Magnetic-field-induced superconductivity in layered organic molecular crystals with localized magnetic moments

$\lambda -(\mathrm{BETS}{)}_2{\mathrm{FeCl}}_4$ undergoes transitions from an antiferromagnetic insulator to a metal and then to a superconductor as a magnetic field is increased. We use a Hubbard-Kondo model to clarify the role of the ${\mathrm{Fe}}^{3+}$ magnetic ions in these phase transitions. In the high-field regime, the magnetic field acting on the electron spins is compensated by the exchange field $H_e$ due to the magnetic ions. We show how $H_e$ can be extracted from the observed splitting of the Shubnikov–de Haas frequencies. We predict the field range for field-induced superconductivity in other materials.