Characterizing an effective magnetic field during asymmetric creep motion of Dzyaloshinskii domain walls.

Understanding the role of Landau Lifshitz Gilbert dynamics in describing magnetic domain wall (DW) motion in the creep regime is complicated by the presence of static pinning, but has regained interest due to recently observed directional growth in thin films with significant interfacial Dzyaloshinskii-Moriya interaction. Here, we delve into this directional domain growth behaviour in Pt/Co/Ni-based multi-layers under the influence of combined longitudinal and perpendicular magnetic fields via magneto-optical Kerr effect microscopy. Observations, including the onset field,µ0Honset, where the growth direction reverses by 180 degrees, align with the transient steady-state model predictions. By systematically varying the applied perpendicular magnetic field, we estimate the strength of an effective perpendicular field that acts on the DW during creep movement, which was expectedly found to be much smaller than the applied external field itself. This work further adds to the complexity of asymmetric domain expansion in the creep regime, but also highlights the range of magnetic information that can be extracted from careful analysis of this behavior.

Spin Waves in Ferromagnetic Nanorings with Interfacial Dzyaloshinskii-Moriya Interactions: II. Directional Effects.

A theory is presented to study the effect of interfacial Dzyaloshinskii-Moriya interactions (DMIs) on the static and dynamic magnetic properties in single-layered ferromagnetic nanorings. A microscopic (Hamiltonian-based) approach is used that also includes the antisymmetric DMI besides the competing symmetric (bilinear) exchange interactions, magnetic dipole-dipole interactions, and an applied magnetic field. Here, the axial vector of the DMI is taken to be in the plane of the nanoring (by contrast with earlier studies) and we explore cases where it is either parallel or perpendicular to the in-plane magnetic field. Significantly, with this orientation for the DMI axial vector, the inhomogeneous static magnetization is tilted to have a component perpendicular to the plane giving a surface texture. This effect is studied in both the low-field vortex and high-field onion states. There is a consequent modification to the discrete set of spin-wave modes in both states through their frequencies and spatial amplitudes. We present combined analytical and numerical results for the static properties and dynamical magnetization in ferromagnetic nanorings, including the variation with applied field.

Linear response theories for interatomic exchange interactions.

The linear response is a perturbation theory establishing the relationship between given physical variable and the external field inducing this variable. A well-known example of the linear response theory in magnetism is the susceptibility relating the magnetization with the magnetic field. In 1987, Liechtensteinet alcame up with the idea to formulate the problem of interatomic exchange interactions, which would describe the energy change caused by the infinitesimal rotations of spins, in terms of this susceptibility. The formulation appears to be very generic and, for isotropic systems, expresses the energy change in the form of the Heisenberg model, irrespectively on which microscopic mechanism stands behind the interaction parameters. Moreover, this approach establishes the relationship between the exchange interactions and the electronic structure obtained, for instance, in the first-principles calculations based on the density functional theory. The purpose of this review is to elaborate basic ideas of the linear response theories for the exchange interactions as well as more recent developments. The special attention is paid to the approximations underlying the original method of Liechtensteinet alin comparison with its more recent and more rigorous extensions, the roles of the on-site Coulomb interactions and the ligand states, and calculations of antisymmetric Dzyaloshinskii-Moriya interactions, which can be performed alongside with the isotropic exchange, within one computational scheme. The abilities of the linear response theories as well as many theoretical nuances, which may arise in the analysis of interatomic exchange interactions, are illustrated on magnetic van der Walls materials CrX3(X=Cl, I), half-metallic ferromagnet CrO2, ferromagnetic Weyl semimetal Co3Sn2S2, and orthorhombic manganitesAMnO3(A=La, Ho), known for the peculiar interplay of the lattice distortion, spin, and orbital ordering.

Hidden Valley Polarization, Piezoelectricity, and Dzyaloshinskii-Moriya Interactions of Janus Vanadium Dichalcogenides.

