Enhancement of superconductivity by polarization of magnetic impurities in disordered films

Physical Review B: Condensed Matter and Materials Physics. 2026. Vol. 114. No. 7. Article 074505.

Seleznev G., Fominov Yakov V.

Dirty superconducting films with magnetic impurities can exhibit nontrivial behavior in a magnetic field that
polarizes the impurity spins. As predicted by Kharitonov and Feigelman (KF) [JETP Lett. 82, 421 (2005)],
this polarization reduces the exchange scattering rate. Consequently, a parallel magnetic field can enhance
the critical temperature Tc when magnetic-field pair breaking is weak, as realized for strong spin-orbit scat-
tering and small film thickness. Recently, Llanos et al. [Nat. Phys. 22, 856 (2026)] observed a pronounced
enhancement of Tc consistent with the KF theory. The same experiment also reported an enhancement of
the perpendicular upper critical field H⊥c2 and a suppression of the London penetration depth λL by a parallel magnetic field. These quantities were not considered in the original KF theory. To address this gap, we develop
a theoretical framework based on Gor’kov’s diagrammatic technique for dirty superconductors. We extend
the KF theory in two experimentally relevant directions: (i) to arbitrary temperatures T < Tc and several
superconducting observables and (ii) to arbitrary magnetic-field orientations. As a result, we demonstrate
theoretically the suppression of λL and the enhancement of H⊥c2 by a parallel magnetic field, in agreement with
experiment.

Keywords: superconductivity, сверхпроводимость, беспорядок, magnetic moment,, магнитный момент,, disorder