The orientation of a chiral magnetic domain wall in a racetrack determines its dynamical properties. In equilibrium, magnetic domain walls are expected to be oriented perpendicular to the stripe axis. We demonstrate the appearance of a unidirectional domain wall tilt in out-of-plane magnetized stripes with biaxial anisotropy and Dzyaloshinskii--Moriya interaction (DMI). The tilt is a result of the interplay between the in-plane easy-axis anisotropy and DMI. We show that the additional anisotropy and DMI prefer different domain wall structure: anisotropy links the magnetization azimuthal angle inside the domain wall with the anisotropy direction in contrast to DMI, which prefers the magnetization perpendicular to the domain wall plane. Their balance with the energy gain due to domain wall extension defines the equilibrium magnetization the domain wall tilting. We demonstrate that the Walker field and the corresponding Walker velocity of the domain wall can be enhanced in the system supporting tilted walls.
The longitudinal spin-Seebeck effect (SSE) in magnetic insulator$|$non-magnetic metal heterostructures has been theoretically studied primarily with the assumption of an isotropic interfacial exchange coupling. Here, we present a general theory of the SSE in the case of an antisymmetric Dzyaloshinskii-Moriya interaction (DMI) at the interface, in addition to the usual Heisenberg form. We numerically evaluate the dependence of the spin current on the temperature and bulk DMI using a pyrochlore iridate as a model insulator with all-in all-out (AIAO) ground state configuration. We also compare th…
We present a general approach for studying the dynamics of domain walls in biaxial ferromagnetic stripes with functionally graded Dzyaloshinskii-Moriya interaction (DMI). By engineering the spatial profile of the DMI parameter we propose the concept of a diode, which implements filtering of domain walls of certain topological charge and helicity. We base our study on phenomenological Landau-Lifshitz-Gilbert equations with additional Zhang-Li spin-transfer terms using a collective variable approach. In the effective equations of motion the gradients of DMI play the role of a driving force which…
The dynamics of magnetic skyrmion driven by spin-polarized current is theoretically studied in the chiral ferromagnetic film with spatially modulated Dzyaloshinskii-Moriya interaction. Three cases including linear, sinusoidal, and periodic rectangular modulations have been considered, where the increase, decrease, and the periodic modification of the size and velocity of the skyrmion have been observed in the microscopic simulations. These phenomena are well explained by the Thiele equation, where an effective force on the skyrmion is induced by the inhomogeneous Dzyaloshinskii-Moriya interact…
The influence of the Dzyaloshinskii-Moriya interaction in ultra-thin ferromagnetic films and chiral magnonic crystals on the behavior of spin waves is reviewed. During the last decade, it has been shown, both theoretically and experimentally, that this anisotropic exchange interaction produces non-reciprocal features on the spin-wave spectrum of a magnetic system, a phenomenon that occurs both for bulk and interfacial Dzyaloshinskii-Moriya coupling. More recently, the concept of a chiral magnonic crystal has been introduced, where the interfacial Dzyaloshinskii-Moriya interaction is periodic. …
In this paper, boundary conditions for Landau-Lifshitz equations at the interface between two ferromagnets with different Dzyaloshinskii-Moriya interactions are derived. We calculated and verified the analytical expression for the energy flux density continuity for the spin-wave propagation through the interface between two ferromagnets with/without Dzyaloshinskii-Moriya interactions considering the boundary conditions mentioned. Analytical expressions for reflection, transmission coefficients and the nonreciprocity factor are calculated in the case of spin-wave propagation through a double la…
The analytical model is developed for description of skyrmions and skyrmion-like magnetic structures in a two-sublattice antiferromagnet with uniaxial magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Relativistic contraction of skyrmion size in the direction of motion is demonstrated for subcritical case when the skyrmion velocity is less than spin wave velocity in antiferromagnet. Lorentz-like supercritical transformation are found for skyrmion-like magnetic structures moving with velocity greater than spin wave velocity in antiferromagnet.
