Investigation of Rayleigh region in strip like amorphous FINEMET samples after different heat treatments

•The influence of thermal treatment on magnetization processes in the low magnetic field range (Rayleigh region) was investigated.•Thermal treatment has a significant impact on magnetic properties of the FINEMET alloy.•Changes of magnetic properties are caused by significant minimization of internal mechanical stresses induced during material preparation.•This reflects in decrease of the total magnetic anisotropy Keff to 25% of the initial value.•The sample volume magnetized in the Rayleigh region by reversible motion of domain walls increases fivefold.