Joint analysis of DES Year 3 data and CMB lensing from SPT and Planck
  II: Cross-correlation measurements and cosmological constraints
  Cross-correlations of galaxy positions and galaxy shears with maps of
gravitational lensing of the cosmic microwave background (CMB) are sensitive to
the distribution of large-scale structure in the Universe. Such
cross-correlations are also expected to be immune to some of the systematic
effects that complicate correlation measurements internal to galaxy surveys. We
present measurements and modeling of the cross-correlations between galaxy
positions and galaxy lensing measured in the first three years of data from the
Dark Energy Survey with CMB lensing maps derived from a combination of data
from the 2500 deg$^2$ SPT-SZ survey conducted with the South Pole Telescope and
full-sky data from the Planck satellite. The CMB lensing maps used in this
analysis have been constructed in a way that minimizes biases from the thermal
Sunyaev Zel'dovich effect, making them well suited for cross-correlation
studies. The total signal-to-noise of the cross-correlation measurements is
23.9 (25.7) when using a choice of angular scales optimized for a linear
(nonlinear) galaxy bias model. We use the cross-correlation measurements to
obtain constraints on cosmological parameters. For our fiducial galaxy sample,
which consist of four bins of magnitude-selected galaxies, we find constraints
of $\Omega_{m} = 0.272^{+0.032}_{-0.052}$ and $S_{8} \equiv \sigma_8
\sqrt{\Omega_{m}/0.3}= 0.736^{+0.032}_{-0.028}$ ($\Omega_{m} =
0.245^{+0.026}_{-0.044}$ and $S_{8} = 0.734^{+0.035}_{-0.028}$) when assuming
linear (nonlinear) galaxy bias in our modeling. Considering only the
cross-correlation of galaxy shear with CMB lensing, we find $\Omega_{m} =
0.270^{+0.043}_{-0.061}$ and $S_{8} = 0.740^{+0.034}_{-0.029}$. Our constraints
on $S_8$ are consistent with recent cosmic shear measurements, but lower than
the values preferred by primary CMB measurements from Planck.
