  Inspired by the discovery of the spin-$\frac{1}{2}$ doubly charmed baryon
$\Xi_{cc}^{++}$ and the subsequent theoretical studies of its magnetic moments,
we study the magnetic moments of its spin-$\frac{3}{2}$ heavy quark spin
symmetry counterparts, up to the next-to-leading order in covariant baryon
chiral perturbation theory (BChPT) with the extended-on-mass-shell
renormalization (EOMS) scheme. With the tree-level contributions fixed by the
quark model while the two low energy constants (LECs) $C$ and $H$ controlling
the loop contributions determined in two ways: the quark model (case 1) and
lattice QCD simulations together with the quark model (case 2), we study the
quark mass dependence of the magnetic moments and compare them with the
predictions of the heavy baryon chiral perturbation theory (HB ChPT). It is
shown that the difference is sizable in case 1, but not in case 2 due to the
smaller LECs $C$ and $H$, similar to the case of spin-$\frac{1}{2}$ doubly
charmed baryons. Second, we predict the magnetic moments of the
spin-$\frac{3}{2}$ doubly charmed baryons and compare them with those of other
approaches. The predicted magnetic moments in case 2 for the spin-$\frac{3}{2}$
doubly charmed baryons are closer to those of other approaches. In addition,
the large differences in case 1 and case 2 for the predicted magnetic moments
may indicate the inconsistency between the quark model and the lattice QCD
simulations, which should be checked by future experimental or more lattice QCD
data.
