## Effects of thermal and quantum fluctuations on the phase diagram of a spin-1 {sup 87}Rb Bose-Einstein condensate

We investigate the effects of thermal and quantum fluctuations on the phase diagram of a spin-1 {sup 87}Rb Bose-Einstein condensate (BEC) under the quadratic Zeeman effect. Due to the large ratio of spin-independent to spin-dependent interactions of {sup 87}Rb 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 broken-axisymmetry phase. In this phase, a magnetized condensate induces spin coherence of noncondensed atoms in different magnetic sublevels, resulting in temperature-dependent magnetization of themore »