Peng Li

In resonant modes of atomic force microscopy (AFM), such as tapping mode and multifrequency mode, the cantilever typically oscillates at its fundamental or higher-order resonance, with resonance frequencies reaching several hundred kilohertz. Among various amplitude demodulation methods, the lock-in amplifier is widely used in AFM due to its superior signal-to-noise ratio and strong immunity to interference. However, conventional lock-in amplifiers require high-speed, high-resolution analog-to-digital converters (ADCs) to oversample the high-frequency vibration signal, thereby imposing huge demands on fast data acquisition and real-time processing hardware. However, in most AFM applications, the effective bandwidth contained in the cantilever amplitude variations is much lower than the carrier vibration frequency, typically on the order of several kilohertz. To address this characteristic, a sub-Nyquist sampling-based amplitude demodulation method for resonant-mode AFM is proposed in this work. By exploiting the sub-Nyquist sampling principle, accurate demodulation of the cantilever amplitude is achieved at a sampling rate significantly lower than the Nyquist rate of the vibration signal. The reduced sampling rate provides additional computational time within each sampling period, enabling real-time amplitude demodulation without the need for high-speed ADCs and processing hardware. The proposed method is validated through force–distance curve measurements and imaging experiments. The extracted force-curve characteristics and image quality show good agreement with those obtained using a conventional lock-in amplifier. These results demonstrate that the method provides a practical and cost-effective approach for reducing hardware complexity in resonant-mode AFM systems.

Domain wall (DW) velocity is a key parameter for understanding magnetic domain dynamics in ferromagnetic materials. However, traditional algorithms for DW velocity extraction often suffer from inaccuracies, limiting the precise correlation between microscopic domain dynamics and macroscopic magnetic Barkhausen noise (MBN). In this study, we quantitatively compare the accuracy of multiple optical flow algorithms in DW velocity extraction. First, we establish rigorous error metrics to evaluate optical flow performance. We then optimize the parameters of three optical flow algorithms—Horn–Schunck (H–S), Brox, and Classic + NL—and demonstrate that Classic + NL outperforms the others in both standard test images and experimental domain motion images. Furthermore, we validate the Classic + NL algorithm’s reliability through correlation analysis between the DW velocity and MBN envelope. This framework provides a robust foundation for linking microscopic DW motion with macroscopic MBN responses, advancing the precision of domain dynamics characterization.

Due to the spatial resolution limitation of the magnetic Barkhausen Noise (MBN) sensor, the mechanism by which MBN signals are affected by the elastoplastic evolution process at the grain scale remains unclear. In this study, a high-resolution MBN sensor was used to investigate the distribution of MBN signals near grain boundary in grain-oriented silicon steel under controlled residual plastic strain and applied stress, simulating a cold work hardening process. It was observed that MBN signals near the grain boundary varied with the introduction of applied stress and residual plastic strain. A multi-factor mechanism was analyzed and proposed, incorporating the effects of microstructure, applied stress/strain, and residual stress at the grain scale. These findings provide valuable insights for the subsequent improvement of the micromagnetic theory at the grain scale.