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We consider Dirac, Pauli and Schr\"odinger quantum magnetic Hamiltonians offull rank in ${\rm L}^2 \big(\mathbb{R}^{2d} \big)$, $d \ge 1$, perturbed bynon-self-adjoint (matrix-valued) potentials. On the one hand, we show theexistence of non-self-adjoint perturbations, generating near each point of theessential spectrum of the operators, infinitely many (complex) eigenvalues. Inparticular, we establish point spectrum analogous of B\"ogli results [B\"og17]obtained for non-magnetic Laplacians, and hence showing that classicalLieb-Thirring inequalities cannot hold for our magnetic models. On the otherhand, we give asymptotic behaviours of the number of the (complex) eigenvalues.In particular, for compactly supported potentials, our results establishnon-self-adjoint extensions of Raikov-Warzel [RW02] and Melgaard-Rozenblum[MR03] results. So, we show how the (complex) eigenvalues converge to thepoints of the essential spectrum asymptotically, i.e., up to a multiplicativeexplicit 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.

Spectral non-self-adjoint analysis of complex Dirac, Pauli and Schr\"odinger operators of full rank with constant magnetic fields