Due to the lack of inversion symmetry and the discovery of room-temperature ferromagnetism, two-dimensional semiconducting vanadium-based van der Waals transition-metal dichalcogenides (V-TMDs) are drawing attention for their possible application in spintronics and valleytronics. Here, we show the functional properties enriched by the broken inversion, out-of-plane mirror, and time-reversal symmetries of Janus H-VXY TMDs (X, Y = S, Se, Te). By first-principles calculations, we reveal the intrinsic xy easy-plane magnetism of the Janus vanadium-based TMD monolayers and systematically study their hidden valley polarization and giant magneto band structure. Their strong nearest-neighbor exchange strengths lead to near-room-temperature magnetic phase transitions. The Janus H-VXY system also exhibits piezoelectricity with nonzero e31 and e21. Interestingly, it is found that the right-handed Dzyaloshinskii-Moriya interaction has nonzero in-plane components in our Janus system, with fluctuating magnitudes determined by competence between relaxed bond-angle and atomic index of ligands.

Strain-Control of Cycloidal Spin Order in a Metallic Van der Waals Magnet.

The manipulation of magnetism through strain control is a captivating area of research with potential applications for low-power devices that do not require dissipative currents. Recent investigations of insulating multiferroics have unveiled tunable relationships among polar lattice distortions, Dzyaloshinskii-Moriya interactions (DMI), and cycloidal spin orders that break inversion symmetry. These findings have raised the possibility of utilizing strain or strain gradient to manipulate intricate magnetic states by changing polarization. However, the effectiveness of manipulating cycloidal spin orders in "metallic" materials with screened magnetism-relevant electric polarization remains uncertain. In this study, the reversible strain control of cycloidal spin textures in a metallic van der Waals magnet, Cr1/3 TaS2 , through the modulation of polarization and DMI induced by strain is demonstrated. With thermally-induced biaxial strains and isothermally-applied uniaxial strains, systematic manipulation of the sign and wavelength of the cycloidal spin textures is realized, respectively. Additionally, unprecedented reflectivity reduction under strain and domain modification at a record-low current density are also discovered. These findings establish a connection between polarization and cycloidal spins in metallic materials and present a new avenue for utilizing the remarkable tunability of cycloidal magnetic textures and optical functionality in van der Waals metals with strain.

Topological Spin Textures in a Non-Collinear Antiferromagnet System.

Topologically protected magnetic "whirls" such as skyrmions in antiferromagnetic materials have recently attracted extensive interest due to their nontrivial band topology and potential application in antiferromagnetic spintronics. However, room-temperature skyrmions in natural metallic antiferromagnetic materials with merit of probable convenient electrical manipulation have not been reported. Here, room-temperature skyrmions are realized in a non-collinear antiferromagnet, Mn3 Sn, capped with a Pt overlayer. The evolution of spin textures from coplanar inverted triangular structures to Bloch-type skyrmions is achieved via tuning the magnitude of interfacial Dzyaloshinskii-Moriya interaction. Beyond that, the temperature can induce an unconventional transition from skyrmions to antiferromagnetic meron-like spin textures at ≈220 K in the Mn3 Sn/Pt samples. Combining with the theoretical calculations, it is found that the transition originates from the temperature dependence of antiferromagnetic exchange interaction between kagome sublayers within the Mn3 Sn crystalline unit-cell. These findings open the avenue for the development of topological spin-swirling-based antiferromagnetic spintronics.

Transformation from Magnetic Soliton to Skyrmion in a Monoaxial Chiral Magnet.

Topological spin textures are of great interest for both fundamental physics and applications in spintronics. The Dzyaloshinskii-Moriya interaction underpins the formation of single-twisted magnetic solitons or multi-twisted magnetic skyrmions in magnetic materials with different crystallographic symmetries. However, topological transitions between these two kinds of topological objects have not been verified experimentally. Here, the direct observation of transformations from a chiral soliton lattice (CSL) to magnetic skyrmions in a nanostripe of the monoaxial chiral magnet CrNb3 S6  using Lorentz transmission electron microscopy is reported. In the presence of an external magnetic field, helical spin structures first transform into CSLs and then evolve into isolated elongated magnetic skyrmions. The detailed spin textures of the elongated magnetic skyrmions are resolved using off-axis electron holography and are shown to comprise two merons, which enclose their ends and have unit total topological charge. Magnetic dipolar interactions are shown to play a key role in the magnetic soliton-skyrmion transformation, which depends sensitively on nanostripe width. The findings here, which are consistent with micromagnetic simulations, enrich the family of topological magnetic states and their transitions and promise to further stimulate the exploration of their emergent electromagnetic properties.

Loss of classicality in alternating spin-12/spin-1 chain, in the presence of next-neighbor couplings and Dzyaloshinskii-Moriya interactions.

