arXiv 2103.123432021-03cond-mat.mes-hall

拓扑霍尔效应的Skyrmion尺寸依赖性：实空间计算

Skyrmion-size dependence of the topological Hall effect: A real-space calculation

Akira Matsui, Takuya Nomoto, Ryotaro Arita

发表信息：: Phys. Rev. B 104, 174432 (2021)
DOI：: 10.1103/PhysRevB.104.174432

摘要：

受最近发现的具有短间距Skyrmion晶格的磁体的启发，我们研究了拓扑霍尔效应的Skyrmion尺寸依赖性。通过大规模的实空间计算，我们发现霍尔电导率在实空间和动量空间的Berry曲率都起决定性作用的交叉区域出现极值。我们还研究了最佳skyrmion尺寸（$λ_{\rm sk}^*$）如何依赖于巡游电子的寿命（$τ$）和电子与局域自旋之间的耦合常数（$J$）。对于前者，我们证明了$λ_{\rm sk}^{*}$与$\sqrtτ$成正比，这表明$λ_{\rm sk}^{*}$对$τ$的敏感性远低于传统的预期，即$λ_{\rm sk}^{*}$与平均自由路径$\propto τ$成正比。对于后者，我们表明，非绝热性大大抑制拓扑霍尔效应时，由skyrmion的大小和费米速度确定的时间尺度是短于$1/J$。但它对$λ_{\rm sk}^{*}$的影响不大，在很宽的$J$和$τ$范围内，$λ_{\rm sk}^{*}$约为晶格常数的10倍。

英文摘要：

Motivated by the recent discoveries of magnets harboring short-pitch skyrmion lattices, we investigate the skyrmion-size dependence of the topological Hall effect. By means of large-scale real-space calculations, we find that the Hall conductivity takes its extreme value in the crossover region where both the real-space and momentum-space Berry curvature play a crucial role. We also investigate how the optimum skyrmion size ($λ_{\rm sk}^*$) depends on the lifetime of itinerant electrons ($τ$) and coupling constant between electrons and localized spins ($J$). For the former, we show that $λ_{\rm sk}^{*}$ is proportional to $\sqrtτ$, which indicates that $λ_{\rm sk}^{*}$ is much less sensitive to $τ$ than the conventional expectation that $λ_{\rm sk}^{*}$ is proportional to the mean-free path $\propto τ$. For the latter, we show that the non-adiabaticity considerably suppresses the topological Hall effect when the time scale determined by the skyrmion size and Fermi velocity is shorter than $1/J$. However, its effect on $λ_{\rm sk}^{*}$ is not so siginificant and $λ_{\rm sk}^{*}$ is about ten times the lattice constant in a wide range of $J$ and $τ$.

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