Superconducting Vortices in CeCoIn$_5$: Beyond the Abrikosov-Ginzburg-Landau Paradigm

We report on the magnetic field ($H$) dependence of the form factor $|F|^2$ of the vortex lattice (VL) in CeCoIn$_5$ obtained by small angle neutron scattering for $H$ applied along the crystallographic $c$-axis. Superconductivity (SC) in CeCoIn$_5$ has several unconventional aspects to it: The $d$-wave SC is in competition with antiferromagnetic order, as suggested by the presence of an magnetic QCP located at the upper critical field $H_{c2}$ determined by the Pauli effect. At both 50 and 500~mK we observe an $H$-independent $|F|^2$ up to 2~T. With further increasing $H$, $|F|^2$ continues to increase all the way up to $H_{c2}$. This finding is in contrast to that normally observed in type-II SC's, where $|F|^2$ decreases with increasing $H$. It suggests a departure from the Abrikosov-Ginzburg-Landau paradigm, where the properties of the vortex state can be described by the coherence length $\xi$ and the penetration depth $\lambda$.