Fig. 5: Cartoon illustration about the establishment of heavy-electron state and simulations of Planar Hall Effect (PHE).

The schematic Fermi surface is from theoretical calculations in ref. ²³. The hatched balls signify Kondo entanglement of f (blue) and conduction (red) electrons. Above incoherent Kondo scale \({T}_{K}^{on}\), the f electrons are fully localized, and only light-mass cylindrical sheets from Co/Ga orbitals are present along Γ-Y. For \({T}^{* } < T < {T}_{K}^{on}\), the c-f hybridization is incoherent. Below coherent Kondo scale T^*, Kondo coherence sets in, two fluids coexist, and fluctuating new flat sheets with heavy mass start to appear. Well below T^*, coherent heavy-electron state is stabilized. The right-column panels are simulations based on this hypothesis. The simulations are made with the parameters Δσ^c = 0.10, and Δσ^h = −0.04. Temperature dependent w(T) and a₄ are employed to characterize the weight of transport conductivity contributed by the heavy fermion quasiparticles and the four-fold oscillation mode: a w = 0.0 and a₄ = 0.0 for \(T > {T}_{K}^{on}\); b w = 0.0 and a₄ = − 1.0 for \({T}^{* } < T < {T}_{K}^{on}\); c w = 0.7 and a₄ = − 0.3 for T < T^*; and d w = 1.0 and a₄ = 0.0 for well below T^*. The color bars signify the values of \({\rho }_{xz}^{{{{\rm{PHE}}}}}(\varphi )\).