  In the framework of Einstein-Maxwell-axion theory we consider a static field
configuration in the outer zone of a magnetic star. We assume that this field
configuration is formed by the following interacting quartet: a spherically
symmetric gravitational field of the Reissner-Nordstr\"om type, pseudoscalar
field, associated with an axionic dark matter, strong intrinsic magnetic field,
and axionically induced electric field. Based on the analysis of the solutions
to the master equations of the model, we show that the structure of the formed
field configuration reveals the following triple effect. First, if the strong
magnetic field of the star has the dipole component, the axionic halo around
the magnetic star with spherically symmetric gravitational field is no longer
spheroidal, and the distortion is induced by the axion-photon coupling; second,
due to the distortion of the axionic halo the magnetic field is no longer pure
dipolar, and the induced quadruple, octupole, etc., components appear thus
redistributing the magnetic energy between the components with more steep
radial profiles than the dipolar one; third, the interaction of the axionic and
magnetic fields produces the electric field, which inherits their multipole
structure. We attract attention to possible applications of the predicted field
restructuring to the theory of axionic rotating magnetars.
