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.

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