Strongly enhanced lifetime of higher-order bimerons and antibimerons

Abstract

Magnetic bimerons, similar to skyrmions, are topologically nontrivial spin textures characterized by topological charge $Q$. Most studies so far have focused on low-$Q$ solitons ($|Q| \leq 1$), such as skyrmions, bimerons, and vortices. Here, we present the first calculations of the lifetimes of high-$Q$ bimerons and demonstrate that they are fundamentally more stable than high-$Q$ skyrmions over a wide range of temperature. To obtain realistic results, our chosen system is an experimentally feasible van der Waals interface, Fe$_3$GeTe$_2$/Cr$_2$Ge$_2$Te$_6$. We show that the lifetimes of high-$Q$ (anti)bimerons can exceed the lifetime of those with $|Q|=1$ by 3 orders of magnitude. Remarkably, this trend remains valid even when extrapolated to room temperature (RT), as the lifetimes are dominated by entropy rather than energy barriers. This contrasts with high-$Q$ skyrmions, whose lifetimes fall with $|Q|$ near RT. We attribute this fundamental difference between skyrmions and bimerons to their distinct magnetic texture symmetries, which lead to different entropy-dominated lifetimes.

Figures (4)

• Figure 1: (a) Side view of the Fe$_3$GeTe$_2$/Cr$_2$Ge$_2$Te$_6$ (FGT/CGT) van der Waals heterostructure and the calculated exchange interactions and DMI as a function of distance $r_{ij}$ between sites $i$ and $j$ in arbitrary nearest neighbors of its CGT layer. (b) Top view of relaxed zero-field spin textures with $Q$ ranging from $-5$ to 5 for both bimerons and skyrmions. Scale bar, 5 nm. (c) The binding energy $E_\text{bd}$ of bimerons (bi) and skyrmions (sk) as a function of $Q$. Negative values indicate that high-$Q$ states are energetically more favorable than separated low-$Q$ solitons. The right part displays the interfacial DMI energy densities, defined as $\varepsilon_{ij} = (\hat{\mathbf{r}}_{ij} {\times} \hat{z}) \cdot \left( \mathbf{m}_i {\times} \mathbf{m}_j \right)$, for low-$Q$ skyrmions (1), antiskyrmions (2), $Q = -2$ skyrmions (3), and low-$Q$ bimerons (4). Red, blue, and white indicate positive, negative, and vanishing Néel DMI energy contributions, respectively, corresponding to Néel-type domain walls with opposite directions and Bloch-type domain walls. For solitons with the same polarity, regions with opposite $\varepsilon$ can bind energy freely.
• Figure 2: (a) Minimum energy path (MEP) of bimerons (left) and skyrmions (right) with $Q$ ranging from $-5$ to $5$. The inset shows the definition of energy barrier ($\Delta E$), corresponding to stepwise transitions between neighboring topological charges. (b) Total energy barriers for bimerons (red) and skyrmions (black) as a function of $Q$. (c) Same as (a), but showing the energy decomposition: exchange (open circles), DMI (filled squares), and MAE (filled triangles). (d) Schematic illustration of the energy curve during the binding of a $Q = -5$ bimeron and its collapse to a $Q = -4$ bimeron. The inset shows the spin configurations of a $Q = -1$ bimeron, the $Q = -5$ bimeron and its SP, and the $Q = -4$ bimeron. The energy barrier mainly comes from the collapse of one meron pair, as indicated by the red arrow and rectangles. The right part of (e) shows its approximation with two subprocesses. The exchange energy contributions for $\Delta E - \Delta E_\text{I}$ (f) and $E_\text{II}$ (e) are shown below, corresponding to the energy barrier and the binding energy, respectively. The consistency between the two panels indicates that the increase in exchange energy arises from the unbinding process $\text{I}$.
• Figure 3: Dependence of (a) the pre-exponential factor $\Gamma_{0}$ (with $T = 1 \,\text{K}$, cf. Eq. (\ref{['pf']}), (b) the dynamical prefactor $\Lambda$, (c) the contribution of nonzero modes to $\Gamma_{0}$ within the harmonic approximation, $\sqrt{H_{\mathrm{A}}/H_{\mathrm{\ddagger}}}$, and (d) the contribution of zero modes to $\Gamma_{0}$, ${Z_{\mathrm{\ddagger}}/Z_{\mathrm{A}}}$, on the topological charge $Q$ for bimerons and skyrmions. (e-f) Characteristic lengths of translational (green), rotational (purple), and helicity (blue) modes for bimerons and skyrmions, respectively. Solid and dotted lines correspond to the initial and SP states, respectively. The translational mode increases linearly with $Q$, effectively reducing $\Gamma_0$. The inset in (c) displays the helicity mode of antiskyrmions ($Q = 1$), characterized by $\Delta \gamma = \theta_{\text{hel}}$. This mode is degenerate with the rotational mode only in the initial state, where the symmetric magnetic textures impose the relation $\theta_{\text{hel}} = 2\theta_{\text{rot}}$, but it becomes a nonzero mode at the SP.
• Figure 4: (a) Lifetimes of bimerons (bi) and antibimerons (abi) at $B = 0$ T shown over inverse temperature for different $Q$. (b) Same as (a) but for skyrmions (sk) and antiskyrmions (ask). (c-d) corresponding high-temperature ($T = 300$ K) behavior, zoomed in from (a) and (b), respectively. The markers highlight the lifetimes of $|Q|=1$ (blue) and $|Q|=3$ (red) bimerons and antiskyrmions at 10 K and room temperature (RT). For comparison, the skyrmion lifetime in Pd/Fe/Ir(111) at $B = 3.9$ T (dashed-dotted lines) is given Malottki2019.