The majority of stars reside in multiple systems, especially binaries. The formation and early evolution of binaries is a longstanding problem in star formation that is not fully understood. In particular, how the magnetic field observed in star-forming cores shapes the binary characteristics remains relatively unexplored. We demonstrate numerically, using the ENZO-MHD code, that a magnetic field of the observed strength can drastically change two of the basic quantities of a binary system: the orbital separation and mass ratio of the two components. Our calculations focus on the protostellar mass accretion phase, after a pair of stellar seeds have already formed. We find that, in dense cores magnetized to a realistic level, the angular momentum of the gas accreted by the protobinary is greatly reduced by magnetic braking. Accretion of strongly braked material shrinks the protobinary separation by a large factor compared to the non-magnetic case. The magnetic braking also changes the evolution of the mass ratio of unequal-mass protobinaries by producing gas of low specific angular momentum that accretes preferentially onto the primary rather than the secondary. This is in contrast with the preferential mass accretion onto the secondary previously found for protobinaries accreting from an unmagnetized envelope, which tends to drive the mass ratio towards unity. In addition, the magnetic field greatly modifies the morphology and dynamics of the protobinary accretion flow. It suppresses the circumstellar and circumbinary disks that feed the protobinary in the non-magnetic case; the binary is fed instead by a fast collapsing pseudodisk whose rotation is strongly braked. The magnetic braking-driven inward migration of binaries from their birth locations may be constrained by high-resolution observations of the orbital distribution of deeply embedded protobinaries, especially with ALMA.
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