We have considered and alternating spin-12/spin-1 chain with nearest-neighbor (NN) (J1), next-nearest neighbor (NNN) (J2) antiferromagnetic (AFM) Heisenberg interactions along withz-component of the Dzyaloshinskii-Moriya (DM) (Dz) interaction. The Hamiltonian has been studied using (a) linear spin-wave theory and (b) density matrix renormalization group. The system had been reported earlier as a classical ferrimagnet only when NN exchange interactions are present. Both the AFM NNN interactions and DM interactions introduce strong quantum fluctuations and due to which all the signatures of ferrimagnetism vanishes. We find that the nonzeroJ2introduces strong quantum fluctuations in each of the spin sites due to which thez-components of both spin-1 and spin-1/2 sites average out to be zero. The ground state becomes a singlet. The presence ofJ1along withDzintroduces a short range order but develops long range order along theXYplane.J1along withJ2induces competing phases with structure factor showing sharp and wide peaks, at two different angles reflecting the spin spiral structure locally as well as in the underlying lattice. Interestingly, we find that theDzterm removes the local spin spiral structure inz-direction, while developing a spiral order in theXYplane.

Dynamic Symmetry Breaking in Chiral Magnetic Systems.

The Dzyaloshinskii-Moriya interaction (DMI) in magnetic systems stabilizes spin textures with preferred chirality, applicable to next-generation memory and computing architectures. In perpendicularly magnetized heavy-metal/ferromagnet films, the interfacial DMI originating from structural inversion asymmetry and strong spin-orbit coupling favors chiral Néel-type domain walls (DWs) whose energetics and mobility remain at issue. Here, a new effect is characterized in which domains expand unidirectionally in response to a combination of out-of-plane and in-plane magnetic fields, with the growth direction controlled by the in-plane field strength. These growth directionalities and symmetries with applied fields cannot be understood from static treatments alone. The authors theoretically demonstrate that perpendicular field torques stabilize steady-state magnetization profiles highly asymmetric in elastic energy, resulting in a dynamic symmetry breaking consistent with the experimental findings. This phenomenon sheds light on the mechanisms governing the dynamics of Néel-type DWs and expands the utility of field-driven DW motion to probe and control chiral DWs.

Interplay between Spin-Orbit Torques and Dzyaloshinskii-Moriya Interactions in Ferrimagnetic Amorphous Alloys.

Ferrimagnetic thin films are attractive for low-power spintronic applications because of their low magnetization, small angular momentum, and fast spin dynamics. Spin orbit torques (SOT) can be applied with proximal heavy metals that also generate interfacial Dzyaloshinskii-Moriya interactions (DMI), which can stabilize ultrasmall skyrmions and enable fast domain wall motion. Here, the properties of a ferrimagnetic CoGd alloy between two heavy metals to increase the SOT efficiency, while maintaining a significant DMI is studied. SOT switching for various capping layers and alloy compositions shows that Pt/CoGd/(W or Ta) films enable more energy-efficient SOT magnetization switching than Pt/CoGd/Ir. Spin-torque ferromagnetic resonance confirms that Pt/CoGd/W has the highest spin-Hall angle of 16.5%, hence SOT efficiency, larger than Pt/CoGd/(Ta or Ir). Density functional theory calculations indicate that CoGd films capped by W or Ta have the largest DMI energy, 0.38 and 0.32 mJ m-2 , respectively. These results show that Pt/CoGd/W is a very promising ferrimagnetic structure to achieve small skyrmions and to move them efficiently with current.

Imaging and Tailoring the Chirality of Domain Walls in Magnetic Films.

Electric-current-induced magnetization switching is a keystone concept in the development of spintronics devices. In the last few years this field has experienced a significant boost with the discovery of ultrafast domain wall motions and very low threshold currents in structures designed to stabilize chiral spin textures. Imaging domain-wall spin textures in situ, while fabricating magnetic multilayer structures, is a powerful way to investigate the forces stabilizing this type of chirality, and informs strategies to engineer structures with controlled spin textures. Here, recent results applying spin-polarized low-energy electron microscopy to image chiral domain walls in magnetic multilayer films are summarized. Providing a way to measure the strength of the asymmetric exchange interaction that causes the chirality, this approach can be used to tailor the texture and handedness of magnetic domain walls by interface engineering. These results advance understanding of the underlying physics and offer new insights toward the design of spintronic devices.