As atmospheric neutrinos propagate through the Earth, vacuum-like oscillations are modified by Standard-Model neutral- and charged-current interactions with electrons. Theories beyond the Standard Model introduce heavy, TeV-scale bosons that can produce nonstandard neutrino interactions. These additional interactions may modify the Standard Model matter effect producing a measurable deviation from the prediction for atmospheric neutrino oscillations. The result described in this paper constrains nonstandard interaction parameters, building upon a previous analysis of atmospheric muon-neutrino disappearance with three years of IceCube-DeepCore data. The best fit for the muon to tau flavor changing term is $epsilon_{mu tau}=-0.0005$, with a 90% C.L. allowed range of $-0.0067 <epsilon_{mu tau}< 0.0081$. This result is more restrictive than recent limits from other experiments for $epsilon_{mu tau}$. Furthermore, our result is complementary to a recent constraint on $epsilon_{mu tau}$ using another publicly available IceCube high-energy event selection. Together, they constitute the worlds best limits on nonstandard interactions in the $mu-tau$ sector.
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