We consider the superconducting state in a clean crystal with antiferromagnetic (AF) structure of localized magnetic moments taking into account the exchange interaction between magnetic moments and conduction electrons. We assume that the localized moments order at the Neel temperature $T_N$ due to the RKKY interaction predominantly. In such crystals, the periodic exchange field acting on conducting electrons results in the formation of an insulating gap on the Fermi surface for electrons moving in directions that depend on the orientation of the wave vector of AF ordering. We assume a scenario in which the Cooper pairing occurs in the open parts of the Fermi surface at the temperature $T_c$. We show that at high amplitudes of exchange field $h_e>T_c/{\mu }_B$, the structure of superconducting state just below the temperature $T_c$ depends on the relation between $T_c$ and $T_N$. At low ratio $T_c/T_N$, a nonuniform superconducting state, like the Fulde-Farrell-Larkin-Ovchinnikov high-field phase, should exist, while at bigger ratio superconducting order parameter is uniform. The nonuniform structure of superconducting state may be probed by tunneling measurements.

• Received 2 June 2015
• Revised 26 October 2015

DOI:https://doi.org/10.1103/PhysRevB.93.014501