Extensive efforts are currently being devoted to developing a new electronic technology, called spintronics, where the spin of electrons is explored to carry information. [1,2] Several techniques have been developed to generate pure spin currents in many materials and structures. [3-10] However, there is still no method available that can be used to directly detect pure spin currents, which carry no net charge current and no net magnetization. Currently, studies of pure spin currents rely on measuring the induced spin accumulation with optical techniques [5, 11-13] or spin-valve configurations. [14-17] However, the spin accumulation does not directly reflect the spatial distribution or temporal dynamics of the pure spin current, and therefore cannot monitor the pure spin current in a real-time and real-space fashion. This imposes severe constraints on research in this field. Here we demonstrate a second-order nonlinear optical effect of the pure spin current. We show that such a nonlinear optical effect, which has never been explored before, can be used for the non-invasive, non-destructive, and real-time imaging of pure spin currents. Since this detection scheme does not rely on optical resonances, it can be generally applied in a wide range of materials with different electronic bandstructures. Furthermore, the control of nonlinear optical properties of materials with pure spin currents may have potential applications in photonics integrated with spintronics.
Reply to Comment on `Theory of microwave-induced zero-resistance states in two-dimensional electron systems' and on `Microwave-induced zero-resistance states and second-harmonic generation in an ultraclean two-dimensional electron gas'
Comments on the formula to extract current-induced torques from the harmonic Hall voltage measurements
The University of Tokyo（东京大学）；Research Institute of Electrical Communication (RIEC), Tohoku University（东北大学电气通信研究所）；Trans-Scale Quantum Science Institute (TSQS), The University of Tokyo（东京大学跨尺度量子科学研究所）
Third Harmonic Characterization of Antiferromagnetic Heterostructures
反铁磁材料的电开关是自旋电子学的一个重要发展方向，它有望实现高速度、低能耗的有源反铁磁器件。在这一新兴领域，有一个积极的辩论机制的电流驱动的反铁磁体开关。谐波表征是研究重金属/铁磁体系中电流诱导自旋轨道矩和自旋Seebeck效应的有力工具。然而，谐波测量技术从未在反铁磁异质结构中得到验证。在这里，我们报告的第一时间谐波测量Pt/ $α$ -Fe $_2$ O $_3$双层膜，这是我们的高阶谐波电压的模型解释。与铁磁异质结构中所有的电流感应效应都出现在二次谐波信号中相比，Pt/ $α$ O $_3$中的类阻尼力矩和热致磁弹性效应贡献出现在三次谐波电压中.我们的结果为研究反铁磁材料的电流感生磁化动力学提供了一条新的途径，促进了反铁磁自旋电子器件的应用。
Current-induced second harmonic generation in inversion-symmetric Dirac and Weyl semimetals
二次谐波是一种基本的非线性光学现象，广泛应用于材料实验探测和光学器件中。偶阶非线性光学响应包括二次谐波通常需要反转对称性的破缺，因此已被用来研究非中心对称材料。在这里，我们从理论上研究了在直流电流下，通过创建一个非平衡稳态打破反转对称的反转对称狄拉克和Weyl半金属的二次谐波。基于解析和数值计算，我们发现Dirac和Weyl半金属在有限电流作用下表现出很强的二次谐波。我们对狄拉克半金属Cd $_3$ As $_2$和磁性Weyl半金属Co $_3$ Sn $_2$ S $_2$的实验估计表明，在中红外或远红外光下，对于实际应用的电流密度，诱导磁化率$χ^{(2)}$可以达到$10^5~\mathrm{pm}\cdot\mathrm{V}^{-1}$。该值比典型的非线性光学材料大10 $^2$ -10 $^4$倍。我们还讨论了观察电流诱导二次谐波的实验方法，并结合最近的实验对其他拓扑半金属中的电流诱导二次谐波进行了评论。
