Controllable topological phase transition <i>via</i> ferroelectric–paraelectric switching in a ferromagnetic single-layer M_IM_IIGe₂X₆ family

Recently, the emergence of two-dimensional (2D) multiferroic materials has opened a new perspective for exploring topological states. However, instances of tuning topological phase transitions through ferroelectric (FE) polarization in 2D ferromagnetic (FM) materials are relatively rare. Here, we found that 11 single layer (SL) materials, named the M_IM_IIGe₂X₆ family, possess both FE and FM properties. Among them, 5 SL materials exhibit controllable topological phase transition <i>via</i> ferroelectric-paraelectric switching. Taking the SL ReIrGe₂S₆ as an example, we find that the paraelectric (PE) and FE phases exhibit half-metal and magnetic semiconductor behavior, respectively. In the spin-down channel of the PE phase, a critical-type Weyl point (WP) is observed with a robust Fermi arc edge state. In contrast, the FE phase of the SL ReIrGe₂S₆ clearly identifies 0D corner states in both spin channels. Therefore, under the control of external fields, the SL ReIrGe₂S₆ undergoes a transformation from PE to FE by overcoming the energy barrier of 0.62 eV, subsequently realizing the phase transition from the Weyl semimetal to the high order topological insulator. These findings not only combine topological states with multiferroics but also pave the way for the experimental discovery of 2D tunable topological phase transition.