title: Frustrated classical Heisenberg and XY models in two dimensions with nearest-neighbor biquadratic exchange: exact solution for the ground-state phase diagram.
abstract: The ground-state phase diagram is determined exactly for the frustrated classical Heisenberg model plus nearest-neighbor biquadratic exchange interactions on a two-dimensional lattice. A square- and a rhombic-symmetry version are considered. There appear ferromagnetic, incommensurate-spiral, "up-up-down-down" (UUDD), and canted ferromagnetic states, a nonspiral coplanar state that is an ordered vortex lattice, plus a noncoplanar ordered state (a "conical vortex lattice"). In the rhombic case, which adds biquadratic terms to the Heisenberg model used widely for insulating manganites, the UUDD state found is the E-type state observed; this, along with accounting essentially for the variety of ground states observed in these materials, shows that this model probably contains the long-sought mechanism behind the UUDD state.
authors.affiliation: Department of Physics, University of Missouri, Columbia, Missouri, USA.
authors.forename: L X
authors.initials: LX
authors.lastname: Hayden
authors.forename: T A
authors.initials: TA
authors.lastname: Kaplan
authors.forename: S D
authors.initials: SD
authors.lastname: Mahanti