III–V semiconductors exhibit dynamic nuclear self-polarization (DYNASP) owing to the contact hyperfine interaction (HFI) between optically excited conduction electrons and lattice nuclei. In the self-polarization process at a low temperature, electron spin state and the nuclear polarization (magnetization) exchange a positive feedback, increasing energy splitting of the conduction electron states, thereby a large nuclear polarization. This phenomenon was theoretically predicted previously for conduction electrons excited linearly and elliptically polarized light. The polarization of the conduction electrons was represented by a parameterα in a formula for nuclear polarization (Eq. (9) in Ref. [1]); however, the effect of external magnetic fields on the nuclear polarization was not considered. Therefore, this study introduces this effect by further extending the previous studies. Herein, α′ represents the combination of the effects of elliptically polarized electrons and an external magnetic field, which is used in the equations presented in previous studies. When α′ = 0, a large nuclear polarization is obtained below critical temperature Tc, but no polarization occurs above Tc. When α′ > 0, the nuclear polarization is enhanced above Tc. Below Tc, the nuclear polarization follows a hysteresis curve when α′ is partially manipulated by adjusting the degree of the polarization of the exciting laser.