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In this work, we investigate the discrete spectrum generated by complexmatrix-valued perturbations for a class of 2D and 3D Pauli operators withnonconstant magnetic fields. We establish a simple criterion for the potentialsto produce discrete spectrum near the low ground energy of the operators.Moreover, in case of creation of nonreal eigenvalues, this criterion specifiesalso their location.

A simple criterion for the existence of nonreal eigenvalues for a class of 2D and 3D Pauli operators