The high-field superconducting state in ${\mathrm{CeCoIn}}_5$ has been studied by transverse field muon spin rotation measurements with an applied field parallel to the crystallographic $c$ axis close to the upper critical field ${\mu }_0{H}_{c2}=4.97\mathrm{T}$. At magnetic fields ${\mu }_{0}H\ge 4.8\mathrm{T}$ the muon Knight shift is enhanced and the superconducting transition changes from second order towards first order as predicted for Pauli-limited superconductors. The field and temperature dependence of the transverse muon spin relaxation rate $\sigma$ reveal paramagnetic spin fluctuations in the field regime from $2\mathrm{T}\le {\mu }_{0}H<4.8\mathrm{T}$. In the normal state close to $H_{c2}$ correlated spin fluctuations as described by the self-consistent renormalization theory are observed. The results support the formation of a mode-coupled superconducting and antiferromagnetically ordered phase in ${\mathrm{CeCoIn}}_5$ for $H$ directed parallel to the $c$ axis.

• Received 28 September 2009

DOI:https://doi.org/10.1103/PhysRevLett.103.237003