  Broad-lined type Ic supernovae (SNe Ic-BL) are peculiar stellar explosions
that distinguish themselves from ordinary SNe. Some SNe Ic-BL are associated
with long-duration (\gtrsim 2 s) gamma-ray bursts (GRBs). Black holes and
magnetars are two types of compact objects that are hypothesized to be central
engines of GRBs. In spite of decades of investigations, no direct evidence for
the formation of black holes or magnetars has been found for GRBs so far. Here
we report the finding that the early peak (t \lesssim 50 days) and late-time (t
\gtrsim 300 days) slow decay displayed in the light curves of both SNe 1998bw
(associated with GRB 980425) and 2002ap (not GRB-associated) can be attributed
to magnetar spin-down with initial rotation period P0 \sim 20 ms, while the
intermediate-time (50 \lesssim t \lesssim 300 days) linear decline is caused by
radioactive decay of 56Ni. The connection between the early peak and late-time
slow decline in the light curves is unexpected in alternative models. We thus
suggest that GRB 980425 and SN 2002ap were powered by magnetars.
