Model the suppression of magnetoresistance at large out-of-plane magnetic fields

Develop a theoretical analysis of the large-out-of-plane-magnetic-field regime in the ferro-Josephson phenomenological model for twisted graphene, specifically to explain the suppression of magnetoresistance signals that the small-b2cperp model does not capture.

Background

The phenomenological ferro-Josephson model is formulated for small out-of-plane magnetic fields, where adjacent domains retain opposite spin polarizations and the domain-wall width and in-plane spin polarization vary with field. Within this regime, the model accounts for the growth of resistance with increasing absolute out-of-plane field by reducing the domain-wall width and the number of in-plane moments participating in the dynamics.

The paper states that the experimentally observed suppression of magnetoresistance at large out-of-plane fields is not explained by the model. It suggests that, when the spin Zeeman energy and the intervalley spin-orbit scale become comparable, the high-anisotropy domain may deviate from the out-of-plane direction, increasing its in-plane spin polarization and reducing the resistance. A quantitative analysis of this large-field regime is therefore left unresolved.

References

However, the suppression of MR signals at large $B_{\perp}$ is not captured in our model. For instance, when $g{\mu_B}B_{\perp} + \Delta_I\sim 0$, the spin in the high-anisotropy domain might deviate from $z$ direction, leading to larger in-plane spin polarization and smaller $R$. We leave the analysis of the large $B_{\perp}$ regime for future study.

— Signatures of a ferro-Josephson effect in twisted graphene  (2608.25257 - Su et al., 26 Aug 2026) in Methods, subsection a2Phenomenological modelb2, final comments on the model's regime of applicability