  Aims: We present a study of the superbubble (SB) 30 Dor C and the newly
identified MCSNR J0536-6913 in the LMC. Methods: All available XMM-Newton data
(exposure times of 420 ks EPIC-pn, 556 ks EPIC-MOS1, 614 ks EPIC-MOS2) were
used to characterise the thermal X-ray emission in the region. An analysis of
the non-thermal X-rays is also presented and discussed in the context of
emission mechanisms previously suggested in the literature. These data are
supplemented by X-ray data from Chandra, optical data from the MCELS, and radio
data from ATCA and MOST. Results: The brightest thermal emission was found to
be associated with a new supernova remnant, MCSNR J0536-6913. X-ray spectral
analysis of MCSNR J0536-6913 suggested an ejecta-dominated remnant with lines
of O, Ne, Mg, and Si, and a total 0.3-10 keV luminosity of ~8E+34 erg/s. Based
on derived ejecta abundance ratios, we determined the mass of the stellar
progenitor to be either ~18 M_sun or as high as >40 M_sun, though the spectral
fits were subject to assumptions (e.g., uniform temperature and well-mixed
ejecta). The thermal emission from the SB exhibited enrichment by alpha-process
elements, evidence for a recent core-collapse SNR interaction with the SB
shell. We detected non-thermal X-ray emission throughout 30 Dor C, with the
brightest regions being highly correlated with the H-alpha and radio shells. We
created a non-thermal spectral energy distribution for the north-eastern shell
of 30 Dor C which was best-fit with an exponentially cut-off synchrotron model.
Conclusions: Thermal X-ray emission from 30 Dor C is very complex, consisting
of a large scale SB emission at the eastern shell wall with the brightest
emission due to MCSNR J0536-6913. The fact that the non-thermal spectral energy
distribution of the SB shell was observed to roll-off is further evidence that
the non-thermal X-rays from 30 Dor C are synchrotron in origin.
