Dark Energy Survey Year 1 Results: Cross-correlation between Dark Energy Survey Y1 galaxy weak lensing and South Pole Telescope<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo>+</mml:mo><mml:mrow><mml:mi>P</mml:mi><mml:mi>l</mml:mi><mml:mi>a</mml:mi><mml:mi>n</mml:mi><mml:mi>c</mml:mi><mml:mi>k</mml:mi></mml:mrow></mml:mrow></mml:math> CMB weak lensing

We cross-correlate galaxy weak lensing measurements from the Dark Energy Survey (DES) year-one data with a cosmic microwave background (CMB) weak lensing map derived from South Pole Telescope (SPT) and Planck data, with an effective overlapping area of $1289\text{ }\text{ }{\mathrm{deg}}^{2}$. With the combined measurements from four source galaxy redshift bins, we obtain a detection significance of $5.8\ensuremath{\sigma}$. We fit the amplitude of the correlation functions while fixing the cosmological parameters to a fiducial $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, finding $A=0.99\ifmmode\pm\else\textpm\fi{}0.17$. We additionally use the correlation function measurements to constrain shear calibration bias, obtaining constraints that are consistent with previous DES analyses. Finally, when performing a cosmological analysis under the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, we obtain the marginalized constraints of ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{m}}=0.26{1}_{\ensuremath{-}0.051}^{+0.070}$ and ${S}_{8}\ensuremath{\equiv}{\ensuremath{\sigma}}_{8}\sqrt{{\mathrm{\ensuremath{\Omega}}}_{\mathrm{m}}/0.3}=0.66{0}_{\ensuremath{-}0.100}^{+0.085}$. These measurements are used in a companion work that presents cosmological constraints from the joint analysis of two-point functions among galaxies, galaxy shears, and CMB lensing using DES, SPT, and Planck data.