Can atmospheric neutrino experiments provide the first hint of leptonicCPviolation?

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The measurement of a nonzero value of the 1--3 mixing angle has paved the way for the determination of leptonic $CP$ violation. However, the current generation long-baseline experiments T2K and $\mathrm{NO}\ensuremath{\nu}\mathrm{A}$ have limited sensitivity to ${\ensuremath{\delta}}_{CP}$. In this paper, we show, for the first time, the significance of atmospheric neutrino experiments in providing the first hint of $CP$ violation in conjunction with T2K and $\mathrm{NO}\ensuremath{\nu}\mathrm{A}$. In particular, we find that adding atmospheric neutrino data from a magnetized iron calorimeter detector at the India-Based Neutrino Observatory to T2K and $\mathrm{NO}\ensuremath{\nu}\mathrm{A}$ results in a twofold increase in the range of ${\ensuremath{\delta}}_{CP}$ values for which a $2\ensuremath{\sigma}$ hint of $CP$ violation can be obtained. In fact, in the parameter region unfavorable for the latter experiments, the first signature of $CP$ violation may well come from the inclusion of atmospheric neutrino data.