  This work is part of the BinaMIcS project, the aim of which is to understand
the interaction between binarity and magnetism in close binary systems. All the
studied spectroscopic binaries targeted by the BinaMIcS project encompass hot
massive and intermediate-mass stars on the main sequence, as well as cool stars
over a wide range of evolutionary stages. The present paper focuses on the
binary system FK Aqr, which is composed of two early M dwarfs. Both stars are
already known to be magnetically active based on their light curves and
detected flare activity. In addition, the two components have large convective
envelopes with masses just above the fully convective limit, making the system
an ideal target for studying effect of binarity on stellar dynamos. We use
spectropolarimetric observations obtained with ESPaDOnS at CFHT in September
2014. Mean Stokes I and V line profiles are extracted using the least-squares
deconvolution (LSD) method. The radial velocities of the two components are
measured from the LSD Stokes I profiles and are combined with interferometric
measurements in order to constrain the orbital parameters of the system. The
longitudinal magnetic fields Bl and chromospheric activity indicators are
measured from the LSD mean line profiles. The rotational modulation of the
Stokes V profiles is used to reconstruct the surface magnetic field structures
of both stars via the Zeeman Doppler imaging (ZDI) inversion technique. Maps of
the surface magnetic field structures of both components of FK Aqr are
presented for the first time. Our study shows that both components host similar
large-scale magnetic fields of moderate intensity (Bmean ~ 0.25 kG); both are
predominantly poloidal and feature a strong axisymmetric dipolar component.
(abridged)
