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• Magnetization relaxation at different probe widths, sensing currents, and Hall geometries. • Current shunting, Joule heating, and current-induced SOT are responsible for coercivity response. • Dependence of domain wall propagation on probe widths. • Device behavior at different circumstances is crucial for practical use. The understanding of the characteristics of a magnetic layer in a different environment is crucial for any spintronics application. Before practical applications, thorough scrutiny of such devices is compulsory. Here we study such a potential Hall device of MgO-capped Hf/GdFeCo bilayer (FeCo-rich) for magnetization relaxation around nucleation fields at different voltage probe line widths and dc sensing currents. The device is characterized by anomalous Hall measurements in transverse and longitudinal Hall geometries for two different probe widths A (5 µ m) and B (1 µ m). The coercivities of the Hall loops (ρ xy - H and R xx - H) drop with increasing the sense current for both the probes. For probe B, the sharp and large drop in coercivity (ρ xy - H loops) at comparatively lower sensing currents is observed, which is attributed to the negligible current shunting and presence of pinning site at B caused by the patterning process. The average domain wall velocities at various sensing currents for probe B are found to be smaller than probe A, from the transverse and longitudinal Hall geometry magnetization relaxation measurements, which agrees with pinning sites and Joule heating effect at probe B. The notch position in the pattern and the longitudinal Hall resistance curve peak shape suggest the domain wall propagation direction from probe B to probe A in the current channel. This study highlights the domain wall propagation at different nucleation fields, sensing currents, and the Hall probe aspect ratios. [ABSTRACT FROM AUTHOR]