Twisted exchange interaction between localized spins embedded in a one- or two-dimensional electron gas with Rashba spin-orbit coupling

We study theoretically the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in one- and two-dimensions in presence of a Rashba spin-orbit (SO) coupling. We show that rotation of the spin of conduction electrons due to SO coupling causes a twisted RKKY interaction between localized spins which consists of three different terms: Heisenberg, Dzyaloshinsky-Moriya, and Ising interactions. We also show that the effective spin Hamiltonian reduces to the usual RKKY interaction Hamiltonian in the twisted spin space where the spin quantization axis of one localized spin is rotated.Comment: 4pages, no figur

What's in a Rule: Two-Dimensional Rule Use in Category Learning

Current theories of rules in category learning define rules as one-dimensional boundaries. However, recent evidence suggests that rules may also be two-dimensional boundaries. Four experiments are presented that test for two-dimensional rule use in categories with stimuli composed of integral or separable and commensurate or noncommensurate dimensions. Participant categorization behaviors were organized into groups based upon displayed strategies. These groups were modeled by three models of category learning, ALCOVE, ATRIUM, and a version of ATRIUM modified to use two-dimensional rules. Evidence was found supporting two-dimensional rule use in categories containing stimuliwith commensurate dimensions