Magnetic neutron diffraction study of BaFe$_{2(1-x)}$Co$_{2x}$As$_{2}$ critical exponents through the tricritical doping

We present temperature dependent magnetic neutron diffraction measurements of BaFe$_{2(1-x)}$Co$_{2x}$As$_{2}$ for x~=~0.039, 0.022, and 0.021 as-grown single crystals. We are motivated to investigate the magnetic tricritical point in the (x,T) plane near x$^{m}_{tr}$$\approx$0.022,[1] as well as to systematically probe the character of the magnetic phase transition across a range of dopings. All samples show long range antiferromagnetic order that may be described near the transition by $I\propto(1-T/T_N )^{2\beta}$ with $\beta$~=~0.291 for x~=~0.039, $\beta$~=~0.208 for x~=~0.022, and $\beta$~=~0.198 for x~=~0.021, showing a monotonic increase from the parent BaFe$_{2}$As$_{2}$ compound, $\beta$~=~0.103.[2] We will discuss the results based on theoretical predictions for the behavior of the order parameter in the vicinity of a tricritical point.\\[4pt] [1] M.G. Kim, R.M. Fernandes, A. Kreyssig, J.W. Kim, A. Thaler, S.L. Bud'ko, P.C. Canfield, R.J. McQueeney, J. Schmalian, and A.I. Goldman, Phys. Rev. B 83, 134522 (2011). \newline [2] S.D. Wilson, Z. Yamani, C.R. Rotundu, B. Freelon, E. Bourret-Courchesne, and R.J. Birgeneau, Phys. Rev. B 79, 184519 (2009).