Investigating the role of disorder in superconductors is an essential part of characterizing the fundamental superconducting properties as well as assessing potential applications of the material. In most cases, the information available on the defect matrix is poor, making such studies difficult, but the situation can be improved by introducing defects in a controlled way, as provided by neutron irradiation. In this work, we analyze the effects of neutron irradiation on a Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ single crystal. We mainly concentrate on the magnetic properties which were determined by magnetometry. Introducing disorder by neutron irradiation leads to significant effects on both the reversible and the irreversible magnetic properties, such as the transition temperature, the upper critical field, the anisotropy, and the critical current density. The results are discussed in detail by comparing them with the properties in the unirradiated state.
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