Nonlinear Transverse Conductivity in Antiferroic Types of Magnetic Toroidal Metal

We have performed careful measurements of nonlinear transverse conductivity (NLTC) at zero field in the intermetallic compound HoAgGe with two distinct magnetic toroidal (MT) structures. Below 7 K (MT1 phase), the NLTC signal becomes observable and significantly increases with decreasing temperature, whereas between 7 and 11.6 K (MT2 phase), it remains nearly zero. However, this result is incompatible with the previous research, which assigned the former and latter MT phases as antiferro- and ferro-MT structures, respectively. This discrepancy stems from an inappropriate assignment of MT structures in prior studies. Our analysis, based on multipole theory, redefines the MT1 and MT2 phases as ferri- and antiferro-MT structures, respectively, providing a coherent framework to explain the observed NLTC in HoAgGe. These findings not only establish NLTC as a robust diagnostic tool for identifying MT metals but also highlight its potential for exploring phenomena driven by the antiferroic interactions of MT dipoles.