  White dwarfs with surface magnetic fields in excess of $1 $MG are found as
isolated single stars and relatively more often in magnetic cataclysmic
variables. Some 1,253 white dwarfs with a detached low-mass main-sequence
companion are identified in the Sloan Digital Sky Survey but none of these is
observed to show evidence for Zeeman splitting of hydrogen lines associated
with a magnetic field in excess of 1MG. If such high magnetic fields on white
dwarfs result from the isolated evolution of a single star then there should be
the same fraction of high field white dwarfs among this SDSS binary sample as
among single stars. Thus we deduce that the origin of such high magnetic fields
must be intimately tied to the formation of cataclysmic variables. CVs emerge
from common envelope evolution as very close but detached binary stars that are
then brought together by magnetic braking or gravitational radiation. We
propose that the smaller the orbital separation at the end of the common
envelope phase, the stronger the magnetic field. The magnetic cataclysmic
variables originate from those common envelope systems that almost merge. We
propose further that those common envelope systems that do merge are the
progenitors of the single high field white dwarfs. Thus all highly magnetic
white dwarfs, be they single stars or the components of MCVs, have a binary
origin. This hypothesis also accounts for the relative dearth of single white
dwarfs with fields of 10,000 - 1,000,000G. Such intermediate-field white dwarfs
are found preferentially in cataclysmic variables. In addition the bias towards
higher masses for highly magnetic white dwarfs is expected if a fraction of
these form when two degenerate cores merge in a common envelope. Similar
scenarios may account for very high field neutron stars.
