Electric field switching of altermagnetic spin-splitting in multiferroic skyrmions

Abstract

Magnetic skyrmions are localized magnetic structures that retain their shape and stability over time, thanks to their topological nature. Recent theoretical and experimental progress has laid the groundwork for understanding magnetic skyrmions characterized by negligible net magnetization and ultrafast dynamics. Notably, skyrmions emerging in materials with altermagnetism, a novel magnetic phase featuring lifted Kramers degeneracy-have remained unreported until now. In this study, we demonstrate that BiFeO3, a multiferroic renowned for its strong coupling between ferroelectricity and magnetism, can transit from a spin cycloid to a Neel-type skyrmion under antidamping spin-orbit torque at room temperature. Strikingly, the altermagnetic spin splitting within BiFeO3 skyrmion can be reversed through the application of an electric field, revealed via the Circular photogalvanic effect. This quasiparticle, which possesses a neutral topological charge, holds substantial promise for diverse applications-most notably, enabling the development of unconventional computing systems with low power consumption and magnetoelectric controllability.

Figures (16)

• Figure 1: Concept of magnetoelectric altermagnet. a, Crystal structure of BFO, with Bi atoms in red, Fe atoms in yellow, and O atoms in purple. The illustration shows the ferroelectric polarization $\mathbf{P}$ along the [111] direction and the octahedral rotation of oxygen, which induces a homogeneous DMI ($\mathbf{D}_1$) parallel to the polarization as well as an inhomogeneous DMI ($\mathbf{D}_2$); the magnetic moments within the unit cell exhibit antiferromagnetic arrangement. b, c, Spin-splitting energy dispersion of BFO. The splitting energy value is calculated for the highest band below the Fermi energy, revealing the spin-polarized band structure in $\mathbf{K}$-space. The ferroelectric polarizations are along [111] (b) and [$1\bar{1}1$] (c) axis, respectively.
• Figure 1: BFO band structure. a, First Brillouin zone of BFO. The high symmetric points are highlighted. b-d, First-principle calculated band structures for BFO with the ferroelectric polarization $\mathbf{P}$ pointing along [111] (b), [$\bar{1}\bar{1}\bar{1}$] (c) and [$\bar{1}11$] (d) directions, respectively.
• Figure 2: Magnetic structures and phase transition in BFO under spin current injection. a,Calculated phase diagram versus DMI and injected current densities $J_c$. Insets schematically illustrate the spin cycloid ground state (left), magnetic stripes (top right), and skyrmion (bottom right). b, Schematic of the experimental setup. The SOC layer is deposited on the BFO film and the scan nitrogen vacancy microscope (SNVM) is placed atop for imaging. A spin current $J_s$, generated via the spin Hall effect in the SOC layer, is injected into BFO, which triggers a phase transition from the cycloid state to the skyrmion. The directions of the SNVM axis and the sample structure (including the SOC layer and the BFO layer) are labeled in the figure. c, Magnetic domain image of the spin cycloid in BFO. Red and black arrows in (c) indicate the polarization direction $\mathbf{P}$ and the propagating direction $\mathbf{q}$, respectively, within a single domain. Black dashed lines indicate the domain boundaries. d, Image of skyrmions (highlighted in red circles) after injecting a current of $1.3\times 10^7$ A/cm$^2$ through the SOC layer. The scale bar is 100 nm in (c) while 120 nm in (d). e, Normalized skyrmion number per $\mu$m$^2$ versus applied current density $I$ for two different top electrodes SIO/BFO (red) and Pt/BFO (blue).f, Normalized three-dimensional stray field map $\mathbf{B}(x,y)$ of a single skyrmion, obtained using SNVM on the sample surface, with $x$ and $y$ representing in-plane coordinates. In our experiment, the $x$-axis direction points along [100] while the direction points along [010]. g-i, Reconstructed stray field components along the $x$-axis (g), $y$-axis (h), and $z$-axis (i) directions based on panel (f). j, Simulated configuration of the skyrmion, with the homogeneous DMI ($\mathbf{D}_1$) direction aligned along the [100] direction. k-m, Simulated stray field distributions of the skyrmion in (f) along the $x$-axis (k), $y$-axis (l), and $z$-axis (m) directions. A one-to-one correspondence is observed between panels (g-i) and (k-m), confirming the presence of skyrmions. All experiments are conducted at room temperature.
• Figure 2: The antiferromagnetic order of BFO. A sketch of spin cycloid that propagates along $\mathbf{q}$= [$1\bar{1}0$]. Ferroelectric polarization $\mathbf{P}$ points along [111], while $\mathbf{D}_1$ and $\mathbf{D}_2$ represent homogeneous and inhomogeneous DMI, respectively, with $\mathbf{D}_2\parallel\mathbf{P}$, $\mathbf{D}_2\perp\mathbf{q}$, and $\mathbf{D}_1\parallel\mathbf{S}_1\times\mathbf{S}_2$.
• Figure 3: Electric field manipulation of skyrmions. a,b Left panels: Schematics of skyrmion with $\mathbf{D}_1$ along [$110$] (a) and [$1\bar{1}0$] (b) directions. Right panels: SNVM image of one skyrmion under E= -300 kV/cm (a) and E= 300 kV/cm (b), where corresponding polarization $\mathbf{P}$ aligns perpendicularly along [$110$] (a) and [$\bar{1}10$] (b). The comparison between simulated (left panels) and reconstructed stray field (right panels) along $x$-axis (c,d), $y$-axis (e,f), and $z$-axis (g,h) directions for corresponding skyrmions are shown below in (c,e,g) [based on panel (a)] and (d,f,h) [based on panel (b)]. Red and indigo arrows indicate the directions of $\mathbf{P}$ and $\mathbf{D}_1$, respectively. i-m, SNVM image represented by reconstructed stray field along $z$-axis after five consecutive electric field switching. The scale bar is 50 nm inlength.