Antiferromagnetic Order in Pauli-Limited Unconventional Superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in $\mathrm{CeCo}{\mathrm{In}}_5$. We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-$\mathit{Q}$ magnetic phase.

Figure 1

Fermi surface and the nodal pockets generated by Zeeman field for the tight-binding model described in the text with ${\Delta }_0/t=0.7$, $h/t=0.3$, 0.7. ${\mathit{k}}_{\parallel }$ and ${\mathit{k}}_{\perp }$ correspond to the directions parallel and perpendicular to the Fermi surface near each pocket.

Figure 2

Conditions for pairing of the Fermions at the nodal pockets due to the term $c_{\mathit{k}+{\mathit{Q}}_i\uparrow }^{†}{c}_{\mathit{k}\downarrow }$: a placeholder. Dotted line: Fermi surface, green dots: nodes. Left panel: If $\mathit{k}$ is in the lower pocket, only the term with ${\mathit{Q}}_i=\mathit{Q}$ satisfies the nesting condition and leads to pairing. Right panel: If $\mathit{k}$ is in the upper pocket, only ${\mathit{Q}}_i=-\mathit{Q}$ is relevant.

Figure 3

Phase diagram obtained for $V=3t$ and $J=3.5t$. Open and filled circles indicate first and second order phase transitions, respectively. The red circles are the boundary between the SC and N states, while the blue circles are the boundary for the magnetically ordered phase.