  The origin of magnetic fields in white dwarfs remains a fundamental
unresolved problem in stellar astrophysics. In particular, the very different
fractions of strongly (exceeding 1 MG) magnetic white dwarfs in evolutionarily
linked populations of close white dwarf binary stars cannot be reproduced by
any scenario suggested so far. Strongly magnetic white dwarfs are absent among
detached white dwarf binary stars that are younger than approximately 1 Gyr. In
contrast, in semi-detached cataclysmic variables in which the white dwarf
accretes from a low-mass star companion, more than one third host a strongly
magnetic white dwarf. Here we present binary star evolutionary models that
include the spin evolution of accreting white dwarfs and crystallization of
their cores, as well as magnetic field interactions between both stars. We show
that a crystallization- and rotation-driven dynamo similar to those working in
planets and low-mass stars can generate strong magnetic fields in the white
dwarfs in cataclysmic variables which explains their large fraction among the
observed population. When the magnetic field generated in the white dwarfs
connects with that of the secondary stars, synchronization torques and reduced
angular momentum loss cause the binary to detach for a relatively short period
of time. The few known strongly magnetic white dwarfs in detached binaries,
including AR Sco, are in this detached phase.
