  Electrons in the pyrochore iridates experience a large interaction energy in
addition to a strong spin-orbit interaction. Both features make the iridates
promising for realizing novel states such as the Topological Mott Insulator.
The pyrochlore iridate Eu$_2$Ir$_2$O$_7$ shows a metal-insulator transition at
$T_N \sim$ 120 K below which a magnetically ordered state develops. Using
torque magnetometry, we uncover a highly unusual magnetic response. A magnetic
field $\bf H$ applied in its $a$-$b$ plane produces a nonlinear magnetization
$M_\perp$ orthogonal to the plane. $M_\perp$ displays a $d$-wave field-angle
pattern consistent with octupolar order, with a handedness dictated by field
cooling, leading to symmetry breaking of the chirality $\omega$. A surprise is
that the lobe orientation of the $d$-wave pattern is sensitive to the direction
of the field when the sample is field-cooled below $T_N$, suggestive of an
additional order parameter $\eta$ already present at 300 K.
