  The central engines of some superluminous supernovae (SLSNe) are generally
suggested to be newly born fast rotating magnetars, which spin down mainly
through magnetic dipole radiation and gravitational wave emission. We calculate
the magnetar-powered SLSNe light curves (LCs) with the tilt angle evolution of
newly born magnetars involved. We show that, depending on the internal toroidal
magnetic fields ${\bar B}_{\rm t}$, the initial spin periods $P_{\rm i}$, and
the radii $R_{\rm DU}$ of direct Urca (DU) cores of newly born magnetars, as
well as the critical temperature $T_{\rm c}$ for $^3P_2$ neutron superfluidity,
bumps could appear in the SLSNe LCs after the maximum lights when the tilt
angles grow to $\pi/2$. The value of $T_{\rm c}$ determines the arising time
and the relative amplitude of a bump. The quantity $R_{\rm DU}$ can affect the
arising time and the luminosity of a bump, as well as the peak luminosity of a
LC. Moreover, it is interesting that a stronger ${\bar B}_{\rm t}$ will lead to
both a brighter peak and a brighter bump in a LC. While keeping other
quantities unchanged, the bump in the LC disappears for the magnetar with
smaller $P_{\rm i}$. We suggest that, once the SLSNe LCs with such kinds of
bumps are observed, by fitting these LCs with our model, not only $B_{\rm d}$
and $P_{\rm i}$ of newly born magnetars but also the crucial physical
quantities ${\bar B}_{\rm t}$, $R_{\rm DU}$, and $T_{\rm c}$ could be
determined. Nonobservation of SLSNe LCs with such kinds of bumps hitherto may
already put some (\textit{though very rough}) constraints on ${\bar B}_{\rm
t}$, $P_{\rm i}$, $R_{\rm DU}$, and $T_{\rm c}$. Therefore, observation of
SLSNe LCs may provide a new approach to probe the physics of newly born
magnetars.
