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Magnetic neutron diffraction study of Ba(Fe1-xCox)2As2 critical exponents through the tricritical doping

We present temperature dependent magnetic neutron diffraction measurements on Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ for $x$ = 0.039, 0.022, and 0.021 as-grown single crystals. Our investigations probe the behavior near the magnetic tricritical point in the ($x$,$T$) plane, $x_{tr} \approx $0.022, as well as systematically exploring the character of the magnetic phase transition across a range of doping values. All samples show long range antiferromagnetic order that may be described near the transition by simple power laws, with $β$ =~0.306$\pm$0.060 for $x$ =~0.039, $β$ =~0.208$\pm$0.005 for $x$ =~0.022, and $β$ =~0.198$\pm$0.009 for $x$ =~0.021. For the $x$ =~0.039 sample, the data are reasonably well described by the order parameter exponent $β$ =~0.326 expected for a 3D Ising model while the $x$ =~0.022 and $x$ =~0.021 samples are near the $β$ =~0.25 value for a tricritical system in the mean-field approximation. These results are discussed in the context of existing experimental work and theoretical predictions.