Interfacial Dzyaloshinkii-Moriya interaction defines a rotational sense for the magnetization of two-dimensional films making it responsible for the formation of chiral magnetic structures like spin-spirals and skyrmions in those films. Here we show by means of atomistic calculations that in heterostructures magnetic layers can be additionally coupled by an interlayer Dzyaloshinskii-Moriya interaction across a spacer. We quantify this interaction in the framework of the Levy-Fert model for trilayers consisting of two ferromagnets separated by a non-magnetic spacer yielding non-trivial three-di…
Based on the micromagnetic simulations the magnetization switching in a triangle magnetic element by voltage-control of magnetic anisotropy and Dzyaloshinskii-Moriya interaction under in-plane magnetic field is proposed. The proposed switching scheme is not the toggle switching but the deterministic switching where the magnetic state is determined by the polarity of the applied voltage pulse. The mechanism and conditions for the switching are clarified. The results provide a fast and low-power writing method for magnetoresistive random access memories.
Anisotropic exchange couplings, such as the Dzyaloshinskii-Moriya interaction (DMI), have played a vital role in the formation and dynamics of spin textures. This work predicts an anisotropic conduction electron spin density in metals with heavy magnetic impurities. The polarization of this $Dzyaloshinskii$-$Moriya$ $spin$ $density$ (DM-SD) is not collinear to the localized magnetic moments but rotated by the spin-dependent skew scattering of heavy atoms. The DM-SD induces the DMI between magnetic moments in metals and, therefore, it is the anisotropic extension of the Rutherman-Kittel-Kasuya-…
We formulate a microscopic linear response theory of nonequilibrium magnonic torques and magnon pumping applicable to multiple-magnonic-band uniform ferromagnets with Dzyaloshinskii-Moriya interactions. From the linear response theory, we identify the extrinsic and intrinsic contributions where the latter is expressed via the Berry curvature of magnonic bands. We observe that in the presence of a time-dependent magnetization Dzyaloshinskii-Moriya interactions can act as fictitious electric fields acting on magnons. We study various current responses to this fictitious field and analyze the rol…
Determination of the energy of Dzyaloshinskii-Moriya interaction along with a definition of the basic magnetic characteristics in ferromagnetic/nonmagnetic multilayered systems are both required for the construction of a magnetic skyrmion recording medium. A method for estimating the energy of the effective Dzyaloshinskii-Moriya interaction which compared the periodicities of micromagnetically simulated and experimentally measured demagnetized domain structures was shown in a current paper. Symmetric epitaxial [Co/Pd(111)]5 superlattices with Co layers of varying thickness were used as the sys…
Creation of uni-directional spin-wave emitters by utilizing interfacial Dzyaloshinskii-Moriya interaction
我们提出了一个分析和数值研究的创建一个单向自旋波发射的超薄铁磁薄膜夹在一个不对称的层堆栈。为此，我们扩展自旋波波导中的自旋波的解析描述的结合界面上的Dzyaloshinskiii-Moriya相互作用的自旋波传播的影响。通过探索模型系统Ni $_{81}$ Fe $_{19}$ /Pt，我们表明，通过结合波矢选择性激发源和界面Dzyaloshinskiii-Moriya相互作用产生的频率分裂，可以实现单向自旋波发射。因此，我们专注于设备的特征尺寸和自旋波波长与国家的最先进的激发和检测方案兼容。我们证明了非互易发射的最佳操作条件可以使用所提出的分析形式主义预测
Doppler shift picture of the Dzyaloshinskii--Moriya interaction
我们提出的Dzyaloshinskii-Moriya（DM）相互作用的基础上的多普勒频移的想法的出现的自旋-轨道相互作用下破缺反转对称性诱导的内禀自旋电流的物理图片。这幅图被严格的有效哈密顿理论所证实，该理论揭示了DM系数由内禀自旋电流的大小给出。该表达式可直接应用于第一性原理计算，并阐明了相互作用与电子能带结构之间的关系。对于Skyrmion化合物Mn $_{1-x}$ Fe $_x$ Ge和Fe $_{1-x}$ Co $_x$ Ge，得到了与实验定量一致的结果。
The magnetic interfacial Dzyaloshinskii-Moriya interaction (DMI) in multi-layered thin films can lead to exotic chiral spin states, of paramount importance for future spintronic technologies. Interfacial DMI is normally manifested as an intralayer interaction, mediated via a paramagnetic heavy metal in systems lacking inversion symmetry. Here we show how, by designing synthetic antiferromagnets with canted magnetization states, it is also possible to observe interfacial interlayer-DMI at room temperature. The interlayer-DMI breaks the symmetry of the magnetic reversal process via the emergence…
