Theoretically, rotation-induced chemical mixing in massive stars has far reaching evolutionary consequences, affecting the sequence of morphological phases, lifetimes, nucleosynthesis, and supernova characteristics. Using a sample of 72 presumably single O-type giants to supergiants observed in the context of the VLT-FLAMES Tarantula Survey (VFTS), we aim to investigate rotational mixing in evolved core-hydrogen burning stars initially more massive than $15,M_odot$ by analysing their surface nitrogen abundances. Using stellar and wind properties derived in a previous VFTS study, we constrained the nitrogen abundance by fitting the equivalent widths of relatively strong lines that are sensitive to changes in the abundance of this element. Given the quality of the data, we constrained the nitrogen abundance in 38 cases; for 34 stars only upper limits could be derived, which includes almost all stars rotating at $v_mathrm{e}sin i >200,mathrm{km s^{-1}}$. We analysed the nitrogen abundance as a function of projected rotation rate $v_mathrm{e}sin i$ and confronted it with predictions of rotational mixing. The upper limits on the nitrogen abundance of the rapidly rotating stars are not in apparent violation with theoretical expectations. However, we found a group of N-enhanced slowly-spinning stars that is not in accordance with predictions of rotational mixing in single stars. Among O-type stars with (rotation-corrected) gravities less than $log,g_c = 3.75$ this group constitutes 30$-$40 percent of the population. We found a correlation between nitrogen and helium abundance which is consistent with expectations, suggesting that, whatever the mechanism that brings N to the surface, it displays CNO-processed material.
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