We derive critical field $H_{\mathrm{c}2}$ equations for antiferromagnetic $s$-wave, $d_{x^2\text{−}{y}^2}$-wave, and $d_{xy}$-wave superconductors with effective-mass anisotropy in three dimensions, where we take into account (i) the Jaccarino-Peter mechanism of magnetic-field-induced superconductivity (FISC) at high fields, (ii) an extended Jaccarino-Peter mechanism that reduces the Pauli paramagnetic pair-breaking effect at low fields where superconductivity and an antiferromagnetic long-range order with a canted spin structure coexist, and (iii) the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF) state. As an example, experimental phase diagrams observed in organic superconductor $\kappa \text{−}(\mathrm{BETS}{)}_2{\mathrm{FeBr}}_4$ are theoretically reproduced. In particular, the upper critical field of low-field superconductivity is well reproduced without any additional fitting parameter other than those determined from the critical field curves of the FISC at high fields. Therefore, the extended Jaccarino-Peter mechanism seems to occur actually in the present compound. It is predicted that the FFLO state does not occur in the FISC at high fields in contrast to the compound $\lambda \text{−}(\mathrm{BETS}{)}_2{\mathrm{FeCl}}_4$, but it may occur in low-field superconductivity for $s$-wave and $d_{x^2\text{−}{y}^2}$-wave pairings. We also briefly discuss a possibility of compounds that exhibit unconventional behaviors of upper critical fields.

• Received 3 March 2006

DOI:https://doi.org/10.1103/PhysRevB.74.024518