  The magnetic moment yields an excellent framework to explore the inner
structure of particles determined by the quark-gluon dynamics of QCD, as it is
the leading-order response of a bound system to a weak external magnetic field.
Motivated by this, in this study, the magnetic moments of possible axial-vector
$T_{bc\bar u \bar u}$, $T_{bc\bar d \bar d}$, and $T_{bc\bar u \bar d}$
tetraquarks are obtained with the help of light-cone QCD sum rules. For this
purpose, we assume that these states are represented as a diquark-antidiquark
picture with different structures and interpolating currents. The magnetic
moment results derived using different diquark-antidiquark configurations
differ substantially from each other. This can be translated into more than one
tetraquark state with the same quantum number and quark content yet possessing
different magnetic moments. From the numerical results obtained, we have
concluded that the magnetic moments of the $T_{bc}$ states can project their
inner structure, which can be used for their quantum numbers and quark-gluon
organization. The contribution of individual quarks to the magnetic moments is
also analyzed for completeness. We hope that our predictions of the magnetic
moments of the $T_{bc}$ tetraquarks, together with the results of other
theoretical investigations of the spectroscopic parameters and decay widths of
these interesting tetraquarks, may be valuable in the search for these states
in future experiments and in unraveling the internal structure of these
tetraquarks.
