpg)

Fig. 1. The schematic of the graphene/CrSe heterostructure. Hexagonal CrSe has a layered AFM structure. Each layer contains a non-colinear spin texture with a non-zero magnetization along z. Adjacent layers cancel the moments of each other, resulting in a net antiferromagnet.

![](https://assets.underline.io/uploads/markdown_image/1/image/d699ad42c2ba992a04094c15c97d5021.jpg)

Fig. 2. Quantum oscillations are shifted by field cooling in the heterostructure. The dips corresponding to each Landau level are denoted by dashed lines.

Large Exchange Splitting in Monolayer Graphene Magnetized by an Antiferromagnet

Topological insulators (TI) have gained much interest in the field of spintronics for the generation of pure spin currents. Indeed, three-dimensional TIs are predicted to host exotic properties like topologically protected surface states (TSS), which show Dirac-like band dispersion and spin-momentum locking [1]. One of the main strategies is to take advantages of the spin polarization of the TSSs to manipulate the magnetization of an adjacent ferromagnetic thin film (FM) using the spin-orbit torque (SOT) mechanism [2]. In the past few years, the community attempted to replace the traditional heavy metals by a TI in order to enhance the SOT efficiency with limited success. It now appears that the interface sharpness and the high chemical affinity between Bi-based TIs and classical 3d FMs is a major hurdle to reach the predicted breakthrough in magnetization switching power-efficiency [3]. The emergence of ferromagnetism in two dimensions in 2017, which started a new field in condensed matter physics, could bring a solution to this issue. The van der Waals (vdW) nature of the interaction between the TI and the 2D-FM should limit chemical reactions, interface intermixing and hybridization of state between the two layers. Our approach focuses on stacking and growing 2D-FM (Fe3GeTe2) onto high-quality compensated TIs ((Bi0.4Sb0.6 )2Te3) grown by molecular beam epitaxy. We use both low and high field second harmonic magnetotransport measurement to characterize the SOT generation, finding a strong temperature dependence of the harmonic signals. We also reports the SOT current-induced magnetization switching operation at low critical current density (Jc &lt; 1010 A/m2) in the vdW heterostructure.

![](https://assets.underline.io/uploads/markdown_image/1/image/276785c92c28212f866028b086fcb79c.jpg)

Fig.1: Second harmonic spin-orbit torque measurement in BST/FGT bilayers. a) Measurement geometry. b) Anomalous Hall effect (AHE) recorded by applying the magnetic field along z. c) AHE recorded by sweeping the field along y. d) Damping-like torque second harmonic measurements. e) Field-like torque second harmonic measurements. The sample temperature is 70 K and the applied current density is 1.3 × 1010 A.m-2.

Spin-orbit torques in topological insulator - two-dimensional ferromagnet heterostructures

Iron selenide telluride, FeTeSe is a family of Fe-chalcogenide and Fe-based superconductor. This material is a compound material and possesses an in-plane symmetry breaking. From spintronic viewpoints, FeTeSe allows Ising-type superconductivity, which enables the locking of spin in out-of-plane directions. In addition, FeTeSe can be a great candidate for topological superconductor which can arise the S=1 spin-triplet Cooper pairs at the surface. To detect possible perpendicular spin-triplet states in FeTeSe electrically, ferromagnetic electrodes with perpendicular magnetic anisotropy (PMA) is necessary. However, an interplay of ferromagnetism of the electrodes and superconductivity of FeTeSe has not been sufficiently explored. We prepared exfoliated thin FeTe0.6Se0.4 (FTS) flakes and deposited PMA electrodes on the FTS, which is made of [Pt/Co]10 multilayer (“10” denotes a stacking number). The conventional four-terminal measurement was implemented as the in-plane and perpendicular external magnetic field (Hext) was applied up to 9 T. The superconducting transition is observed at T = 15 K. More importantly, the upper critical field of the FTS is anisotropic and the in-plane upper critical field is measured to be 145 T [1]. Y. Saito et al. reported the enhancement of the in-plane upper critical field of a member of Ising-type superconductivity, MoS2 [2]. Therefore, these results show that the superconductivity of exfoliated thin film FTS is robust and FTS is a potential material for Ising-type superconductor, which can open a new pathway to super-spintronics. More detailed discussion will be given in the presentation.

![](https://assets.underline.io/uploads/markdown_image/1/image/67764886b292d9077025b348fa1b86b9.jpg)

Fig. 1: An optical microscopy image of the mechanically exfoliated FTS single crystal.

![](https://assets.underline.io/uploads/markdown_image/1/image/de178bfdb99000c880b2a6f5e358f073.jpg)

Fig. 2: Temperature dependence of the normalized resistance of the FTS with PMA electrodes, when in-plane magnetic field is applied. The normalization was carried out using the normal-state resistance R0 at 16 K.

Observation of a superconducting state of possible Ising-type topological superconductor FeTe0.6Se0.4, equipping ferromagnetic electrodes with perpendicular magnetic anisotropy

The interfacial Dzyaloshinskii–Moriya interaction (DMI) emerges in ferromagnet/heavy metal thin films with broken z-mirror symmetry, stabilizing Néel domain walls and skyrmions of one chirality as dictated by its Rashba-type field. On the other hand, both Bloch chiralities remain energetically degenerate at static equilibrium for mixed domain walls in films with a moderate DMI. Multiple research groups have nevertheless independently reported significant Bloch chirality asymmetries in the Bz-stabilized domain microstructures of different interfacial DMI systems [1, 2]. In this work, we demonstrate how the asymmetric wall energy landscape in such systems can produce a deterministic Bloch chirality when domain walls are driven away from static equilibrium. For D &lt; Dc, the two ground state domain walls—having Bloch components of opposite chiralities—exhibit different restoring torques and steady state configurations. As dictated by the driving field’s direction and sign of DMI, one wall, which we term the lax wall, becomes labile at a lower Bz prior to the Walker field. At this lability point, the wall lies at an inflection point in its energy landscape and the domain wall susceptibility (χdw ∝ (σΦΦ)-1) diverges. The lax wall therefore reorients at higher fields to the steady state configuration of its counterpart, which we call the locked wall (Fig. 1). Using the Slonczewski equations and the 1D wall energy model, we analytically derived a DMI–Bz phase diagram of steady state domain wall Bloch chirality (Fig. 2), which includes an astroid analogous to the Stoner–Wohlfarth domain switching model. While these equations predict that locked walls precess beyond the Walker field, it was observed that they can instead persist due to DMI-induced asymmetries in vertical Bloch line (VBL) evolution—extending the Bloch monochirality regimes [3]. Here, we generalize these Bloch chirality preferences to arbitrary VBL behavior in these systems, before discussing how the theory of horizontal Bloch line evolution could similarly mediate Bloch chirality preferences [4].

![](https://assets.underline.io/uploads/markdown_image/1/image/c78283a8de7f53f55949028b259b7207.jpg)

Steady state Bloch monochirality via DMI-induced asymmetric evolution of lax & locked walls.

![](https://assets.underline.io/uploads/markdown_image/1/image/e73fbc654808325ad8a75b63241d4af0.jpg)

DMI–Bz phase diagram of steady state domain wall Bloch chirality

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