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The relevance of the quasi-two-dimensional spin-1/2 frustrated quantumantiferromagnet due to its possibility of modelling the high-temperaturesuperconducting parent compounds has resulted in numerous theoretical andexperimental studies. This paper presents a detailed research of the influenceof the varying exchange interactions on the model magnetic properties withinthe framework of self-consistent spin-wave theory based on Dyson-Maleevrepresentation. Beside the nearest neighbour interaction within the plane, theplanar frustration up to the third nearest neighbours, cyclic interaction andthe interlayer coupling are taken into account. The detailed description of theelementary spin excitations, staggered magnetization, spin-wave velocityrenormalization factor and ground-state energy is given. The results arecompared to the predictions of the linear spin-wave theory and when possiblealso to the second-order perturbative spin-wave expansion results. Finally,having at our disposal improved experimental results for the in-plane spin-wavedispersion in high-$T_c$ copper oxide $\mbox{La}_2\mbox{CuO}_4$, theself-consistent spin-wave theory is applied to that compound in order tocorrect earlier obtained set of exchange parameters and high temperaturespin-wave dispersion.

Effects of frustration and cyclic exchange on the spin-1/2 Heisenberg antiferromagnet within the self-consistent spin-wave theory