Strongly pinned skyrmionic bubbles and higher-order nonlinear Hall resistances at the interface of Pt/FeSi bilayer

Engineering of magnetic heterostructures for spintronic applications has entered a new phase, driven by the recent discoveries of topological materials and exfoliated van der Waals materials. Their low-dimensional properties can be dramatically modulated in designer heterostructures via proximity effects from adjacent materials, thus enabling the realization of diverse quantum states and functionalities. Here we investigate spin-orbit-coupling proximity effects of Pt on the recently discovered quasi-two-dimensional ferromagnetic state at the FeSi surface. Skyrmionic bubbles (SkBs) are formed as a result of the enhanced interfacial Dzyloshinsky-Moriya interaction. The strong pinning effects on the SkBs are evidenced from the significant dispersion in size and shape of the SkBs and are further identified as a greatly enhanced threshold current density required for depinning of the SkBs. The robust integrity of the SkB assembly leads to the emergence of higher-order nonlinear Hall effects in the high current density regime, which originate from nontrivial Hall effects due to the noncollinearity of the spin texture, as well as from the current-induced magnetization dynamics via the augmented spin-orbit torque.

Figure 1

Magnetic properties at the interface between Pt ($t=3$ nm) and FeSi ($t=5$ nm). (a) Schematic picture of the Pt/FeSi bilayer. As a consequence of the spin-orbit-coupling (SOC) proximity of Pt, the interfacial Dzyaloshinsky-Moriya (DM) interaction twists the spins at the ferromagnetic-metal (FM) surface of FeSi with the nonmagnetic-insulating (NI) bulk, inducing noncollinear spin textures. Here ${\mathit{D}}_{12}$ represents the DM vector acting on spins ${\mathit{S}}_1$ and ${\mathit{S}}_2$. (b) Temperature dependence of the magnetization $M$ under an out-of-plane magnetic field ${\mu }_0{H}_{\mathrm{out}}=0.1$ T. The kink around $T=295$ K represents the helimagnetic ordering. (c) and (d) Out-of-plane and in-plane magnetic-field dependence of magnetization at various temperatures. The measured data (color dots) are smoothed (color lines) for clarity. The unit area corresponds to $\sqrt{3}{a}^2$, where $a$ is the lattice constant of the cubic unit cell of FeSi.

Figure 2

Magnetic force microscopy (MFM) imaging of the Hall-bar patterned Pt/FeSi bilayer under out-of-plane magnetic fields $H_{\mathrm{out}}$ at $T=10.8$ K. (a) Experimental setup for MFM imaging. The Au/Ti electrode pads (yellow regions) are used for the injection of current pulses and the detection of Hall voltages. Inset shows schematic illustrations of the expected magnetic structures, i.e., a transverse-conical state (cycloidal spin modulation with an in-plane ferromagnetic component) and a skyrmionic-bubble state (bimeron in an in-plane magnetization background). (b)–(e) MFM images at ${\mu }_0{H}_{\mathrm{out}}=0$ T (b), 0.4 T (c), 0.6 T (d), and 1.0 T (e). No current pulses were applied before taking the MFM images. The line scans along #b1, #c1, and #c2 (dashed lines) are shown in the insets of panels (b) and (c). The scale bars represent 2 $\mu \mathrm{m}$.

Figure 3

Current-induced changes in the magnetic domain pattern at zero magnetic field. (a) and (b) Magnetic force microscopy (MFM) images after the injection of the pulse train (i.e., successive three-current pulses with current density $J=1.5\times {10}^{11}$ A/${\mathrm{m}}^2$, with a duration of 10 ms, and at intervals of 1 s) in the positive (a) and negative (b) directions. (c) Difference between the MFM images [panels (a) and (b)] with the opposite current polarities. (d)–(f) MFM images [panels (d) and (e)] and difference image [panel (f)] in the case of the higher current density $J=2.5\times {10}^{11}$ A/${\mathrm{m}}^2$. The scale bars represent 2 $\mu \mathrm{m}$. (g) Current density $J$ dependence of the total difference integrated over the scanned area. The typical threshold current density $J_{\mathrm{c}}$ is estimated as the intersection of the dashed lines.

Figure 4

Fundamental $R_{yx}^{\left(1f\right)}$ and higher-order harmonic $R_{yx}^{\left(nf\right)}$ Hall resistances in response to the ac current $I=I_{0}sin\left(2\pi ft\right)$ ($I_0=30$ mA and $f=111$ Hz). (a)–(d) Out-of-plane magnetic-field $H_{\mathrm{out}}$ dependence of fundamental $R_{yx}^{\left(1f\right)}$ (a), second-harmonic $R_{yx}^{\left(2f\right)}$ (b), third-harmonic $R_{yx}^{\left(3f\right)}$ (c), and fifth-harmonic $R_{yx}^{\left(5f\right)}$ (d) at $T=10$ K. Fitting curves (gray lines) are produced on the basis of the spin-orbit-torque model (see main text and Supplemental Material [57] for details). (e) Schematic illustrations of the models for understanding mechanisms of nonlinear Hall effects: (i) oscillation of magnetization by a damping-like spin-orbit torque and (ii) deflection of conduction electrons by vector and scalar spin chiralities. (f) Comparison of the respective maximum values of $R_{yx}^{\left(nf\right)}$ ($n=1$–7) at $T=10$ K. No clear signals of forth- and sixth-harmonics are detected around zero magnetic field. (Also see Supplemental Material [57], Fig. S4.)