We present a computational method to determine the exchange constants in isotropic spin models. The method uses the Hamiltonian and overlap matrices computed from density functional schemes that are based on nonorthogonal basis sets. We demonstrate that the new method as implemented in the SIESTA code reproduces the Heisenberg interactions of simple metallic bulk ferromagnets as obtained from former well--established computational approaches. Then we address $sp$ magnetism in graphene nanostructures. For fluorinated graphene we obtain exchange interactions in fairly good agreement with previous calculations using maximally localized Wannier functions and we confirm the theoretical prediction of a 120$^\circ$ Néel state. Associated with the magnetic edge-states of a zigzag graphene nanoribbon we find rapidly decaying exchange interactions, however, with an unconventional distance dependence of $\exp(-\sqrt{r/δ})$. We show that the stiffness constant derived from the exchange interactions is consistent with previous estimate based on total energy differences of twisted spin configurations. We highlight that our method is an efficient tool for the analysis of novel hybrid nano-structures where metallic and organic components are integrated to form exotic magnetic patterns.
Direct measurement of proximity-induced magnetism at the interface between a topological insulator and a ferromagnet
当拓扑绝缘体（TI）与铁磁体接触时，时间反转和反转对称性在界面处都被破坏。在TI表面形成能隙，其电子通过短程交换相互作用获得净磁矩。磁TI可以承载各种奇异的量子现象，如大质量狄拉克费米子，马约拉纳费米子，量子反常霍尔效应和沿畴界的手征边缘电流。然而，在掩埋界面处的感生磁性的选择性测量仍然是一个挑战。使用磁二次谐波产生，我们直接探测在铁磁绝缘体（FMI）EuS和三维TI Bi 2Se 3之间的界面处诱导的面内和面外磁化。我们的研究结果不仅可以表征在TI-FMI接口的磁性，但也奠定了基础，成像磁畴和域边界的磁性TI表面。
Probing Magnetism in Insulating Cr2Ge2Te6 by Induced Anomalous Hall Effect in Pt
二维铁磁体Cr2 Ge 2 Te 6（CGT）在居里温度以下电阻很大，因此通过电输运探测其磁性变得非常困难。然而，通过与Pt形成异质结构，我们在沉积在CGT的薄（< 50 nm）剥离薄片上的5 nm厚的Pt中观察到明显的异常霍尔效应（AHE）。AHE磁滞回线持续到~ 60 K，这与从体磁化测量获得的CGT的居里温度很好地匹配。具有狭窄开口的倾斜AHE环指示磁畴形成，这通过低温磁力显微镜（MFM）成像来证实。这些结果清楚地表明，CGT将其磁化印记在Pt层的AHE信号中。密度泛函理论计算的CGT/Pt异质结构表明，感生铁磁性的Pt可能是主要负责所观察到的AHE。我们的研究结果建立了一个强大的方式调查磁性的二维绝缘铁磁体，可以潜在的单层设备。
