Quaternary alloy ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x{\mathrm{As}}_{1-y}{\mathrm{P}}_y$ hosts magnetic and electronic properties that can be tuned by varying the P concentration “$y$”, Mn concentration “$x$” and by annealing. In this work we make use of this tunability to probe the origin of the anomalous Hall effect (AHE) in ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x{\mathrm{As}}_{1-y}{\mathrm{P}}_y$ thin films grown on GaAs that host perpendicular magnetic anisotropy. Specifically, we find that AHE in this class of materials is determined primarily by two contributions: an intrinsic band component arising from the Berry curvature, and a component determined by hopping conduction. As we vary the properties of ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x{\mathrm{As}}_{1-y}{\mathrm{P}}_y$ from the metallic to the semi-insulating regime by changing the value of $y$ and by postgrowth annealing, we observe a clear crossover from a Berry-curvature-induced AHE to one that is caused by hopping. The transition occurs approximately at the point where the numbers of localized and itinerant holes become comparable. In this hopping regime, the conductivity follows the Efros-Shklovskii scaling law versus temperature indicating the presence of a Coulomb gap, but the AHE remains robustly present. These results indicate that ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x{\mathrm{As}}_{1-y}{\mathrm{P}}_y$ can host an interesting interplay between magnetism and Coulomb interactions.

中文翻译：

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Ga1−xMnxAs1−yPya 中反常霍尔效应的交叉行为跨越金属-绝缘体转变

四元合金 ${嘎}_{1-X}{锰}_X{\mathrm{作为}}_{1-是}{\mathrm{磷}}_{是}$ 拥有可以通过改变 P 浓度来调整的磁性和电子特性“$是$”，锰浓度“$X$”并通过退火。在这项工作中，我们利用这种可调性来探测异常霍尔效应 (AHE) 的起源${嘎}_{1-X}{锰}_X{\mathrm{作为}}_{1-是}{\mathrm{磷}}_{是}$在具有垂直磁各向异性的 GaAs 上生长的薄膜。具体来说，我们发现这类材料中的 AHE 主要由两个贡献决定：由 Berry 曲率产生的固有带分量和由跳跃传导决定的分量。当我们改变属性时${嘎}_{1-X}{锰}_X{\mathrm{作为}}_{1-是}{\mathrm{磷}}_{是}$ 通过改变值从金属到半绝缘状态 $是$通过生长后退火，我们观察到从浆果曲率诱导的 AHE 到由跳跃引起的 AHE 的明显交叉。过渡大约发生在局部和巡回孔的数量变得可比的点上。在这种跳跃状态下，电导率遵循 Efros-Shklovskii 标度定律与温度的关系，表明存在库仑间隙，但 AHE 仍然稳健存在。这些结果表明${嘎}_{1-X}{锰}_X{\mathrm{作为}}_{1-是}{\mathrm{磷}}_{是}$ 可以在磁性和库仑相互作用之间进行有趣的相互作用。