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

Taking advantage of the anomalous Hall effect, we electrically probe low-frequency magnetization fluctuations at room temperature in a thin ferromagnetic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>Pt</a:mi><a:mo>/</a:mo><a:mi>Co</a:mi><a:mo>/</a:mo><a:msub><a:mi>AlO</a:mi><a:mi>x</a:mi></a:msub></a:mrow></a:math> 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>1</b:mn><b:mo>/</b:mo><b:msup><b:mi>f</b:mi><b:mi>β</b:mi></b:msup></b:mrow></b:math> with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>β</c:mi><c:mo>≈</c:mo><c:mn>2.0</c:mn></c:mrow></c:math>. In contrast, quasistationary magnetization configurations are connected with a magnetic noise power density with an exponent <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>β</d:mi><d:mo>≈</d:mo><d:mn>1.0</d:mn></d:mrow></d:math>. 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. Published by the American Physical Society 2024