# Optically Pumped Magnetometer Measuring Fatigue-Induced Damage in Steel
## 1 Introduction  
Magnetic material testing methods are well-established for non-destructive testing (NDT) of materials or devices composed of steel, cast iron, or other ferromagnetic materials [1]. The fundamental principle involves an outer field \(H\) applied to a ferromagnetic material to measure the response of the specimen to the exciting field \(H\). This concept is utilized by some of the most frequently applied NDT techniques, such as magnetic flux leakage (MFL), magnetic Barkhausen noise (MBN), and more recently, metal magnetic memory (MMM) [2]. Using either one of these techniques as a kind of \"magnetic microscope\", one can investigate the microstructure of ferromagnetic materials [3]. Additionally, these NDT techniques can routinely be applied to industrial in-line monitoring of manufacturing processes. Alternatively, testing is possible based on the phenomenon of mechanical stresses altering the intrinsic magnetization state of ferromagnetic materials. This effect is the so-called magneto-mechanical Villari effect, which is also known as the magnetoelasticor piezomagnetic effect [4; 5]. It was used to indirectly measure the fatigue state through the magnetic response of a ferromagnetic material exposed to cyclic loading [6]. In this scenario, a sensor is positioned in the specimens' vicinity to measure the magnetic stray field originating from the specimen. Then, piezomagnetic hysteresis curves are used to identify early signs of fatigue damage in materials [7]. The shape of these hysteresis curves evolves continuously and to some extent irreversibly due to magnetic domain wall motion, their pinning at defect sites, and the generation/elimination of defects [8]. Relevant microscopic defects for such interactions include dislocations, grain boundaries, precipitates, and non-magnetic inclusions. However, stress concentrations associated with macroscopic plasticity traces and cracks also affect the magnetic stray field. Many attempts have been made to correlate the magnetic response of the material to the microstructural changes produced by fatigue, but the quantification of damage in the material remains a difficult challenge. To lay the groundwork, we combine highly sensitive quantum sensors with miniaturized specimens, which permits detailed microstructural investigation. Previous work in this direction used specimens with rather large volumes under load (\(V_{specimen}\sim\)few cm\({}^{3}\)). This hampers a more detailed mechanistic understanding and its correlation to the magnetic response with damage because localized defect events, such as macroscopic crack initiation (typically a multiple of grain size), occur in larger volumes [9; 10; 11; 12]. In contrast, we investigate magnetic stray fields originating from fatigue loading of mesoscale ferromagnetic specimens (\(V_{specimen}\sim\) 0.1 mm\({}^{3}\)). The smaller volume confines the fatigue process. Thus, damage will affect a more significant volume of the specimen and thereby be more visible in the piezomagnetic signal. Therefore, we propose the retrieval of more comprehensive magnetic information of the complete specimen volume by using optically pumped magnetometers (OPMs) [13]. The main objective is to exploit the high magnetic sensitivity of such sensors to find signs of materials' fatigue before the formation of visible surface-residing cracks. The small volume of the mesoscale specimen produces only very faint magnetic signals that are only retrievable by high-sensitivity sensors, such as OPMs. Thus, this holds the potential to facilitate correlations between magnetic signals and localized damage events, such as plastic deformation, macroscopic crack initiation, and crack growth. The small specimen size also permits complementary characterization techniques across the whole specimen, e.g., electron backscatter diffraction or spatially resolved magnetometry [14], to reveal internal microstructural features. Furthermore, the small specimen sizes lead to comparatively high spatial resolution in computer tomography-based porosity analyses.