Hidden Topology of Domain Walls in ↑↑↓↓-type Ferroic Systems

In ↑↑↓↓-type magnetism, we discovered the hidden topology of translational domain walls with specific winding numbers Q_n, which can be well explained by our continuous model based on antiphase order parameter n. Here, we propose a domain wall-related mechanism to demonstrate the electric-field response, involving the microscopic process of generating and separating particle-like domain walls. Our study provides a unique perspective to understand the domain walls and their related phenomena in ↑↑↓↓-type magnetism. It also realizes an electric-field controlled quantized manipulation of magnetic domain walls, contributing to microscopic spintronic applications with ultra-low energy-consumption.