Coexistence of superconductivity and magnetism inCa1−xNaxFe2As2: Universal suppression of the magnetic order parameter in 122 iron pnictides

Abstract

We present a detailed investigation of the magnetic and superconducting properties of ${\mathrm{Ca}}_{1\ensuremath{-}x}{\mathrm{Na}}_{x}{\mathrm{Fe}}_{2}{\mathrm{As}}_{2}$ single crystals with $x=0.00$, 0.35, 0.50, and 0.67 by means of the local probe techniques M\ossbauer spectroscopy and muon spin relaxation experiments. With increasing Na-substitution level, the magnetic order parameter is suppressed. For $x=0.50$ we find a microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature ${T}_{c}$. A systematic comparison with other 122 pnictides reveals a square-root correlation between the reduction of the magnetic order parameter and the ratio of the transition temperatures ${T}_{c}/{T}_{N}$, which can be understood in the framework of a Landau theory. In the optimally doped sample with ${T}_{c}\ensuremath{\approx}34$ K, diluted magnetism is found and the temperature dependence of the penetration depth and superfluid density are obtained, proving the presence of two superconducting $s$-wave gaps.