  Many long-duration gamma-ray bursts (GRBs) were observed by {\it Swift}/XRT
to have plateaus in their X-ray afterglow light curves. This plateau phase has
been argued to be evidence for long-lasting activity of magnetar
(ultra-strongly magnetized neutron stars) central engines. However, the
emission efficiency of such magnetars in X-rays is still unknown. Here we
collect 24 long GRB X-ray afterglows showing plateaus followed by steep decays.
We extend the well-known relationship between the X-ray luminosity
${L_{\mathrm{X}}}$ and spin-down luminosity $L_{\mathrm{sd}}$ of pulsars to
magnetar central engines, and find that the initial rotation period $P_{0}$
ranges from 1 ms to 10 ms and that the dipole magnetic field $B$ is centered
around $10^{15}$ G. These constraints not only favor the suggestion that the
central engines of some long GRBs are very likely to be rapidly rotating
magnetars but also indicate that the magnetar plateau emission efficiency in
X-rays is close to 100%.
