  Inspired by the recent discovery of the $\Xi_{cc}^{++}$ by the LHCb
Collaboration, we study the magnetic moments of the spin-1/2 doubly charmed
baryons up to the next-to-leading order in covariant baryon chiral perturbation
theory with the extended-on-mass-shell renormalization scheme. There are three
low energy constants at this order, $a_1$, $a_2$ and $g_a$. The latest lattice
QCD simulations allow us to fix a combination of $a_1$ and $a_2$, while the
axial-vector coupling $g_a$ can be determined in three different ways, either
by fitting to the lattice QCD data, or by the quark model, or by the heavy
antiquark diquark symmetry. The magnetic moments of the spin-1/2 doubly charmed
baryons $\Xi^d_{cc}$ and $\Xi^s_{cc}$ can then be predicted. We compare our
results with those obtained in the heavy baryon chiral perturbation theory and
other approaches, and point out some inconsistencies between the lattice QCD
simulations and the quark model.
