In transition metals and their compounds, the orbital degrees of freedom gives rise to an orbital current, in addition to the ordinary spin and charge currents. We reveal that considerably large spin and anomalous Hall effects observed in transition metals originate from an orbital Hall effect (OHE). To elucidate the origin of these novel Hall effects, a simple periodic $s\mathrm{\text{−}}d$ hybridization model is proposed as a generic model. The giant positive OHE originates from the orbital Aharonov-Bohm phase factor, and induces spin Hall conductivity that is proportional to the spin-orbit polarization at the Fermi level, which is positive (negative) in metals with more than (less than) half filling.

• Received 29 May 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.016601