  A magnetic dynamo driven by differential rotation generated when stars merge
can explain strong fields in certain classes of magnetic stars, including the
high field magnetic white dwarfs (HFMWDs). In their case the site of the
differential rotation has been variously proposed to be within a common
envelope, the massive hot outer regions of a merged degenerate core or an
accretion disc formed by a tidally disrupted companion that is subsequently
incorporated into a degenerate core. We synthesize a population of binary
systems to investigate the stellar merging hypothesis for observed single
HFMWDs. Our calculations provide mass distribution and the fractions of white
dwarfs that merge during a common envelope phase or as double degenerate
systems in a post common envelope phase. We vary the common envelope efficiency
parameter alpha and compare with observations. We find that this hypothesis can
explain both the observed incidence of magnetism and the mass distribution of
HFMWDs for a wide range of alpha. In this model, the majority of the HFMWDs are
of the Carbon Oxygen type and merge within a common envelope. Less than about a
quarter of a per cent of HFMWDs originate from double degenerate stars that
merge after common envelope evolution and these populate the high-mass tail of
the HFMWD mass distribution.
