Investigation of weak antilocalization and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>π</mml:mi></mml:math>-Berry phase by quantum oscillation in ferromagnetic Weyl semimetals

In this paper, we present a comprehensive study of the CeAlSi and NdAlGe system, focusing on its quantum transport properties. Our investigation reveals the presence of weak antilocalization in magnetoresistance of both samples. The semiclassical model and Hikami-Larkin-Nagaoka fitting indicate the presence of strong spin-orbit coupling and quantum interference effects arising from three-dimensional bulk states. Additionally, we observe pronounced Shubnikov-de Haas (SdH) oscillations, with a dominant frequency of 20.74 T, extending to temperatures as high as 50 K for CeAlSi. Similarly, NdAlGe also exhibits SdH oscillations at magnetic fields above 5 T with a fundamental frequency of 28.39 T, within the temperature range of 1.8 K to 9 K. By performing Lifshitz-Kosevich fitting on the SdH oscillations, we extract approximately $\ensuremath{\pi}$-Berry phase in both samples, further confirming the nontrivial topology of the band structure in these materials. The nature of SdH oscillations and Landau level index fitting indicates the dominance of Zeeman splitting and $4f$ electron exchange interactions in these compounds. Additionally, the position of the Weyl fermions relative to the Fermi energy, along with other parameters such as the cross-sectional area of the Fermi surface, effective mass, lifetime of charge carriers, Dingle temperature, mobility, and charge-carrier density, is also determined from the SdH oscillations. These findings provide valuable insights into the quantum transport phenomena in ferromagnetic CeAlSi and NdAlGe, highlighting their importance as platforms for exploring type-II Weyl semimetal behavior. Furthermore, their high mobility and low effective mass demonstrate their potential for applications in low-power electronic and high-speed communication devices.