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We report on the discovery and energy dependence of hard phase lags in the2.14 Hz pulsed profiles of GRO J1744-28. We used data from XMM-Newton andNuSTAR. We were able to well constrain the lag spectrum with respect to thesoftest (0.3--2.3 keV) band: the delay shows increasing lag values reaching amaximum delay of $\sim$ 12 ms, between 6 and 6.4 keV. After this maximum, thevalue of the hard lag drops to 7 ms, followed by a recovery to a plateau at 9ms for energies above 8 keV. NuSTAR data confirm this trend up to 30 keV, butthe measurements are statistically poorer, and therefore, less constraining.The lag-energy pattern up to the discontinuity is well described by alogarithmic function. Assuming this is due to a Compton reverberationmechanism, we derive a size for the Compton cloud $R_{\rm{cc}}$ $\sim$ 120$R_{\rm g}$, consistent with previous estimates on the magnetospheric radius.In this scenario, the sharp discontinuity at $\sim$ 6.5 keV appears difficultto interpret and suggests the possible influence of the reflected component inthis energy range. We therefore propose the possible coexistence of bothCompton and disk reverberation to explain the scale of the lags and its energydependence.

Discovery of hard phase lags in the pulsed emission of GRO J1744-28