Electric-field control of skyrmions in multiferroic heterostructure via magnetoelectric coupling

Abstract

Room-temperature skyrmions in magnetic multilayers are considered to be promising candidates for the next-generation spintronic devices. Several approaches have been developed to control skyrmions, but they either cause significant heat dissipation or require ultrahigh electric fields near the breakdown threshold. Here, we demonstrate electric-field control of skyrmions through strain-mediated magnetoelectric coupling in ferromagnetic/ferroelectric multiferroic heterostructures. We show the process of non-volatile creation of multiple skyrmions, reversible deformation and annihilation of a single skyrmion by performing magnetic force microscopy with in situ electric fields. Strain-induced changes in perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction strength are characterized experimentally. These experimental results, together with micromagnetic simulations, demonstrate that strain-mediated magnetoelectric coupling (via strain-induced changes in both the perpendicular magnetic anisotropy and interfacial Dzyaloshinskii-Moriya interaction is responsible for the observed electric-field control of skyrmions. Our work provides a platform to investigate electric-field control of skyrmions in multiferroic heterostructures and paves the way towards more energy-efficient skyrmion-based spintronics.

Fig. 1. Structure and skyrmion characterizations.

a Schematic of the sample configuration. b Cross-sectional HAADF-STEM image of the multilayer and corresponding EDX mapping for element distributions of Pt (green), Co (red) and Ta (blue) with a scale bar of 5 nm. c Out-of-plane magnetic hysteresis. d–f Magnetic-domain evolutions with increasing magnetic field with the same scale bar of 1 μm. g Line-cut profile along the yellow dot line in the inset with Gaussian fitting (red curve), the inset is magnified individual skyrmion with a scale bar of 100 nm. h Representative L-TEM image of skyrmions with a scale bar of 1 μm.

Fig. 2. Variations of strain, interfacial DMI, and magnetic anisotropy.

a Out-of-plane strain variations of PMN-PT(001) substrate. b Wave-vector dependence of Δf under different electric fields with the interfacial DMI values in the inset with the error bar obtained from the standard error of Lorentzian fitting. c Angle-dependent FMR resonance field H_r(θ) and corresponding Kittel formula fitting (solid lines). d K_eff versus electric-field curve.

Fig. 3. Skyrmion creation.

MFM images at E = +0 kV/cm (a), −4 kV/cm (b), −0 kV/cm (c), and +4 kV/cm (d) with B_bias = 60 mT. Corresponding simulation results of strain-mediated skyrmion creation with ${\epsilon }_{\left[110\right]}={\epsilon }_{\left[-110\right]}=0$ (initial state) and D = 0.772 mJ/m² (e), ${\epsilon }_{\left[110\right]}={\epsilon }_{\left[-110\right]}=-0.189\%$ and D = 0.585 mJ/m² (f), ${\epsilon }_{\left[110\right]}={\epsilon }_{\left[-110\right]}=-0.034\%$ and D = 0.685 mJ/m² (g), and ${\epsilon }_{\left[110\right]}={\epsilon }_{\left[-110\right]}=-0.010\%$ and D =  0.727 mJ/m² (h), with the blue and red contrasts corresponding to magnetizations pointing up and down, respectively. The scale bar is 1 μm. Evolutions of in-plane biaxial compressive strain ${\epsilon }_{\mathrm{in-plane}}={\epsilon }_{\left[110\right]}={\epsilon }_{\left[-110\right]}$ (i), magnetoelastic energy density f_mel (j), and intrinsic energy density f_intrin (k). The time stages are t₀ (E = +0 kV/cm), t₁ (E = −4 kV/cm), t₂ (E = −0 kV/cm), and t₃ (E = + 4 kV/cm), respectively. The insets of k are the corresponding individual skyrmion evolutions with a scale bar of 50 nm.

Fig. 4. Skyrmion deformation.

Isolated skyrmion morphology at E = +0 kV/cm (a), −4 kV/cm (b), −0 kV/cm (c), +4 kV/cm (d), +0 kV/cm (e), and −4 kV/cm (f) with B_bias = 55 mT. g, h Skyrmion line-cut profiles along the major and minor axes in a and b with Gaussian fittings (solid lines), respectively. The insets in a–f show the simulation results of strain-mediated deformation of one single skyrmion with ${\epsilon }_{\left[-110\right]}\mathrm{=}{\epsilon }_{\left[110\right]}\mathrm{=}0$ D  = 0.772 mJ/m² for +0 kV/cm (a), ${\epsilon }_{\left[-110\right]}=-0.169\%$, ${\epsilon }_{\left[110\right]}=0$, D  = 0.585 mJ/m² for −4 kV/cm (b), ${\epsilon }_{\left[-110\right]}={\epsilon }_{\left[110\right]}=-0.023\%$ D = 0.685 mJ/m² for −0 kV/cm (c), and ${\epsilon }_{\left[-110\right]}={\epsilon }_{\left[110\right]}=-0.012\%$ D = 0.727 mJ/m² for +4 kV/cm (d). The scale bar is 100 nm.

Fig. 5. Skyrmion creation/annihilation.

Isolated skyrmion morphology at E = +0 kV/cm (a), −4 kV/cm (b), −0 kV/cm (c), +4 kV/cm (d), +0 kV/cm (e), and −4 kV/cm (f) with B_bias = 55 mT. The insets in a–f show the simulation results of strain-mediated annihilation and reappearance of one single skyrmion with ${\epsilon }_{\left[-110\right]}={\epsilon }_{\left[110\right]}=0$, D = 0.772 mJ/m² for E = +0 kV/cm (a, e); ${\epsilon }_{\left[-110\right]}={\epsilon }_{\left[110\right]}=-0.0425\%$, D = 0.585 mJ/m² for E = −4 kV/cm (b, f); ${\epsilon }_{\left[-110\right]}={\epsilon }_{\left[110\right]}=-0.0415\%$, D = 0.685 mJ/m² for E = −0 kV/cm (c); and ${\epsilon }_{\left[-110\right]}={\epsilon }_{\left[110\right]}=-0.012\%$, D = 0.727 mJ/m² for E = +4 kV/cm (d). A 20-nm diameter pinning site with ~5% lower perpendicular anisotropy was specified, as indicated by the dashed circle in the center. The scale bar is 100 nm.