Structural and magnetic instabilities of two-dimensional quantum spin systems

Abstract

We present a study of the magnetic order and the structural stability of two-dimensional quantum spin systems in the presence of spin-lattice couplings. For a square lattice it is demonstrated that the plaquette deformation yields the strongest gain in magnetic energy. The analysis of the dimer-dimer response function further shows that lattice distortions may generally coexist with magnetic long-range order, in contrast to the one-dimensional case. Similarly, the coupling to Einstein phonons is found to reduce, but not to eliminate, the staggered magnetic moment. In addition, we consider the renormalization of the square lattice phonon spectrum due to spin-phonon coupling in the adiabatic approximation. Toward low temperatures, significant softening mainly of zone boundary phonons is found, especially around the $(\ensuremath{\pi},0)$ point of the Brillouin zone. This result is compatible with the tendency to plaquette formation in the static limit. We also point out the importance of a ``magnetic pressure'' on the lattice due to spin-phonon coupling. At low temperatures, this results in a tendency toward shear instabilities of the lattice.