We present ALMA measurements of a merger shock using the thermal Sunyaev-Zeldovich (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.
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