Ground state of the two-dimensional Dzyaloshinski-Moriya antiferromagnet

Abstract

A finite-size exact diagonalization technique is applied for the two-dimensional spin- 1 2 Heisenberg Hamiltonian with the Dzyaloshinski-Moriya(DM) interaction to examine the ground state magnetic structure of the insulating CuO 2 plane in the low-temperature orthorhombic (LTO) and tetragonal (LTT) phases of the La 2CuO 4-type crystal. It is demonstrated that the weak ferromagnetism induced in the LTO phase is accompanied by a stabilization of the antiferromagnetism with the planar anisotropy. It is predicted that there are two possibilities in the magnetic ground states in the LTT phase, depending on the direction of the DM vector: the weak ferromagnetic state similar to that of the LTO phase and the antiferromagnetic state characterized by the strong uniaxial anisttropy of the quantum-mechanical origin. A fluctuation for the chiral outlet state is suppressed in the former but is enchanged in the latter.