A quantum geometric mechanism for chiral domain wall metastability: Application to twisted transition-metal dichalcogenides

Abstract

Band topology can have an imprint on the excitations of a ferromagnet. A known example is quantum Hall ferromagnets and their lattice analogs; when both flavors have the same Chern number $C$, a smooth skyrmion texture binds charge $-eC$ per unit winding. Here, we consider instead the case of conjugate Chern bands related by time-reversal. We show that, despite the vanishing net charge response, a smooth texture can be associated with a dipole response---a domain wall (DW) with an in-plane winding along its length can bind a nonzero dipole density transverse to the wall. The strength of this dipole density is controlled by a dimensionless coefficient $c_G$. Although not quantized, the geometric dipole coefficient $c_G$ is a moment of the second Chern form of the occupied projector in mixed (momentum and order-parameter) space and is generally nonzero. The dipole-decorated DW can thus become metastable at a finite radius due to the competition between dipolar repulsion and the usual surface tension, even at a finite Zeeman field. In a realistic model of twisted MoTe$_2$, we find that $c_G$ drops sharply across a transition within the valley-polarized (VP) phase from a $C=1$ to a $C=0$ ferromagnet. This naturally explains recent pump-probe experiments~\cite{exp} at hole filling $\nu=1$, in which a long-lived excitation survives reverse fields far exceeding the saturation field but disappears at an intermediate displacement field despite only weak changes in conventional magnetic diagnostics. Metastable spin textures thus serve as a sensitive probe of band quantum geometry, and as an intrinsic bottleneck for fast optical control of moir\'e ferromagnets in Chern-conjugate bands.