Dynamics of current-induced switching in the quantum anomalous Hall effect

Technical Summary: Dynamics of Current-Induced Switching in the Quantum Anomalous Hall Effect

Problem and Context
Ferromagnetic topological insulators in the quantum anomalous Hall (QAH) regime host chiral, dissipationless edge states determined by the sample's internal magnetization. While these materials offer potential for quantum transport, metrology, and non-reciprocal components, a critical challenge remains the ability to reversibly switch the magnetization to control the edge state's propagation direction. Previous studies have reported current-induced magnetization switching under vastly different conditions: one compatible with spin-orbit torque mechanisms and another that was not. The specific dynamics and underlying physical mechanisms governing current-induced switching in the QAH regime, particularly regarding the timescales and the role of thermal effects versus spin-transfer torques, required further investigation.

Methodology
The authors investigated the switching dynamics in thin films of V-doped (Bi,Sb)₂Te₃ (V-BST) using time-resolved measurements. The experimental setup involved:

• Sample Preparation: Devices fabricated from 8 nm thick V-BST films grown by molecular beam epitaxy, capped with 4 nm of Al₂O₃.
• Measurement Conditions: Transport measurements were conducted at a base temperature of 20 mK.
• Pulsing Technique: A pulse generator delivered high-amplitude voltage pulses (up to ~10 V) with durations ($\tau$) ranging from 25 ns to 100 µs via a low-attenuation coaxial line.
• Detection: Longitudinal ($R_{xx}$) and transverse ($R_{xy}$) resistances were measured using standard lock-in techniques (7 Hz, 1 nA) between pulses.
• Protocol: Samples were initialized in a fully magnetized state using a large external field, then subjected to a series of pulses while the magnetic field was set to a value opposing the initial magnetization ($-H_c < H < 0$). The evolution of resistance was tracked after an increasing number of pulses ($i$) to observe the progressive reversal.

Key Results

1. Switching Dynamics: The Hall resistance ($R_{xy}$) was observed to decrease progressively with the number of pulses, eventually saturating at the quantized value for the opposite magnetization direction. Concurrently, $R_{xx}$ increased significantly before decreasing, indicating a transient state where edge states wrap around magnetic domains.
2. Time-Dependence: When the data was rescaled to plot resistance against the total cumulative time under excitation ($t = i\tau$), curves obtained with different pulse widths overlapped perfectly. This demonstrates that the switching depends solely on the total time the sample spends under voltage drive, not on the specific pulse frequency or duration.
3. Stretched Exponential Behavior: The time evolution of $R_{xy}(t)$ over more than three decades was well-described by a stretched exponential function: $R_{xy}(t) = R_0 (1 - 2 \exp(-(t/t_{sw})^\beta))$. The stretching parameter $\beta \approx 0.8$ suggests a disordered magnetic landscape where multiple small domains reverse independently with a broad distribution of switching times.
4. Scaling Laws: The switching time ($t_{sw}$) exhibited extreme sensitivity to both the pulse amplitude ($V$) and the external magnetic field ($H$).
   • $t_{sw}$ varied by approximately 9 orders of magnitude as voltage increased from 0.1 V to 1 V.
   • $t_{sw}$ varied by 4 orders of magnitude as the opposing magnetic field increased from 0.3 T to 0.7 T.
5. Mechanism Identification:
   • Exclusion of Spin-Transfer Torques: The observations were inconsistent with spin-transfer torque mechanisms. Switching did not occur under in-plane magnetic fields, and the direction of the current pulse did not influence the switching, ruling out current-direction-dependent torques.
   • Confirmation of Thermal Activation: The authors propose a heat-driven mechanism. High-amplitude pulses drive currents exceeding the QAH breakdown threshold, generating Joule heating ($P_{diss} \propto V^2$). This elevates the electron temperature ($T_e$) significantly above the lattice temperature ($T_p$).
   • Arrhenius Law: The switching time follows an Arrhenius law, $t_{sw} \propto \exp(E(H)/k_B T_e)$, where the energy barrier $E(H)$ depends on the magnetic field. The data fits a model where $T_e \propto V^{2/\alpha}$ (with $\alpha \approx 3.8$), confirming that the exponential reduction in switching time is driven by the elevation of electronic temperature.

Significance and Claims
The paper claims to elucidate the mechanism of current-induced magnetization switching in ferromagnetic topological insulators within the QAH regime. The primary contribution is the demonstration that the reversal process is governed by thermal activation facilitated by Joule heating, rather than spin-transfer torques.

The authors state that their understanding of these magnetization dynamics opens pathways for the local, controlled manipulation of chiral edge states via thermal effects. They suggest that future studies could leverage this technique to probe percolative transport through disordered magnetic landscapes and achieve localized heating to create and manipulate domain walls in a controlled fashion. The work does not claim to have achieved specific device applications (such as memory or logic gates) but rather establishes the fundamental physical mechanism and measurement technique required for such developments.