  We consider Dirac, Pauli and Schr\"odinger quantum magnetic Hamiltonians of
full rank in ${\rm L}^2 \big(\mathbb{R}^{2d} \big)$, $d \ge 1$, perturbed by
non-self-adjoint (matrix-valued) potentials. On the one hand, we show the
existence of non-self-adjoint perturbations, generating near each point of the
essential spectrum of the operators, infinitely many (complex) eigenvalues. In
particular, we establish point spectrum analogous of B\"ogli results [B\"og17]
obtained for non-magnetic Laplacians, and hence showing that classical
Lieb-Thirring inequalities cannot hold for our magnetic models. On the other
hand, we give asymptotic behaviours of the number of the (complex) eigenvalues.
In particular, for compactly supported potentials, our results establish
non-self-adjoint extensions of Raikov-Warzel [RW02] and Melgaard-Rozenblum
[MR03] results. So, we show how the (complex) eigenvalues converge to the
points of the essential spectrum asymptotically, i.e., up to a multiplicative
explicit constant, as $$ \frac{1}{d!} \Bigg(\frac{\vert \ln r \vert}{\ln \vert
\ln r \vert} \Bigg)^d, \quad r \searrow 0, $$ in small annulus of radius $r >
0$ around the points of the essential spectrum.
