We construct a semiclassical theory for electrons in a non-Hermitian periodic system subject to perturbations varying slowly in space and time. We derive the energy of the wave packet to first order in the gradients of the perturbations. Applying the theory to the specific case of a uniform external magnetic field, we obtain an expression for the orbital magnetization energy. Using the principles of non-Hermitian dynamics, we define a physically meaningful non-Hermitian generalization of the angular momentum operator and show that it is compatible with the real part of the orbital magnetic moment. The imaginary part of the orbital magnetic moment is also discussed and shown to originate from an imaginary counterpart to the angular momentum that gives rise to a non-Hermitian generalization of the Aharonov-Bohm effect.

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• Dissipative dynamics
• Geometric & topological phases
• Light-matter interaction
• Magnetism
• Semiclassical physics
• Non-Hermitian systems