We investigate the nature of the ordering among magnetic adatoms, randomly deposited on the surface of topological insulators. Restricting ourselves to dilute impurity and weak coupling (between itinerant fermion and magnetic impurities) limit, we show that for arbitrary amount of chemical doping away from the apex of the surface Dirac cone the magnetic impurities tend to arrange themselves in a spin-density-wave pattern, with the periodicity approximately $π/k_F$, where $k_F$ is the Fermi wave vector, when magnetic moment for impurity adatoms is isotropic. However, when magnetic moment possesses strong Ising or easy-axis anisotropy, pursuing both analytical and numerical approaches we show that the ground state is ferromagnetic for low to moderate chemical doping, despite the fragmentation of the system into multiple ferromagnetic islands. For high doping away from the Dirac point as well, the system appears to fragment into many ferromagnetic islands, but the magnetization in these islands is randomly distributed. Such magnetic ordering with net zero magnetization, is referred here as ferromagnetic spin glass, which is separated from the pure ferromagnet state by a first order phase transition. We generalize our analysis for cubic topological insulators (supporting three Dirac cones on a surface) and demonstrate that the nature of magnetic orderings and the transition between them remains qualitatively the same. We also discuss the possible relevance of our analysis to recent experiments.
We perform ab-initio calculations on Bi$_\mathrm{Se}$ antisite defects in the surface of Bi$_2$Se$_3$, finding strong low-energy defect resonances with a spontaneous ferromagnetism, fixed to an out-of-plane orientation due to an exceptional large magnetic anisotropy energy. For antisite defects in the surface layer, we find semi-itinerant ferromagnetism and strong hybridization with the Dirac surface state, generating a finite energy gap. For deeper lying defects, such hybridization is largely absent, the magnetic moments becomes more localized, and no energy gap is present.
Electrons in moiré flat band systems can spontaneously break time reversal symmetry, giving rise to a quantized anomalous Hall effect. Here we use a superconducting quantum interference device to image stray magnetic fields in one such system composed of twisted bilayer graphene aligned to hexagonal boron nitride. We find a magnetization of several Bohr magnetons per charge carrier, demonstrating that the magnetism is primarily orbital in nature. Our measurements reveal a large change in the magnetization as the chemical potential is swept across the quantum anomalous Hall gap consistent with …
The influence of proximity induced ferromagnetism, superconductivity and Fermi-velocity on evolution of Berry phase in Bi$_{2}$Se$_{3}$ topological insulator
Bi $_{2}$ Se $_{3}$是众所周知的3D拓扑绝缘体（TI），其具有归因于能带结构的拓扑的非平凡Berry相$ \left(2n+1\right)π$. Berry相位在存在破坏时间反演对称性的微扰的情况下显示出与$ \left(2n+1\right)π$的非拓扑偏差，并产生具有大质量狄拉克费米子和有限带隙的量子系统。这样的带隙开放是由于铁磁体的交换场或超导体的本征能隙而实现的，所述本征能隙借助于邻近效应影响拓扑绝缘体表面态。在这项工作中，贝里阶段的这种带隙系统与大量狄拉克费米子被认为是。此外，它示出，这样的系统的Berry相也取决于\textit{Fermi} -速度的表面状态，可以调谐为TI膜厚度的函数。
Proximity induced ferromagnetism, superconductivity, and finite-size effects on the surface and edge states of topological insulator nanostructures
Bi $_{2}$ Te $_{3}$和Bi $_{2}$ Se $_{3}$是公知的3D-拓扑绝缘体。由这些材料制成的膜表现出具有狄拉克色散的类金属表面态，并具有高迁移率。高迁移率类金属表面态可以用作基于TI的场效应晶体管的沟道材料。虽然这种晶体管提供了优越的终端特性，但它们存在固有的零带隙问题。表面态的带隙的缺乏阻止了容易的关断机制。在这项工作中，可以采用的技术，很容易打开的TI表面状态的带隙。描述了两种方法：1）用磁化轴可控的铁磁体覆盖表面态。铁磁体的磁化强度作为交换相互作用项纳入哈密顿量。2)一个\textit{s}波超导体，由于邻近效应，当耦合到3D-TI打开表面上的带隙。这种TI超导体异质结建模使用Bogoliubov-de Gennes哈密顿量。还提出了一个比较，证明有限尺寸效应的表面状态的3D-TI和边缘状态的碲化镉/碲化汞/碲化镉为基础的2D-TI。与需要至少100.0 $ \mathrm{nm} $的厚度的2D-TI结构相比，3D-TI纳米结构可以减小到低至10.0 $ \mathrm{nm} $的尺寸。所有的计算使用连续四带k.p哈密顿量。
