Magnetization fluctuations and magnetic after-effect probed via the anomalous Hall effect

Abstract

Taking advantage of the anomalous Hall effect, we electrically probe low-frequency magnetization fluctuations at room temperature in a thin ferromagnetic Pt/Co/AlO𝑥 layer stack with perpendicular magnetic anisotropy. We observe a strong enhancement of the Hall voltage fluctuations within the hysteretic region of the magnetization loop. Analyzing both the temporal evolution of the anomalous Hall voltage and its frequency-dependent noise power density, we identify two types of magnetic noise: abrupt changes in the magnetic domain configuration, evident as Barkhausen-like steps in the Hall voltage time trace, yield a noise power density spectrum scaling with frequency as 1/𝑓𝛽 with 𝛽≈2.0. In contrast, quasistationary magnetization configurations are connected with a magnetic noise power density with an exponent 𝛽≈1.0. The observation of Barkhausen steps and relaxation effects shows that the magnetic system is in a nonstationary state in the hysteresis region, such that the fluctuation-dissipation theorem cannot be expected to hold. However, the time-dependent change in the Hall voltage for constant magnetic field strength resembles the integrated noise power.