当自旋极化的载流子绝热地经过特定的实空间拓扑自旋结构时，这些自旋结构能像外加的磁场一样对载流子施加额外的作用，使载流子获得一定的贝里相位，系统因此产生类似于霍尔效应一样的横向电压。但和霍尔电压不同，这种电压既不和外加磁场成正比，也不和系统的磁化强度成正比，这一效应被称之为'几何霍尔效应'或'拓扑霍尔效应'，是倒空间贝里相位所产生的反常霍尔效应在实空间所对应的物理现象。产生该效应的主要原因是系统中存在的拓扑自旋结构，这种拓扑自旋结构的一个典型代表是自旋电子学领域中被广泛研究的磁斯格明子。近年来在B20化合物和重金属多层结构的研究中发现，磁斯格明子能够存在于特定对称破缺的材料或者界面，而'几何霍尔效应'也成为探测磁斯格明子等拓扑自旋结构的一种实验手段。

北京大学量子材料科学中的何庆林研究员和合作者在三维拓扑绝缘体和反铁磁体的界面处发现了拓扑自旋结构存在的实验证据，即几何霍尔效应。更重要的是，由于材料系统的巧妙设计，利用了拓扑绝缘体(Bi，Sb)2Te3强大的自旋轨道耦合作用，以及A型反铁磁MnTe的界面交换耦合，拓扑绝缘体的表面态被磁化；同时，利用界面处反铁磁体的尼尔序对所产生的拓扑自旋结构的钉轧效应，实验上能实现控制拓扑自旋结构的产生和湮灭。如图所示，当在尼尔温度以上时，对系统外加一个垂直方向的磁场并将系统冷却至低温，由于拓扑绝缘体的表面态被磁化，产生了反常霍尔效应。这时候，反铁磁体在界面处会有大量受这种场冷作用而被钉轧的自旋结构。在磁化强度接近饱和的磁场附近，界面处形成大量中心自旋方向和钉轧自旋方向平行的拓扑自旋结构，因此在该磁场附近所产生的几何拓扑效应非常明显；当外加磁场反向时，同样在磁化强度接近饱和的磁场附近，这时候界面会形成反拓扑自旋结构，其中心自旋方向和反铁磁中钉轧自旋结构反平行。因此，反拓扑自旋结构不容易在钉轧自旋结构附近形成，因此只能产生少量的反拓扑自旋结构，几何拓扑效应微弱。以上新的效应是基于传统的交换偏置作用，但又从中提炼出新的物理现象：传统的交换偏置作用利用反铁磁有序实现对铁磁体中的磁矩翻转的调控，而在这个研究中，反铁磁有序所调控的是拓扑自旋结构，也即调节了拓扑电荷的形成机制。

该工作于2018年7月17日发表在知名学术期刊《自然-通讯》上。论文链接：https://www.nature.com/articles/s41467-018-05166-9.

该项工作由量子中心的何庆林研究员、美国加州大学洛杉矶分校的王康隆教授团队、美国国家标准与技术研究院的Alexander J. Grutter博士和Brian J. Kirby博士、美国先进光源实验室的Padraic Shafer博士和Elke Arenholz博士、北京工业大学的韩晓东教授团队、美国加州大学河滨分校的Roger K. Lake教授团队合作完成。其中，何庆林研究员、Gen Yin博士、Alexander J. Grutter博士为文章第一作者，何庆林研究员和王康隆教授为文章共同通讯作者。该项工作得到了国家重点研发计划（2018YFA0305601）和中组部“青年千人”计划的支持。

图：拓扑电荷的交换偏置机制示意图。在反铁磁体表面的钉轧自旋能帮助正拓扑电荷的成核（红色圆），但抑制负拓扑电荷的成核（绿色圆）。 Figure: A schematic demonstration of the exchange-biased topological charges. The anchoring spins in the AFM layer assist the nucleation of positive topological charges (red circles) while prohibit the negative ones (green circles).

Nature Communications reports Prof Qing Lin He et al.’s study on exchange biasing the topological charge using antiferromagnetism

Spin-polarized carriers adiabatically moving through certain real-space topological spin textures can obtain a Berry’s phase as though they were in an applied magnetic field, resulting in a transverse carrier transport. Induced by this transverse transport, an extra Hall voltage can be observed, which is proportional to neither the applied external field nor the total magnetization. This spin-texture-induced extra Hall component is usually referred to as the 'topological' or 'geometric' Hall effect (GHE), which is a real-space counterpart of the k-space Berry phase in an intrinsic anomalous Hall effect (AHE). GHE is typically observed near magnetic reversal, within a window of the applied magnetic field and the temperature. Since the discovery of magnetic skyrmions in B20 compounds and heavy-metal multilayers, GHE has been considered as an experimental signature of topological spin textures (such as skyrmions) and, along with other real-space detection methods, it enables mapping of the magnetic topological phase diagram.

Recently, Prof Qing Lin He in ICQM – Peking University reported an experimental observation of the GHE modulated by uncompensated pinned spins in the antiferromagnetic (AFM) layer at the interface between an intrinsic TI thin film of (Bi,Sb)2Te3 and an AFM layer of MnTe. This suggests that a topologically nontrivial chiral spin texture is induced in the TI through interactions with the spin-polarized Mn planes of the MnTe. We find that the magnetic topological charge can be manipulated by a ‘seeding effect’ of pinned spins in the AFM layer. Systematic experimental results of the carrier magneto-transport, neutron scattering, and magnetic X-ray absorption spectroscopy support that the interfacial FM layer is induced in the TI through proximity interactions with the AFM layer.

Experimentally, it has been shown that special domain nucleation patterns can be induced by the spins in an adjacent AFM layer due to interfacial exchange coupling. In the following, it will be shown that this exchange coupling can result in a ‘seeding effect’ for the spin-texture topology. The microscopic picture is schematically shown by the four scenarios illustrated in the figure. After positive field cool (FC), some pinned spins can be frozen in the AFM layer along the FC direction (black arrows) due to thermoremanence. When the applied field sweeps to (i), positive topological charges [red circles with up central spins in (i)] are created through interactions with the pinned spins. After the saturation along a negative field (ii), these positive topological charges are annihilated. When the field scans to (iii), negative topological charges are prohibited by the pinning spins and therefore are more likely to nucleate outside the spin-pinned regions, but with a lower density [green circles with down central spins in (iii)]. These negative charges again vanish after magnetic saturation (iv). A similar modulation of topological charge occurs after a negative FC.

The above work was published on Nature Communications on July 17, 2018. The link to this paper is: https://www.nature.com/articles/s41467-018-05166-9.

This work was carried out by Prof Qing Lin He in ICQM, the group led by Prof Kang L Wang in UCLA, Dr. Alexander J. Grutter and Dr. Brian J. Kirby in National Institute of Standards and Technology (NIST), Dr. Padraic Shafer and Dr. Elke Arenholz in Advanced Light Source (ALS), the group led by Prof Xiaodong Han in Beijing University of Technology, and the group led by Prof Roger K. Lake in UC-Riverside. Prof Qing Lin He, Dr. Gen Yin, and Dr. Alexander J. Grutter are the first authors of the paper, while Prof Qing Lin He and Prof Kang L. Wang are the corresponding authors. This work is supported in part by the National Key R&D Program of China (Grant No. 2018YFA0305601) and the National Thousand-Young-Talents Program.