  Motivated by the latest discovery of doubly-charmed tetraquark $T^+_{cc}$ by
LHCb collaboration, we have studied the magnetic moments of the possible
doubly-heavy pentaquark states with quantum numbers $J^P = 1/2^-$ and $J^P =
3/2^-$ within the light-cone sum rules method. In the analysis, these possible
pentaquark states are considered in diquark-diquark-antiquark structure. The
magnetic moments of hadrons encode helpful details about the distributions of
the charge and magnetization inside the hadrons, which help us to figure out
their geometric configurations. As a by product, the electric quadrupole and
magnetic octupole moments of the spin-3/2 doubly-heavy pentaquark states are
also extracted. These values show a non-spherical charge distribution. It will
be interesting and useful to examine the magnetic moments of these possible
doubly-heavy pentaquark states with different theoretical approaches.
