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We measure the cross-correlation between galaxy weak lensing data from theKilo Degree Survey (KiDS-1000, DR4) and cosmic microwave background (CMB)lensing data from the Atacama Cosmology Telescope (ACT, DR4) and the PlanckLegacy survey. We use two samples of source galaxies, selected with photometricredshifts, $(0.1<z_{\rm B}<1.2)$ and $(1.2<z_{\rm B}<2)$, which produce acombined detection significance of the CMB lensing/weak galaxy lensingcross-spectrum of $7.7\sigma$. With the lower redshift galaxy sample, for whichthe cross-correlation is detected at a significance of $5.3\sigma$, we presentjoint cosmological constraints on the matter density parameter, $\Omega_{\rmm}$, and the matter fluctuation amplitude parameter, $\sigma_8$, marginalisingover three nuisance parameters that model our uncertainty in the redshift andshear calibration, and the intrinsic alignment of galaxies. We find ourmeasurement to be consistent with the best-fitting flat $\Lambda$CDMcosmological models from both Planck and KiDS-1000. We demonstrate the capacityof CMB-weak lensing cross-correlations to set constraints on either theredshift or shear calibration, by analysing a previously unused high-redshiftKiDS galaxy sample $(1.2<z_{\rm B}<2)$, with the cross-correlation detected ata significance of $7\sigma$. This analysis provides an independent assessmentfor the accuracy of redshift measurements in a regime that is challenging tocalibrate directly owing to known incompleteness in spectroscopic surveys.

Strong detection of the CMB lensingxgalaxy weak lensingcross-correlation from ACT-DR4,PlanckLegacy and KiDS-1000