Using muon spin rotation (μSR) we investigated the magnetic and superconducting properties of a series of Ba(Fe${}_{1-x}$Co${}_x$)${}_2$As${}_2$ single crystals with $0\le x\le 0.15$. Our study details how the antiferromagnetic order is suppressed upon Co substitution and how it coexists with superconductivity. In the nonsuperconducting samples at $0<x<0.04$ the antiferromagnetic order parameter is only moderately suppressed. With the onset of superconductivity this suppression becomes faster and it is most rapid between $x=0.045$ and 0.05. As was previously demonstrated by μSR at $x=0.055$ [P. Marsik et al., Phys. Rev. Lett. 105, 57001 (2010)], the strongly weakened antiferromagnetic order is still a bulk phenomenon that competes with superconductivity. The comparison with neutron diffraction data suggests that the antiferromagnetic order remains commensurate whereas the amplitude exhibits a spatial variation that is likely caused by the randomly distributed Co atoms. A different kind of magnetic order that was also previously identified [C. Bernhard et al., New J. Phys. 11, 055050 (2009)] occurs at $0.055<x<0.075$ where $T_{\mathrm{c}}$ approaches the maximum value. The magnetic order develops here only in parts of the sample volume and it seems to cooperate with superconductivity since its onset temperature coincides with $T_{\mathrm{c}}$. Even in the strongly overdoped regime at $x$ $=$ 0.11, where the static magnetic order has disappeared, we find that the low-energy spin fluctuations are anomalously enhanced below $T_{\mathrm{c}}$. These findings point toward a drastic change in the relationship between the magnetic and superconducting orders from a competitive one in the strongly underdoped regime to a constructive one in near-optimally and overdoped samples.

• Received 1 July 2012

DOI:https://doi.org/10.1103/PhysRevB.86.184509