  By fitting the bolometric light curves of 31 super-luminous supernovae
(SLSNe) with the magnetar engine model, we derive the ejecta masses and
magnetar parameters for these SLSNe. The lower boundary of magnetic field
strengths of SLSN magnetars can be set just around the critical field strength
$B_{\rm c}$ of electron Landau quantization. In more details, SLSN magnetars
can further be divided into two subclasses of magnetic fields of
$\sim(1-5)B_{\rm c}$ and $\sim(5-10)B_{\rm c}$, respectively. It is revealed
that these two subclasses of magnetars are just associated with the
slow-evolving and fast-evolving bolometric light curves of SLSNe. In
comparison, the magnetars harbored in gamma-ray bursts (GRBs) and associated
hypernovae are usually inferred to have much higher magnetic fields with a
lower boundary about $\sim10B_{\rm c}$. This robustly suggests that it is the
magnetic fields that play the crucial role in distinguishing SLSNe from
GRBs/hypernovae. The rotational energy of SLSN magnetars are found to be
correlated with the masses of supernova ejecta, which provides a clue to
explore the nature of their progenitors. Moreover, the distribution of ejecta
masses of SLSNe is basically intermediate between those of normal core-collapse
supernovae and hypernovae. This could indicate an intrinsic connection among
these different stellar explosions.
