The skin effect, where bulk modes collapse into boundary modes, is a key phenomenon in topological non-Hermitian systems, and it has been predominantly studied in spinless systems. Recent studies illustrate the magnetic suppression of the first-order skin effect while ignoring spin. However, the physical significance of a magnetic field in the non-Hermitian skin effect with spin remains elusive. Here, we systematically explore non-Hermitian systems based on generalized Hatano-Nelson models with SU(2) gauge potential fields. We demonstrate that the first-order skin effect can be anomalously induced by a magnetic field through Zeeman coupling in a topologically trivial system without any skin effect at zero field. The direction of such magnetically induced skin modes can be controlled by simply changing the amplitude and polarity of the magnetic field. We also demonstrate a transition between non-Bloch $\mathcal{PT}$ and anti-$\mathcal{PT}$ symmetries in the system, and we uncover the spin-dependent mechanism of non-Bloch $\mathcal{PT}$ symmetry. Moreover, when an external magnetic field is applied, the skin effect exhibits a transition from bidirectional to unidirectional. Our results pave the way for exploring the non-Hermitian skin effect in systems with SU(2) gauge fields, leveraging chirality and nonreciprocity.

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• Skin effect
• Topological phases of matter
• Non-Hermitian systems