  Semiconductor quantum dots provide a spin-coupled system of an electron and
nuclei via enhanced hyperfine interaction. We showed that the nuclear spin
polarization in single quantum dots can have three stable branches under a
longitudinal magnetic field. The states were accompanied by hysteresis loops
around the boundaries of each branch with a change in the excitation condition.
To explain these findings, we incorporated the electron spin relaxation caused
by the nuclear spin fluctuation into the previously-studied dynamic nuclear
spin polarization mechanism. The model reproduces the new features of nuclear
spin polarization and the associated strong reduction in the observed electron
spin polarization, and can refer to the tristability of nuclear spin
polarization.
