Using Chandra data taken on 2008 June, we detected pulsations at 2.59439(4) s in the soft gamma-ray repeater SGR 1627-41. This is the second measurement of the source spin period and allows us to derive for the first time a long-term spin-down rate of (1.9 +/- 0.4)E-11 s/s. From this value we infer for SGR 1627-41 a characteristic age of 2.2 kyr, a spin-down luminosity of 4E+34 erg/s (one of the highest among sources of the same class), and a surface dipole magnetic field strength of 2E+14 G. These properties confirm the magnetar nature of SGR 1627-41; however, they should be considered with caution since they were derived on the basis of a period derivative measurement made using two epochs only and magnetar spin-down rates are generally highly variable. The pulse profile, double-peaked and with a pulsed fraction of (13 +/- 2)% in the 2-10 keV range, closely resembles that observed by XMM-Newton in 2008 September. Having for the first time a timing model for this SGR, we also searched for a pulsed signal in archival radio data collected with the Parkes radio telescope nine months after the previous X-ray outburst. No evidence for radio pulsations was found, down to a luminosity level 10-20 times fainter (for a 10% duty cycle and a distance of 11 kpc) than the peak luminosity shown by the known radio magnetars.
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