Local optical control of ferromagnetism and chemical potential in a topological insulator
许多涉及拓扑绝缘体（TI）的实验需要对时间反演对称性和化学势进行空间控制。我们展示了可重构的微米尺度的光学控制的磁化强度（打破时间反转对称性）和化学势的铁磁薄膜的Cr-（Bi，Sb）$_2$ Te $_3$生长在SrTiO $_3$。通过光学调制薄膜的磁化率，我们在它们的回复磁化中写入和擦除任意图案，然后用克尔显微镜成像。此外，通过光学操纵的空间电荷层在下面的SrTiO $_3$衬底，我们控制的局部化学势的薄膜。这种光学选通效应使我们能够在薄膜中写入和擦除pn结，我们用光电流显微镜研究。这两种效应都是持久的，并且可以在几微米尺度上独立地形成图案和成像。动态光学控制的磁化强度和化学势的TI可能是有用的努力，以了解和控制的边缘状态预测在磁畴壁的量子异常霍尔绝缘体。
We have previously reported ferromagnetism evinced by a large hysteretic anomalous Hall effect in twisted bilayer graphene (tBLG). Subsequent measurements of a quantized Hall resistance and small longitudinal resistance confirmed that this magnetic state is a Chern insulator. Here we report that, when tilting the sample in an external magnetic field, the ferromagnetism is highly anisotropic. Because spin-orbit coupling is negligible in graphene such anisotropy is unlikely to come from spin, but rather favors theories in which the ferromagnetism is orbital. We know of no other case in which fer…
Nonmagnetic-Doping Induced Quantum Anomalous Hall Effect in Topological Insulators
在磁掺杂拓扑绝缘体中实验观察到量子反常霍尔效应。然而，超低温（通常低于300 mK），这主要是由于不均匀的磁性掺杂，成为一个艰巨的挑战，潜在的应用。本文提出了一种\textit{nonmagnetic}掺杂策略，在拓扑绝缘体中产生铁磁性并实现QAHE。我们数值计算表明，磁矩可以诱导由氮或碳取代在Bi $_2$ Se $_3$，Bi $_2$ Te $_3$，和Sb $_2$ Te $_3$，但只有氮掺杂的Sb $_2$ Te $_3$表现出长程铁磁性和保持大的体带隙。我们进一步表明，其相应的薄膜可以在17-29开尔文的温度下窝藏QAHE，这比类似系统中的典型温度高两个数量级。我们提出的\textit{nonmagnetic}掺杂方案可能为拓扑绝缘体中高温QAHE的实验实现提供新的思路。
In bilayer graphene rotationally faulted to theta=1.1 degrees, interlayer tunneling and rotational misalignment conspire to create a pair of low energy flat band that have been found to host various correlated phenomena at partial filling. Most work to date has focused on the zero magnetic field phase diagram, with magnetic field (B) used as a probe of the B=0 band structure. Here, we show that twisted bilayer graphene (tBLG) in a B as low as 2T hosts a cascade of ferromagnetic Chern insulators with Chern number |C|=1,2 and 3. We argue that the emergence of the Chern insulators is driven by th…
Direct evidence of ferromagnetism in a quantum anomalous Hall system
量子反常霍尔（QAH）系统由于其不需要外加磁场就能实现无耗散导电而具有重要的应用价值。在磁掺杂拓扑绝缘体薄膜中实现了QAH效应。然而，在最初的工作中，全量子化需要极低的温度（$T< 50\,$ mK），尽管通过调制掺杂或磁性元件的共掺杂已经显著改善了它。在这些薄膜中已经显示出改善的铁磁性，但缺乏长程铁磁有序的直接证据。在这里，我们提出了直接可视化的长程铁磁有序的Cr和V共掺杂（Bi，Sb）$_2$ Te $_3$薄膜使用低温磁力显微镜与$\textit{in-situ}$运输。磁化反转过程揭示了典型的铁磁畴行为，即，畴成核和可能的畴壁传播，这与在端元中观察到的弱得多的磁信号形成对比，这可能是由于超顺磁性行为。所观察到的长程铁磁有序解决了QAH系统中的主要挑战之一，并通过探索磁性拓扑绝缘体为高温无耗散传导铺平了道路。
The flat bands resulting from moiré superlattices in magic-angle twisted bilayer graphene (MATBG) and ABC-trilayer graphene aligned with hexagonal boron nitride (ABC-TLG/hBN) have been shown to give rise to fascinating correlated electron phenomena such as correlated insulators and superconductivity. More recently, orbital magnetism associated with correlated Chern insulators was found in this class of layered structures centered at integer multiples of n0, the density corresponding to one electron per moiré superlattice unit cell. Here we report the experimental observation of ferromagnetism …
Recently, the magnetic domain walls have been experimentally observed in antiferromagnetic topological insulators MnBi$_2$Te$_4$, where we find that the topological zero-line modes (ZLMs) appear along the domain walls. Here, we theoretically demonstrate that these ZLMs are layer-dependent in MnBi$_2$Te$_4$ multilayers. For domain walls with out-of-plane ferromagnetism, we find that ZLMs are equally distributed in the odd-number layers. When domain walls possess in-plane magnetization, the ZLMs can also exist in even-number layers due to in-plane mirror-symmetry breaking. Moreover, the conducti…
