  We study the emergence of hysteresis during the process of quantum phase
transition from an antiferromagnetic to a phase-separated state in a spin-1
Bose Einstein condensate of ultracold atoms. We explicitly demonstrate the
appearance of a hysteresis loop with various quench times showing that it is
rate-independent for large magnetizations only. In other cases scaling of the
hysteresis loop area is observed, which we explain by using the Kibble-Zurek
theory in the limit of small magnetization. The effect of an external harmonic
trapping potential is also discussed.
