  The long-lasting X-ray plateau emission in long gamma-ray bursts (GRBs) shows
observational evidence for ongoing energy injection, which may be from magnetar
spindown due to energy released via either magnetic dipole (MD) or
gravitational wave (GW) radiation. In this paper, by systematically analyzing
the {\em Swift}/XRT light curves detected before 2018 July, we find 45 light
curves with a measured redshift that monotonically decay as a smooth broken
power law. By assuming that the central engines of these GRBs are newly born
magnetars, we measure the braking index $n$ of putative millisecond magnetars,
due to MD and GW radiations. The inferred braking indices are not close to 3 or
5, but range between them with a normal distribution ($n_{\rm c}=4.02\pm
0.11$). We define a dimensionless parameter $\Re$, which is the ratio between
the MD and GW components, and find that the energy released via magnetar
spindown in most GRBs of our sample is dominated by GW radiation for $P_0=3$ ms
and $\epsilon=0.005$ and 0.01. On the other hand, we find that $\Re$ and the
braking index $n$ seem to be anticorrelated within a large systematic error at
$t=0$, but depend on the values of the parameters $P_0$ and $\epsilon$. These
results suggest that the contribution of GW radiation cannot be ignored, and
that a larger braking index leads to GWs dominating the energy released during
magnetar spindown if indeed magnetars are operating in some long GRBs.
