  We investigate effects of thermal and quantum fluctuations on the phase
diagram of a spin-1 87Rb Bose-Einstein condensate (BEC) under a quadratic
Zeeman effect. Due to the large ratio of spinindependent to spin-dependent
interactions of 87Rb atoms, the effect of noncondensed atoms on the condensate
is much more significant than that in scalar BECs. We find that the condensate
and spontaneous magnetization emerge at different temperatures when the ground
state is in the brokenaxisymmetry phase. In this phase, a magnetized condensate
induces spin coherence of noncondensed atoms in different magnetic sublevels,
resulting in temperature-dependent magnetization of the noncondensate. We also
examine the effect of quantum fluctuations on the order parameter at absolute
zero, and find that the ground-state phase diagram is significantly altered by
quantum depletion.
