Magnetic properties resulting from localized spins associated with antisite arsenic ions AsGa+ in Be-doped low-temperature-grown GaAs (LT-GaAs) layers were studied by measuring the magnetization of lift-off samples. With fast cooling, the magnetization of samples at 1.8 K becomes significantly lower than that expected from Curie-type paramagnetism in the range of the applied field to 7 T, and a transition from low magnetization to the magnetization of paramagnetism occurs upon the heating of samples to 4.5 K. With slow cooling, on the other hand, samples have a paramagnetic temperature dependence throughout the measurement-temperature range. The magnetization was found to decrease monotonically when a sample was kept at a fixed low temperature. These observations are explained by the cooperative transition of electron states of AsGa defects, which is closely related to the normal-metastable state transition of EL2 defects in semi-insulating GaAs. The results of the magnetization measurements in the present study suggest that AsGa+ ions are spontaneously displaced at low temperature without photoexcitation in Be-doped LT-GaAs. The similarity of the transition observed in this system to the normal-metastable state transition of the EL2 defect was also suggested by first-principle calculations of the electron state of an AsGa defect with a doped Be atom.