Magnetic bimerons as skyrmion analogues in in-plane magnets

A magnetic bimeron is a pair of two merons and can be understood as the in-plane magnetized version of a skyrmion. Here we theoretically predict the existence of single magnetic bimerons as well as bimeron crystals, and compare the emergent electrodynamics of bimerons with their skyrmion analogues. We show that bimeron crystals can be stabilized in frustrated magnets and analyze what crystal structure can stabilize bimerons or bimeron crystals via the Dzyaloshinskii-Moriya interaction. We point out that bimeron crystals, in contrast to skyrmion crystals, allow for the detection of a pure topological Hall effect. By means of micromagnetic simulations, we show that bimerons can be used as bits of information in in-plane magnetized racetrack devices, where they allow for current-driven motion for torque orientations that leave skyrmions in out-of-plane magnets stationary.

Figure 1

Magnetic textures. (a) If the magnetic moments of a magnetic skyrmion (top) are rotated by ${90}^{\circ }$ around the $y$ axis the resulting texture is a magnetic bimeron (bottom), which requires a stabilizing magnetic field $\mathit{B}$ and has net magnetization $\mathit{M}$, both rotated in the same way. The emergent field ${\mathit{B}}_{\mathrm{em}}$ remains out-of plane. (b)–(d) show the necessary geometry of magnetic atoms (black) and heavy metal atoms (blue, green) to generate the DMI vectors (red), which stabilize (e)–(g) isolated skyrmions, bimerons and antiskyrmions, respectively. (h)–(j) show periodic arrays. The color in the magnetic textures indicates the out-of plane component of the magnetization (blue: positive, red: negative). (a) shows schematic representations. (e)–(g) are relaxed metastable textures from propagating the LLG equation in a ferromagnetic background at zero temperature for the parameters: $D=J/3, \left|K\right|=\left|B\right|=J/15$ (here $J$ is the nearest-neighbor exchange constant) and Gilbert damping $\alpha =0.01$. (h)–(j) are results of Monte Carlo simulations at zero temperature, with $D=J, \left|B\right|=\left|K\right|=0.3J$. Magnetic field $\mathit{B}$ and easy-axis anisotropy $\mathit{K}$ point along $z$ for the skyrmion, $x$ for the bimeron and $-z$ for the antiskyrmion; the corresponding DMI vectors have been used.

Figure 2

Hall resistivity (schematic). We compare the signal for a bimeron (red) and a skyrmion (blue). While the signal is purely of topological origin in the bimeron phase (here stable for magnetic fields in $x$ direction between 0.5 and $1\mathrm{T}$), it is superimposed by the ordinary Hall (cf. slope of the gray curve) and the anomalous Hall effect (offset of the gray curve) for the skyrmion (here the stabilizing field is applied along $z$).

Figure 3

Current-driven motion of magnetic bimerons and skyrmions. (a) Superposition of three results of micromagnetic simulations of a bimeron in an in-plane magnet with periodic boundary conditions starting from the orange circle (top left). The bimerons are driven by SOT type (i) (injected spins ${\mathit{s}}_{\mathrm{in}}\parallel \mathit{x},\mathit{y},\mathit{z}$ as indicated). (b) Bimeron (top) and skyrmion (bottom) in a racetrack geometry driven by SOT type (ii) (current along the track $j_x=5\mathrm{MA}/{\mathrm{cm}}^2$, injected spins ${\mathit{s}}_{\mathrm{in}}\parallel \mathit{y}$). The demagnetization field is set to zero. (c) Like (b) but with demagnetization field. (d) Like (c) but at double the current density. In all panels, the trajectory (orange) of the center of the bimeron or skyrmion is indicated; the figures show the results after $10-\mathrm{ns}$ propagation time, except for (d) bottom, where the skyrmion already annihilates after $0.5\mathrm{ns}$.