Hybrid chiral domain walls and skyrmions in magnetic multilayers

Abstract

Noncollinear spin textures in ferromagnetic ultrathin films are currently the subject of renewed interest since the discovery of the interfacial Dzyaloshinskii-Moriya interaction (DMI). This antisymmetric exchange interaction selects a given chirality for the spin textures and allows stabilizing configurations with nontrivial topology including chiral domain walls (DWs) and magnetic skyrmions. Moreover, it has many crucial consequences on the dynamical properties of these topological structures. In recent years, the study of noncollinear spin textures has been extended from single ultrathin layers to magnetic multilayers with broken inversion symmetry. This extension of the structures in the vertical dimension allows room temperature stability and very efficient current-induced motion for both Néel DWs and skyrmions. We show how, in these multilayered systems, the interlayer interactions can actually lead to hybrid chiral magnetization arrangements. The described thickness-dependent reorientation of DWs is experimentally confirmed by studying demagnetized multilayers through circular dichroism in x-ray resonant magnetic scattering. We also demonstrate a simple yet reliable method for determining the magnitude of the DMI from static domain measurements even in the presence of these hybrid chiral structures by taking into account the actual profile of the DWs. The existence of these novel hybrid chiral textures has far-reaching implications on how to stabilize and manipulate DWs, as well as skymionic structures in magnetic multilayers.

Fig. 1. Micromagnetic simulations of hybrid chiral DWs for different DMI values.

(A to D) Cross-sectional view of a half simulation volume for [X(1)/Co(0.8)/Z(1)]₂₀ multilayer with D = −1.0, 0.0, 1.0, and 2.0 mJ m⁻² (top to bottom); the gray lines correspond to the Co layers. Arrows point in the direction of the magnetization, m_z is given by the color of the arrows from red (−1) to blue (+1), while m_y is displayed by the color of the grid from black (−1) to white (+1). (E to H) Polar angle θ inside the DW in each layer for D = −1.0 to 2.0 mJ m⁻². The blue-to-red gradient filling corresponds to the envelop of θ of all profiles in the different layers from bottom to top [see color scale in (E)], while the green line is θ_ave, the averaged θ of all layers across the thickness. (I to L) Azimuthal angle ψ inside the DW in each layer for D = −1.0 to 2.0 mJ m⁻². The blue-to-red lines again correspond to the layers from bottom to top.

Fig. 2. CD-XRMS analysis of different multilayer stacking configurations.

Multilayers with D < 0 and (A) 5 repetitions (sample II), (B) 10 repetitions (sample VII), and (C) 20 repetitions (sample IX) and with D > 0 and (D) 5 repetitions (sample III), (E) 10 repetitions (sample V), and (F) 20 repetitions (sample VIII). The dichroism is normalized for each image and indicated by the color scale from blue (negative) to red (positive). Left insets are the corresponding sum [circularly left (CL) + circularly right (CR)] images evidencing the magnetic distribution ordering. Right insets present schemes of the studied stackings.

Fig. 3. DW profile (black, left scale) and analytical model for estimation of DMI (green, right scale) and dipolar (red, right scale) fields for the top layer of (III) [Pt(1)/Co(0.8)/Ir(1)]₅.

The squares are the result of micromagnetic minimization of the energy, while the lines are the fields obtained from the model. The dashed and dotted blue lines are, respectively, surface and volume charge contributions to the interaction dipolar field (solid blue line). The red line is the total dipolar field from the model (obtained by adding the intralayer demagnetizing field to the interlayer interaction dipolar field). The parameter Δ has been adjusted for the magnetization arctan analytical profile to fit the micromagnetic profile.

Fig. 4. Diagram comparing Adip and ADMI for each multilayer that has been characterized by CD-XRMS.

When |${\mathcal{A}}_{\text{dip}}$| < |${\mathcal{A}}_{\text{DMI}}$|, pure Néel DWs are stabilized, and red (blue) indicates CW (CCW) chirality. The gradient areas correspond to |${\mathcal{A}}_{\text{dip}}$| > |${\mathcal{A}}_{\text{DMI}}$| with more and more pronounced reorientation into flux-closure DWs. Colored squares indicate the chirality as it has been observed by CD-XRMS for each sample labeled by roman numbers, where red stands for CW chirality and blue stands for CCW chirality.

Fig. 5. Micromagnetic simulations of the dynamics of hybrid chiral skyrmions.

(A) Cut view of the simulation volume for a [X(1)/Co(1)/Z(1)]₂₀ multilayer with D = 0.8 mJ m⁻². Arrows point in the direction of the magnetization, and m_z is given by the color of the arrows from red (−1) to blue (1), while m_y is displayed by the color of the grid from black (−1) to white (+1). The m_z component in the top layer is represented in perspective view by the color from red (−1) to blue (1). (B to D) Skyrmion velocities for different values of D and geometries. Right/up pointing blue/red triangles stand for horizontal/transverse velocity components, obtained for (B) opposite injection in bottommost/topmost layers, (C) identical injection in bottommost/topmost layers, and (D) uniform injection. The injection geometry is depicted by the inset in each case.