Nematic order by disorder in spin-2 BECs

The effect of quantum and thermal fluctuations on the phase diagram of spin-2 BECs is examined. They are found to play an important role in the nematic part of the phase diagram, where a mean-field treatment of two-body interactions is unable to lift the accidental degeneracy between nematic states. Quantum and thermal fluctuations resolve this degeneracy, selecting the uniaxial nematic state, for scattering lengths $a_4$ greater than $a_2$, and the square biaxial nematic state for $a_4$ less than $a_2$. Paradoxically, the fluctuation induced order is stronger at higher temperatures, for a range of temperatures below $T_c$. For the experimentally relevant cases of spin-2 $^{87}$Rb and $^{23}$Na, we argue that such fluctuations could successfully compete against other effects like the quadratic Zeeman field, and stabilize the uniaxial phase for experimentally realistic conditions. A continuous transition of the Ising type from uniaxial to square biaxial order is predicted on raising the magnetic field. These systems present a promising experimental opportunity to realize the `order by disorder' phenomenon.