Valence band orbital polarization in III-V ferromagnetic semiconductors

Magnetocrystalline anisotropy (MCA) plays a central role in technological applications of ferromagnetism, from permanent magnetic materials to ultrathin films. Since the MCA influences properties such as domain wall width, spin transfer torque and magnetization dynamics, it is crucial for determining the spintronic functionalities of a material. The MCA has at its heart the spin-orbit interaction leading to a coupling between the magnetization and the crystal lattice. The MCA energy is directly related to the anisotropic part of the spin-orbit interaction 1 , and is shown to be proportional to the difference in the orbital magnetic moment morb along the easy and hard magnetic axes when one of the spin subbands is filled 2 . In cubic transition metal ferromagnets, the MCA is typically rather small (corresponding to a few µeV per atom 3 ), but may be substantially enhanced when the symmetry of the system is reduced 4 . Several new insights into the origin of MCA in a range of materials have been delivered by x-ray magnetic circular and linear dichroism (XMCD and XMLD), due to their element-specific sensitivity to orbital moments 5 and spinorbit coupling anisotropies 6,7 , respectively. A particularly interesting MCA is found in diluted magnetic semiconductors such as Ga1−xMnxAs, where a carrier-mediated interaction between Mn acceptors leads to ferromagnetic order, with a Curie temperature TC up to 173 K for x�7%. At low concentrations, Mn acceptors in GaAs possess a d 5 electronic configuration, with negligible single-ion anisotropy associated with the Mn core 8 . However, in the high concentration ferromagnetic regime, a large uniaxial MCA is observed, which is strongly influenced by epitaxial strain 9 . The MCA in (Ga,Mn)As has been explained semiquantitatively, by considering the combined effects of strain and exchange splitting on a model valence band built from s,p orbitals of the host ions 10 . Within this model, the MCA (and related anisotropic magnetoresistance effects 12 ) results from the induced anisotropy of the strongly spin-orbit coupled (j=3/2) valence hole states, with predominantly As 4p character. The model also predicts a sizeable magnetization of the hole subsystem, of opposite sign to the Mn magnetization 13 .