Thermal ammonolysis of quasi-two-dimensional (quasi-2D) CoTa2O6 yields the O2-/N3- and anionic vacancy ordered Co2+Ta5+2O6-xN2x/3$\Box$x/3 (x $\leq$ 0.15) that exhibits a transition from antiferromagnetism to defect engineered above room-temperature ferromagnetism as evidenced by diffraction, spectroscopic and magnetic characterizations. First-principles calculations reveal the origin of ferromagnetism is a particular CoON configuration with N located at Wyckoff position 8j, which breaks mirror symmetry about ab plane. A pressure-induced electronic phase transition is also predicted at around …
Experimental Verification of Van Vleck Nature of Long-Range Ferromagnetic Order in Vanadium-Doped Three-Dimensional Topological Insulator Sb$_{2}$Te$_{3}$
通过高分辨低温电子能量损失谱（EELS）测量，证明了钒掺杂拓扑绝缘体Sb $_2$ Te $_3$中的长程铁磁（FM）有序具有vanVleck型铁磁性.当样品从室温冷却到T= 10 K时，VEELS谱的两个核心能级峰（L $_3$和L $_2$）的位置和相对振幅都发生了明显的变化。测量和模拟EELS光谱的磁输运和比较证实，这些变化源于发病的FM秩序。晶场分析表明，在V掺杂的Sb $_2$ Te $_3$中，部分填充的芯态有助于FM阶。由于van Vleck磁性是所有状态相加的结果，因此芯层的磁化以直接的方式验证了van Vleck型铁磁性。
The field of oxide spintronics can strongly benefit from the establishment of robust ferromagnetic insulators with near room-temperature Curie temperature. Here we investigate the structural, electronic, and magnetic properties of atomically-precise epitaxially-strained thin films of the double perovskite La$_2$NiMnO$_6$ (LNMO) grown by off-axis radio-frequency magnetron sputtering. We find that the films retain both a strong insulating behavior and a bulk-like Curie temperature in the order of 280 K, nearly independently from epitaxial strain conditions. These results suggest a prospective im…
Dynamic manipulation of magnetism in topological materials is demonstrated here via a Floquet engineering approach using circularly polarized light. Increasing the strength of the laser field, besides the expected topological phase transition, the magnetically doped topological insulator thin film also undergoes a magnetic phase transition from ferromagnetism to paramagnetism, whose critical behavior strongly depends on the quantum quenching. In sharp contrast to the equilibrium case, the non-equilibrium Curie temperatures vary for different time scale and experimental setup, not all relying o…
Multiferroics with intrinsic ferromagnetism and ferroelectricity are highly desired but rather rare, while most ferroelectric magnets are antiferromagnetic. A recent theoretical work [Phys. Rev. B {\bf 99}, 195434 (2019)] predicted that oxyhalides VO$X_2$ ($X$: halogen) monolayers are two-dimensional multiferroics by violating the empirical $d^0$ rule. Most interestingly, the member VOI$_2$ are predicted to exhibit spontaneous ferromagnetism and ferroelectricity. In this work, we extend the previous study on the structure and magnetism of VOI$_2$ monolayer by using density functional theory an…
Interface-Induced Superconductivity in Magnetic Topological Insulator-Iron Chalcogenide Heterostructures
The Pennsylvania State University（宾夕法尼亚州立大学）；Rutgers University（罗格斯大学）；University of Washington（华盛顿大学）；Chinese Academy of Sciences（中国科学院）；Materials Research Institute, The Pennsylvania State University（宾夕法尼亚州立大学材料研究所）；National High Magnetic Field Laboratory（国家高磁场实验室）；Paul Scherrer Institute（保罗谢尔研究所）；National Institute of Standards and Technology（美国国家标准与技术研究院）
