  We present ALMA measurements of a merger shock using the thermal
Sunyaev-Zel'dovich (SZ) effect signal, at the location of a radio relic in the
famous El Gordo galaxy cluster at $z \approx 0.9$. Multi-wavelength analysis in
combination with the archival Chandra data and a high-resolution radio image
provides a consistent picture of the thermal and non-thermal signal variation
across the shock front and helps to put robust constraints on the shock Mach
number as well as the relic magnetic field. We employ a Bayesian analysis
technique for modeling the SZ and X-ray data self-consistently, illustrating
respective parameter degeneracies. Combined results indicate a shock with Mach
number ${\cal M} = 2.4^{+1.3}_{-0.6}$, which in turn suggests a high value of
the magnetic field (of the order of $4-10 ~\mu$G) to account for the observed
relic width at 2 GHz. At roughly half the current age of the universe, this is
the highest-redshift direct detection of a cluster shock to date, and one of
the first instances of an ALMA-SZ observation in a galaxy cluster. It shows the
tremendous potential for future ALMA-SZ observations to detect merger shocks
and other cluster substructures out to the highest redshifts.
