The relative effectiveness of the orbital8 and paramagnetic9 (Pauli) limiting effects in suppressing superconductivity is reflected in the Maki parameter α=√(2Hc20/Hp. A large α indicates a small Pauli limiting field, HP (stronger Pauli limiting), and/or a large orbital limiting field, Hc20. Radovan et al.3 obtain α≈13 by using HP≈4 T, which assumes an electron g-factor of 2 for CeCoIn5. But the experimental value of the superconducting critical field is Hc2=12 T, three times the Pauli (upper) limit used by Radovan et al. Therefore, HP=4 T is unphysical.

HP can be estimated both theoretically and experimentally. It has been estimated by fitting the critical field Hc2 of CeCoIn5 to a model for a d-wave superconductor with an FFLO state10 to give an electron g-factor of 0.64 or HP=12.8 T. A very conservative lower bound of HP>10 T can be made simply by noting that Hc2=10 T at 1 K, where an FFLO state cannot influence Hc2.

Theoretically, the Maki parameter must exceed 9 for an m≠0 LL state to become a ground state5. HP=12.8 T gives α≈4.5, which is a third of the value derived by Radovan et al., and half the minimum required for observation of m≠0 LL superconducting states. The number of observed steps (tens) also seems to be orders of magnitude greater than that expected theoretically5 for a material with α close to that of CeCoIn5. Only one non-zero state (m=1) is expected5 for α≥9, and two such states (m=1,2) appear5 at α≥20, far greater than α≈4.5 for CeCoIn5.

In addition, the number of higher LL states is theoretically expected to increase as the applied field approaches the parallel orientation (Θ→0), with m→∞ at Θ=0 (refs 6, 7). This prediction opposes the trend shown by the results of Radovan et al. Thus, we believe that the observed steps in magne-tization cannot be due to the higher LL states induced by the FFLO effects in CeCoIn5.

The heat-capacity data shown in Fig. 2 of Radovan et al.3 are inconsistent with our data4, and miss a large narrow peak associated with the first-order nature of the superconducting phase transition below 1 K. A related point is that it is also incorrect to identify the order of the phase transition on the basis of the presence or absence of a temperature swing at a phase transition in the described magneto-caloric setup (inset to their Fig. 2). Such swings are expected both at first- and at second-order phase transitions11.