  Recent progress in the understanding of the collective behavior of electrons
and ions have revealed new types of ferroic orders beyond ferroelectricity and
ferromagnetism, such as the ferroaxial state. The latter retains only
rotational symmetry around a single axis and reflection symmetry with respect
to a single mirror plane, both of which are set by an emergent electric
toroidal dipole moment. Due to this unusual symmetry-breaking pattern, it has
been challenging to directly measure the ferroaxial order parameter, despite
the increasing attention this state has drawn. Here, we show that off-diagonal
components of the piezoresistivity tensor (i.e., the linear change in
resistivity under strain) transform the same way as the ferroaxial moments,
providing a direct probe of such order parameters. We identify two new proper
ferroaxial materials through a materials database search, and use
first-principles calculations to evaluate the piezoconductivity of the
double-perovskite CaSnF$_6$, revealing its connection to ferroaxial order and
to octahedral rotation modes.
