Frustrated Bonds and Long Range Order in Quasi-2D Magnets

We employ the Schwinger boson mean-field approach to study the effects of arbitrary frustrated bonds and plaquettes (formed from four frustrated bonds) in two-dimensional ferro- and antiferromagnets on the spin-wave spectrum and the correlation length at finite temperatures. We distinguish between strongly frustrated bonds (plaquettes), when the frustrated coupling $J^\prime$ exceeds the spin canting threshold $J_c$, and weakly frustrated bonds (plaquettes), with $J^\prime <J_c, (J_c-J^\prime)/J_c\sim 1$. It is shown that in antiferromagnets the amplitude of spin-wave scattering on strongly frustrated bonds or plaquettes grows with the decrease of the temperature. A small amount of such defects reduces significantly the spin-wave stiffness and the correlation length at low temperatures. As a result, the quasi-2D N\'eel temperature is sharply suppressed. Quantum fluctuations are also considered and their effect on the spin-wave spectrum is shown to be of the order of $(2S)^{-2}\ln^{-1}2S$ in the large spin limit. For weakly frustrated (nonfrustrated) defect bonds (plaquettes) the spin-wave stiffness renormalization is of the order of the dopant concentration and does not depend on the temperature. The results account for the observed properties of doped quasi-2D $La_2CuO_{4+x}$.