Quantum Spin-Wave Theory for Non-Collinear Spin Structures, a Review

Abstract

In this review, we trace the evolution of the quantum spin-wave theory treating non-collinear spin configurations. Non-collinear spin configurations are consequences of the frustration created by competing interactions. They include simple chiral magnets due to competing nearest-neighbor (NN) and next-NN interactions and systems with geometry frustration such as the triangular antiferromagnet and the Kagomé lattice. We review here spin-wave results of such systems and also systems with the Dzyaloshinskii–Moriya interaction. Accent is put on these non-collinear ground states which have to be calculated before applying any spin-wave theory to determine the spectrum of the elementary excitations from the ground states. We mostly show results obtained by the use of a Green’s function method. These results include the spin-wave dispersion relation and the magnetizations, layer by layer, as functions of T in 2D, 3D and thin films. Some new unpublished results are also included. Technical details and discussion on the method are shown and discussed.

Keywords

• quantum spin-wave theory
• Green’s function theory
• frustrated spin systems
• non-collinear spin configurations
• Dzyaloshinskii–Moriya interaction
• phase transition