PauliLimit

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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