Binary Star Origin of High Field Magnetic White Dwarfs
  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. 
C. A. Tout, D. T. Wickramasinghe, J. Liebert, L. Ferrario and J. E.   Pringle