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Weak coupling theory of topological Hall effect

机译:拓扑霍尔效应的弱耦合理论

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Topological Hall effect (THE) caused by a noncoplanar spin texture characterized by a scalar spin chirality is often described by the Berry phase, or the associated effective magnetic field. This picture is appropriate when the coupling M of conduction electrons to the spin texture is strong (strong coupling regime) and the adiabatic condition is satisfied. However, in the weak coupling regime, where the coupling M is smaller than the electrons' scattering rate, the adiabatic condition is not satisfied and the Berry phase picture does not hold. In such a regime, the relation of the effective magnetic field to the spin texture can be "nonlocal," in contrast to the "local" relation in the strong coupling case. Focusing on continuous but general spin textures, we investigate the THE in various characteristic regions in the weak coupling regime, namely, (1) diffusive and local, (2) diffusive and nonlocal, and (3) ballistic. In the presence of spin relaxation, there arise two more regions in the "weakest coupling" regime: (1') diffusive and local and (2') diffusive and nonlocal. We derived the analytic expression of the topological Hall conductivity (THC) for each region, and found that the condition for the locality of the effective field is governed by transverse spin diffusion of electrons. In region 1, where the spin relaxation is negligible and the effective field is local, the THC is found to be proportional to M, instead of M-3 of the weakest coupling regime. In the diffusive, nonlocal regions (2 and 2'), the effective field is given by a spin chirality formed by "effective spins" that the electrons see during their diffusive motion. Applying the results to a skyrmion lattice, we found that the THC decreases as the skyrmion density is increased in region 2', reflecting the nonlocality of the effective field, and shows a maximum at the boundary to the "local" region. For general spin textures, a scaling-like argument is given to analyze the THC in the nonlocal region. These analytic results are supplemented with numerical calculations for an isolated single skyrmion as well as for periodic textures of skyrmions and merons.
机译:由非平板旋转纹理引起的拓扑霍尔效应(The),其特征在于标量旋转手性,通常由浆果相或相关的有效磁场描述。当传导电子与旋转纹理的连接M强(强耦合方案)和绝热条件时,该图片是合适的。然而,在耦合m小于电子的散射速率的弱耦合状态下,不满足绝热条件,并且浆果相片不保持。在这样的制度中,与强耦合壳中的“局部”关系相比,有效磁场与旋转纹理的关系可以是“非本地”。专注于连续但一般的旋转纹理,我们研究了弱耦合方案中的各种特征区域,即(1)扩散和局部,(2)扩散和非本地,以及(3)弹道。在旋转松弛的情况下,在“最弱的耦合”制度中出现两个更多的区域:(1')扩散和局部和(2')扩散和非本地。我们衍生出每个区域的拓扑霍尔电导率(THC)的分析表达,发现有效场的局部条件通过电子的横向自旋扩散来控制。在区域1中,其中旋转松弛可忽略不计,有效场是局部的,发现THC成比例,而不是最弱的耦合状态的M-3。在扩散,非局部区域(2和2')中,通过通过“有效旋转”形成的旋转手性,使电子在其扩散运动期间看到的旋转手性给出。将结果应用于Skyrmion格子,我们发现,随着区域2'的速度浓度增加,反映了有效场的非单位,并且在边界处显示了“本地”区域的最大值。对于一般的旋转纹理,给出了一种类似的参数来分析非本地区域中的THC。这些分析结果补充了孤立的单个斯基尔次智能的数值计算,以及臭氧和Merons的周期性纹理。

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  • 来源
    《Physical review》 |2019年第17期|174425.1-174425.28|共28页
  • 作者

    Nakazawa Kazuki; Kohno Hiroshi;

  • 作者单位

    Nagoya Univ Dept Phys Nagoya Aichi 4648602 Japan|Osaka Univ Grad Sch Sci Dept Earth & Space Sci Toyonaka Osaka 5600043 Japan;

    Nagoya Univ Dept Phys Nagoya Aichi 4648602 Japan;

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