Recent progress in anomalous Hall and Nernst effects in rare-earth ferromagnets RMn₂Ge₂

Anomalous transverse transport phenomena include two major effects. One is the anomalous Hall effect (AHE). The other is the anomalous Nernst effect (ANE). It is an important probe of the interplay among magnetic order, spin-orbit coupling (SOC), and electronic structure in magnetic materials. Rare-earth-based RMn_2Ge_2 ferromagnets, due to their unique layered structure, tunable magnetism, and complex electronic behavior, have emerged as an important platform for studying these transport phenomena. This paper reviews recent research progress in the ferromagnetic RMn_2Ge_2 (R = \rm La, Ce, Pr, Nd, Sm) system in the study of AHE and ANE, analyzes the modulation of these effects by different rare-earth elements, and discusses the relationship between these effects and magnetic and electronic structures. Recent studies suggest that by adjusting the magnetic structure, the response of these transverse transport phenomena can be significantly altered, providing new directions for the application of low-power electronic devices and energy conversion technologies.