THEORY OF ANOMALOUS HALL-EFFECT IN A HEAVY-FERMION SYSTEM WITH A STRONG ANISOTROPIC CRYSTAL-FIELD

In a heavy fermion system, there exists the anomalous Hall effect caus ed hy localized f-orbital freedom, in addition to the normal Hall effe ct due to the Lorentz force. In 1994, we found that the Hall coefficie nt caused by the anomalous Hall effect (R-H(AHE)) is predominant and t he relation R-H(AHE) proportional to rho(2) (rho is the electrical res istivity) holds at low temperatures in many compounds. In this work, w e study the system where the magnetic susceptibility is highly anisotr opic due to the strong crystalline electric field on f-orbitals. Inter estingly, we find that R-H(AHE) is nearly isotropic in general. This t endency is frequently observed experimentally, which has casted suspic ion that the anomalous Hall effect may be irrelevant in real materials . Our theory corresponds to corrections and generalizations or the pio neering work on ferromagnetic metals by Karplus and Luttinger.