  We consider an antiferromagnetic Bose-Einstein condensate in a traverse
magnetic field with a fixed macroscopic magnetization. The system exhibits two
different critical behaviors corresponding to transitions from polar to
broken-axisymmetry and from antiferromagnetic to broken-axisymmetry phases
depending on the value of magnetization. We exploit both types of system
criticality as a resource in the precise estimation of control parameter value.
We quantify the achievable precision by the quantum Fisher information. We
demonstrate supersensitivity and show that the precision scales with the number
of atoms up to $N^4$ around critically. In addition, we study the precision
based on the error-propagation formula providing the simple-to-measure signal
which coincides its scaling with the quantum Fisher information. Finally, we
take into account the effect of non-zero temperature and show that the sub-shot
noise sensitivity in the estimation of the control parameter is achievable in
the low-temperature limit.
