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Pauli limit
(see Tinkham p. 390-394 on pair breaking).
(see A.M.Clogston Phys Rev Lett.9.266 1962, very clear)
Translated into SI units, normally
{$$ \tag{1}\begin{equation} F_N = F_S + \mu_0H_c^2\end{equation}$$}
Ignoring Van Vleck and orbital contributions to {$\chi$}, for a superconductor with negligible spin orbit pairing the maximum critical field {$H_P$} (Pauli limit) is such that the free energy of the normal state in this field is equal to the minimum superconducting free energy, at {$T=0$}. Now a new limit might be considered, where superconductivity is on the verge of being destroyed, i.e the Meissner effect is negligible. In this case we anticipate a first order transition to the normal state when {$F_N(H_P)=F_S(0)$}, which, in place of Eq. (1), leads to:
{$$ F_N -\chi_P H_P^2= F_S$$}
From this, since {$\chi_P = \mu_0\mu_B^2 N(E_F)$} and the BCS condensation energy is {$\frac 1 2 N(E_F)\Delta^2$}, we get
{$$ \mu_B H_P=\frac{\Delta(0)}{\sqrt{2\mu_0}}$$}
Magnetism.ToleranceFactor
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