Using in-plane field dependence of the precessional flow of chiral domain walls (DWs) to simultaneously determine bulk and interfacial Dzyaloshinskii-Moriya interactions (DMIs) is proposed. It is found that effective fields of bulk and interfacial DMIs have respectively transverse and longitudinal components that affect differently the motion of chiral DWs in magnetic narrow heterostructure strips. The in-plane field dependence of DW velocity has a dome-shape or a canyon-shape, depending on whether the driving force is an in-plane current or an out-of-plane magnetic field. The responses of the…
The Dzyaloshinskii Moriya Interaction (DMI) has laid the foundation for many novel chiral structures such as Skyrmions. In most of the studies so far, the DMI is present in the whole of the magnetic layer. Here, we report our investigations on a ferromagnetic nanowire where DMI is confined to a nanoscale region. We observe that the local modulation of magnetic properties causes oscillation of domain walls under the influence of spin-transfer torque. The oscillation frequency is tunable within a few GHz, making this observation potentially useful for applications in neuromorphic computing.
We show how a Dzyaloshinskii-Moriya interaction can be generated in an ultrathin metal film from the induced internal electric field created by an ultrashort electromagnetic pulse. This interaction does not require structural inversion-symmetry breaking, and its amplitude can be tuned depending on the amplitude of the field. We perform first-principles calculations to estimate the strength of the field-induced magnetoelectric coupling for ferromagnetic Fe, Co, and Ni, and antiferromagnetic Mn, as well as FePt alloys. Last, using atomistic simulations, we demonstrate how an isolated antiferroma…
We theoretically demonstrate that the presence of Dzyaloshinskii-Moriya Interaction (DMI) can lead to enhancement of the spin-motive force (SMF) arising due to field-induced ferromagnetic domain wall motion. A SMF refers to an electric voltage induced by dynamical magnetic textures, which reflects the temporal and spatial variations of the magnetization. A DMI can introduce extra spatial rotation of the magnetization in the domain wall region, which turns out to cause the enhancement of the SMF. We derive an expression for the SMF, and examine the field- and DMI-dependences of the SMF. We find…
We theoretically investigate the radial-spin-wave induced magnetic vortex switching in the presence of Dzyaloshinskii-Moriya interaction (DMI). From micromagnetic simulations, we observe a circular-to-radial vortex phase transition by increasing the DMI strength. The radial spin-wave excitation spectrum for each magnetization configuration is analyzed, showing that the frequency of spin-wave mode with a given radial node number monotonically increases (decreases) with the DMI parameter of the radial (circular) vortex. Interestingly, we find that the DMI can significantly facilitate the polarit…
Synthetic antiferromagnet (SAF) nanostructures with interfacial Dzyaloshinskii-Moriya interaction can host topologically distinct spin textures such as skyrmions and thus are regarded as promising candidates for both spintronics and magnonics applications. Here, we present comprehensive micromagnetic simulations of such material systems and discuss the rich phase diagrams that contain various types of magnetic configurations. Aside from the static properties, we further discuss the resonant excitations of the calculated magnetic states which include individual skyrmions and skyrmioniums. Final…
The antisymmetric Dzyaloshinskii-Moriya interaction (DMI) in noncentrosymmetric systems leads to various nonuniform chiral magnetic textures. Polarized neutron scattering is a powerful method for investigation such chiral distributions. The most used technique is a small-angle neutrons scattering (SANS). Multilayered magnetic films with the interface induced DMI (iDMI) can't be investigated by SANS because of their small volume. The appropriate technique is a polarized neutron reflectometry. Within the framework of the continuum theory of micromagnetics, we explore the impact of the iDMI on th…
