  Dark matter (DM) bars that shadow stellar bars have been previously shown to
form in idealized simulations of isolated disk galaxies. Here, we show that DM
bars commonly occur in barred disk galaxies in the TNG50 cosmological
simulation suite, but do not appear in unbarred disk galaxies. Consistent with
isolated simulations, DM bars are typically shorter than their stellar
counterparts and are $75\%$ weaker as measured by the Fourier $A_2$ moment. DM
bars dominate the shape of the inner halo potential and are easily identified
in the time series of quadrupolar coefficients. We present two novel methods
for measuring the bar pattern speed using these coefficients, and use them to
make a measurement of the pattern speed and rotation axis orientation for one
sample galaxy located in one of the high-time resolution subboxes of TNG50. The
stellar and dark bars in this galaxy remain co-aligned throughout the last 8
Gyr and have identical pattern speeds throughout. Both the pattern speed and
rotation axis orientation of the bars evolve considerably over the last 8 Gyr,
consistent with torques on the bars due to dynamical friction and gas
accretion. While the bar pattern speed generally decreases over the time
course, it is seen to increase after mergers. Rather than remaining static in
time, the rotation axis displays both precession and nutation possibly caused
by torques outside the plane of rotation. We find that the shape of the stellar
and DM mass distributions are tightly correlated with the bar pattern speed.
