  The magnetic dipole moments of the doubly-heavy baryons include significant
data on their inner structure and geometric shape. Moreover, understanding the
electromagnetic properties of doubly-heavy baryons is the key to confinement
and heavy flavor effects. Inspired by this, we extract the magnetic dipole
moments of the spin-$\frac{1}{2}$ bottom-charm baryons utilizing the QCD
light-cone sum rule with considering the distribution amplitudes of the
photon.The magnetic dipole moments are obtained as $\mu_{\Xi_{bc}^{+}} =
-0.50^{+0.14}_{-0.12}~\mu_{N}$, $\mu_{\Xi_{bc}^{0}} =
0.39^{+0.06}_{-0.05}~\mu_{N}$ and $\mu_{\Omega_{bc}^{0}} = 0.38^{+0.05}_{-0.04}
~\mu_{N}$, $\mu_{\Xi_{bc}^{\prime +}} = 0.57^{+0.13}_{-0.12}~\mu_{N}$,
$\mu_{\Xi_{bc}^{\prime 0}} =-0.29^{+0.07}_{-0.06}~\mu_{N}$ and
$\mu_{\Omega_{bc}^{\prime 0}} = -0.26^{+0.06}_{-0.05}~\mu_{N}$. Comparing the
results obtained on the magnetic dipole moments of the
$\Omega^{(\prime)0}_{bc}$ baryon with those of the $\Xi^{(\prime)0}_{bc}$
baryon, the $U$-symmetry is minimally broken. We have compared our results with
other theoretical predictions that could be a useful complementary tool for the
interpretation of the doubly-heavy baryon sector, and we observe that they are
not in mutual agreement with each other.