We have studied the domain wall resistance in W/Ta/CoFeB/MgO heterostructures. The Ta layer thickness is varied to control the type of domain walls via changes in the interfacial Dzyaloshinskii Moriya interaction. We find a nearly constant domain wall resistance against the Ta layer thickness. Adding contributions from the anisotropic magnetoresistance, spin Hall magnetoresistance and anomalous Hall effect describe well the domain wall resistance of the thick Ta layer films. However, a discrepancy remains for the thin Ta layer films wherein chiral Néel-like domain walls are found. These result…
Multilayers of heavy metals and ferromagnets are the basis for the formation of various structures with inhomogeneous chiral magnetic distributions. The most informative method for studying magnetic states in such structures with a high spatial resolution is Lorentz transmission electron microscopy (L-TEM). Here, we report on the observation of chiral Néel domain walls by means of L-TEM in Co/Pt multilayers with perpendicular magnetic anisotropy. We explain the existence of chiral Néel internal structure due to the overcritical, giant interfacial induced Dzyaloshinskii-Moriya interaction. Our …
We theoretically study the effect of Dzyaloshinskii-Moriya interaction (DMI) on the focusing of a spin-wave lens that is constructed by a circular interface between two magnetic films. We analytically derive the generalized Snell's law in the curved geometry and the position of the focal point which exhibits a peculiar off-axial focusing behavior. We uncover a strong dependence of the focal point on both the material parameters and the frequency of incident spin waves. Full micromagnetic simulations compare well with theoretical predictions. Our findings would be helpful to manipulate spin wav…
We study the interaction of surface acoustic waves with spin waves in ultra-thin CoFeB/Pt bilayers. Due to the interfacial Dzyaloshinskii-Moriya interaction (DMI), the spin wave dispersion is non-degenerate for oppositely propagating spin waves in CoFeB/Pt. In combination with the additional nonreciprocity of the magnetoacoustic coupling itself, highly nonreciprocal acoustic wave transmission through the magnetic film is observed. We systematically characterize the magnetoacoustic wave propagation in a thickness series of CoFeB($d$)/Pt samples as a function of magnetic field magnitude and dire…
We have investigated magnetoelectric coupling in the single-molecule magnet $\mathrm{Mn}_{4}\mathrm{Te}_{4}(\mathrm{P}\mathrm{Et}_{3})_{4}$ with tetrahedral spin frustration. Our density functional studies found that an electric dipole moment can emerge with various non-collinear spin orderings. The forms of spin-dependent dipole are determined and consistent with that in non-centrosymmetric magnets driven by the Dzyaloshinskii-Moriya interaction. Writing a parameterized spin Hamiltonian, after solving for eigenvalues and eigenstates we quantified the magnetoelectric coupling by calculating th…
In antiferromagnetic (AFM) thin films, broken inversion symmetry or coupling to adjacent heavy metals can induce Dzyaloshinskii-Moriya (DM) interactions. Knowledge of the DM parameters is essential for understanding and designing exotic spin structures, such as hedgehog Skyrmions and chiral Néel walls, which are attractive for use in novel information storage technologies. We introduce a framework for computing the DM interaction in two-dimensional Rashba antiferromagnets. Unlike in Rashba ferromagnets, the DM interaction is not suppressed even at low temperatures. The material parameters cont…
Interfacial Dzyaloshinskii-Moriya interaction (DMI) is experimentally investigated in Pt/Co/Pt multilayer films under strain. A strong variation (from 0.1 to 0.8 mJ/m$^2$) of the DMI constant is demonstrated at $\pm 0.1\%$ in-plane uniaxial deformation of the films. The anisotropic strain induces strong DMI anisotropy. The DMI constant perpendicular to the strain direction changes sign while the constant along the strain direction does not. Estimates are made showing that DMI manipulation with an electric field can be realized in hybrid ferroelectric/ferromagnetic systems. So, the observed eff…
