Indirect exchange interaction via electrons in spin–orbit coupled bands in semiconductors

Abstract

Indirect coupling between two localized magnetic moments in a semiconductor is considered. This coupling may be of two origins: due t o intraband electron transitions (RKKY) and virtual interband transitions, the latter being of particular importance in materials considered. Strong spinorbit coupling between electronic bands leads to a complicated form of the effective Hamiltonian.It no longer contains a Heisenberg term only. The number of independent constants describing the interaction depends on the symmetry of the interacting pair. The special case of zincblende structure is considered. Several simple models are reviewed and found insufficient to describe the indirect interaction, a t least for closely lying moments, a fact which stresses the necessity of numerical calculations.Es wird die indirekte Kopplung zwischen lokalisierten magnetischen Momenten in einem Halbleiter untersucht. Diese Kopplung kann zwei Ursachen haben: Interband-Elektronenwechselwirkung (RKKY) und virtuelle Interbandubergange, wobei die letzteren in den betrachteten Materialien besonders wichtig sind. Starke Spin-Bahn-Wechselwirkung zwischen Elektronenbandern fiihrt zu einer komplexen Form des effektiven Hamiltonoperators. E r enthalt dann nicht mehr nur einen Heisenbergterm. Die Anzahl der unabhangigen Konstanten, die die Wechselwirkung beschreiben, hangen von der Symmetrie der wechselwirkenden Paare ab. Der spezielle Fall der Zinkblendestruktur wird betrachtet. Einige einfache Modelle werden analysiert und es wird gefunden, da8 sie nicht fahig sind, die indirekte Wechselwirkung zu beschreiben, wenigstens fur eng benachbarte Momente, eine Tatsache, die die Notwendigkeit numerischer Rechnungen bestltigt.

Spin-wave measurements on hexagonalMnTeofNiAs-type structure by inelastic neutron scattering

“…Only calculations accounting for detailed electronic properties, including conduction and valence bands, could give realistic estimates, as pointed out in Ref. 56 and recently performed 57 for exchange interactions between Mn ions in PbTe ͑rocksalt structure͒. Both experiments and calculations revealed indeed a nonmonotonous behavior.…”

Indirect exchange interaction between magnetic impurities in the two-dimensional topological insulator based on CdTe/HgTe/CdTe quantum wells

“…To illustrate interesting physics of the indirect exchange interaction (24) we consider how the energy levels of two manganese impurities situated at a distance R λ 1 are changed due to their interaction. Since λ 1 d (see Table I) we assume that the energy levels E A 1/2 , E A 3/2 , E A 5/2 and E B 1/2 , E B 3/2 , E B 5/2 for two impurities are different.…”

“…The presence of strong spin-orbit coupling in a semiconductor complicates the form of the indirect exchange interaction. In the simplest case, in addition to the Heisenberg term the indirect exchange interaction involves also the magnetic pseudo-dipole interaction [24][25][26]. The latter prevents the system of magnetic impurities from ferromagnetic ordering and favors spin glass state.…”

Superexchange dominates in magnetic topological insulators

“…However, in the case of the BR mechanism, the decay of the interaction with the inter-spin distance is faster [17,18,20] and, therefore, χ(q) beyond q = 0 determines the sign and magnitude of Θ CW and T C . In conclusion, atomistic computations of pair exchange energies J ij are necessary in order to evaluate meaningfully the role of the interband contribution [34].…”