  We determine the critical Zeeman energy splitting of a homogeneous Fermi
superfluid at unitary in terms of the Fermi energy $\epsilon_{\text F}$
according to recent experimental results in LKB-Lhomond. Based on the universal
equations of state for the superfluid and normal phases, we show that there
exist two critical fields $H_{c1}$ and $H_{c2}$, between which a
superfluid-normal mixed phase is energetically favored. Universal formulae for
the critical fields and the critical population imbalance $P_c$ are derived. We
have found a universal relation between the critical fields and the critical
imbalances: $H_{c1}=\gamma\xi\epsilon_{\text F}$ and $H_{c2}=(1+\gamma
P_c)^{2/3}H_{c1}$ where $\xi$ is the universal constant and $\gamma$ is the
critical value of the chemical potential imbalance in the grand canonical
ensemble. Since $\xi$, $\gamma$ and $P_c$ have been measured in the
experiments, we can determine the critical Zeeman fields without the detail
information of the equation of state for the polarized normal phase. Using the
experimental data from LKB-Lhomond, we have found
$H_{c1}\simeq0.37\epsilon_{\text F}$ and $H_{c2}\simeq0.44\epsilon_{\text F}$.
Our result of the polarization $P$ as a function of the Zeeman field
$H/\epsilon_{\text F}$ is in good agreement with the data extracted from the
experiments. We also give an estimation of the critical magnetic field for
dilute neutron matter at which the matter gets spin polarized, assuming the
properties of the dilute neutron matter are close to those of the unitary Fermi
gas.
