The broad family of Hall effects comprises phenomena of ordinary, anomalous, planar, topological, and quantum origin. These effects are ubiquitous in electronic systems and are essential tools for studying the physics of condensed-matter systems and spintronic devices. The anomalous Hall effect [1], for instance, allows for probing the appearance of magnetically-ordered phases, field- and current-induced magnetization reversal, domain wall motion, and spin-orbit torques [2]. The planar Hall effect and the spin Hall magnetoresistance can also be used to track the response of antiferromagnets and magnetic insulators to applied magnetic fields, currents, and heat [3]. Despite the fundamental and technological importance of the Hall effects, their detection has been limited so far to the low frequency regime by their inherent small magnitude. There exist only few examples of time-resolved measurements of the magnetization dynamics using the Hall effect [4]. In contrast, measurements of the GHz dynamics associated with other magnetoresistance effects, such as the tunnel magnetoresistance, have become a common routine [5]. Extending this capability to Hall effects would provide an important tool to investigate a vast range of electronic and magnetic systems. Here we present a novel concept to perform all-electrical time-resolved measurements of any kind of Hall magnetoresistance [6]. Our approach removes the large non-magnetic potential that originates from the current leakage into the transverse arms of the Hall cross (see Fig. 1a). Since this background is much larger than the Hall voltage, it saturates the acquisition range of the measuring instrument (an oscilloscope) and impedes high-frequency measurements of transverse signals. The key idea to suppress the spurious contribution consists of delivering to the Hall cross two counter-propagating electric pulses of opposite polarity. Their synchronous arrival at the device center forces a local virtual ground that hinders the transverse current shunting (see Fig. 1b). Since the current does flow along the longitudinal direction, the Hall voltage is not removed, differently from the non-magnetic transverse potential. The vertical resolution of the oscilloscope can be thus fully exploited to acquire the background-free Hall voltage and sense the associated dynamics. Our approach is simple and, as compared to traditional Hall measurements, requires only an additional component, namely, the balun divider that generates the electric signals of opposite polarity (Fig. 1c). Importantly, the amplitude, duration, and waveform of the electrical excitation can be arbitrarily chosen. Moreover, RF and DC components can be combined in a single setup to perform both low and high frequency measurements. Overall, our technique achieves the signal quality necessary for the single-shot acquisition and, hence, for the detection of stochastic events with a resolution &lt;50 ps. This capability is unique to our technique and is an advantage over standard non-electrical pump-probe schemes that can sense only the reproducible dynamics. We benchmarked our technique by studying the magnetization switching of ferrimagnetic GdFeCo caused by electric pulses with duration ranging between 0.3 and 20 ns. Our time-resolved measurements of the anomalous Hall effect show that the spin-orbit-torque-induced dynamics comprises a fast reversal (equivalent domain wall speed &gt;1 km/s), as typical of ferrimagnets [7,8], and a long, unexpected incubation delay (Fig. 2). We associate this phase with the time required to nucleate a reversed domain assisted by Joule heating. In addition, the single-shot anomalous-Hall traces reveal the existence of broad distributions of the nucleation and reversal times and disclose the stochastic character of the dynamics triggered by the spin-orbit torques.

**References:**

[1] Nagaosa N. et al., Rev. Mod. Phys. 82, 1539–1592 (2010) [2] A. Manchon et al., Rev. Mod. Phys. 91, 035004 (2019) [3] Wadley P. et al., Science (80-. ) 351, 587–590 (2016) [4] Yoshimura Y. et al., Nat. Phys. 12, 157–161 (2016) [5] Grimaldi E. et al., Nat. Nano. 15, 111–117 (2020). [6] Sala G. et al., Nat. Comm (in press) [7] Caretta L. et al., Nat. Nano. 13, 1154-1160 (2018) [8] Cai K. et al., Nat. Electr. 3, 37-42 (2020)

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/a46aed8e02ec335f79b3f1a3e431bc2c.jpg)
Figure 1. Experimental setup for time-resolved Hall effect measurements. a, The current J produced by a pulse VP leaks through the transverse arms of the Hall cross and builds up spurious potential V+ and V-. b, When the two pulses with opposite polarity meet at the center of the Hall cross, they impose a virtual ground and force the current to propagate along the longitudinal direction. The background-free Hall potential VH can thus be acquired with improved sensitivity. c, Schematics of the RF setup. The initial pulse is fed to a balun divider, which splits the signal into two half pulses with opposite polarity that reach the device at the same instant. The current-induced transverse Hall potentials VH are amplified and detected by the oscilloscope, triggered by an attenuated portion of the initial pulse. The lock-in amplifier and the bias-Ts form the DC sub-network (dashed lines).

![](https://assets.underline.io/uploads/markdown_image/1/image/e414760706b85f028c4bee175fccf4ab.jpg)
Figure 2. Spin-orbit torque magnetization switching of GdFeCo measured by time-resolved Hall effect. Normalized anomalous Hall voltage VH measured during the application of 20-ns-long electric pulses. The duration of the initial quiescent phase and reversal are determined by the pulse amplitude.

 Real-time detection of Hall effects: measuring current-induced magnetization switching in the time domain

*Session Chair: Guoqiang Yu, Chinese Academy of Sciences*

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Real-time detection of Hall effects: measuring current-induced magnetization switching in the time domain

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