Critical Magnetic Field

(in superconductors), the specific value of magnetic field strength H_c above which the magnetic field partially or completely penetrates the superconductor. When H < H_c the magnetic field does not penetrate the superconductor, because it is shielded by the surface superconducting current (the Meissner effect).

In type I (soft) superconductors, which include most pure metals, the substance passes into the normal, nonsuperconducting state when H > H_c (phase transition of the first kind). The critical magnetic field H_c corresponding to this transition is related to the difference between the free energies of the normal phase (F_n) and the superconducting phase (F_sc) by the formula F_n − F_sc = H_c²/8π.

The highest value of H_c reaches hundreds of oersteds for pure metals. If the magnetic field is equal to H_c only at some points of the surface on a superconductor of the second kind, an intermediate state develops in it (alternating superconducting and normal phases).

In type II (hard) superconductors (mostly alloys), the penetration of the magnetic field begins with the formation of vortex filaments, in whose cores the magnetic field is largely concentrated. The substance has not yet lost its superconducting properties, and the currents flowing in it are partially shielding it from the external field. For these substances the critical magnetic field H_c,1 that corresponds to the beginning of penetration is smaller than the thermodynamic critical field H_c. Complete penetration of the magnetic field occurs in superconductors at H_c,2, which may be both smaller and larger than H_c. In the hard superconductors, the best known of which are alloys based on niobium, the critical magnetic field H_c,2 ≫ H_c,₁ and reaches hundreds of thousands of oersteds. Second-order phase transitions take place at field values H_c1 and H_c,₂.