  We studied the formation mechanism of the in-plane nuclear field in single
self-assembled In$_{0.75}$Al$_{0.25}$As/Al$_{0.3}$Ga$_{0.7}$As quantum dots.
The Hanle curves with an anomalously large width and hysteretic behavior at the
critical transverse magnetic field were observed in many single quantum dots
grown in the same QD sample. In order to explain the anomalies in the Hanle
curve indicating the formation of a large nuclear field perpendicular to the
photo-injected electron spin polarization, we propose a new model based on the
current phenomenological model for dynamic nuclear spin polarization. The model
includes the effects of the nuclear quadrupole interaction and the sign
inversion between in-plane and out-of-plane g-factors, and the model
calculations reproduce successfully the characteristics of the observed
anomalies in the Hanle curves.
