  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 world's best limits
on nonstandard interactions in the $\mu-\tau$ sector.
