Eur. Phys. J. B (2012) 85: 179
https://doi.org/10.1140/epjb/e2012-30152-9

Regular Article

Exact ground state of a frustrated integer-spin modified Shastry-Sutherland model

¹ Institut für Theoretische Physik, Otto-von-Guericke-Universität Magdeburg, PF 4120, 39016 Magdeburg, Germany
² Universität Osnabrück,Fachbereich Physik, Barbarastr. 7, 49069 Osnabrück, Germany

^a e-mail: johannes.richter@physik.uni-magdeburg.de

Received: 20 February 2012
Received in final form: 29 March 2012
Published online: 30 May 2012

Abstract

We consider a two-dimensional geometrically frustrated integer-spin Heisenberg system that admits an exact ground state. The system corresponds to a decorated square lattice with two coupling constants J₁ and J₂, and it can be understood as a generalized Shastry-Sutherland model. Main elements of the spin model are suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers s and their ground state Φ will be the product state of the local singlet ground states of the trimers. We provide exact numerical data for finite lattices as well as analytical considerations to estimate the range of the existence in dependence on the ratio of the two couplings constants J₂ and J₁ and on the spin quantum number s. Moreover, we find that the magnetization curves as a function of the applied magnetic field shows plateaus and jumps. In the classical limit s → ∞ the model exhibits phases of three- and two-dimensional ground states separated by a one-dimensional (collinear) plateau state at 1/3 of the saturation magnetization.