Static and dynamical properties of frustrated two-dimensional square quantum Heisenberg antiferromagnets

Abstract

Two-dimensional square quantum Heisenberg antiferromagnets with competing interactions up to third neighbors ${(J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ model) are investigated by using the high-temperature series expansion method. From the analyses of the wave-vector-dependent susceptibility $\ensuremath{\chi}(\mathit{k}),$ we find four kinds of the stable paramagnetic phases depending on the coupling constants, i.e., N\'eel, collinear, and two helical paramagnetic phases, ${H}_{1}$ and ${H}_{2}.$ They are characterized by the critical wave vector ${\mathit{k}}_{A}^{c} (A=N,$ C, ${H}_{1},$ or ${H}_{2}),$ at which the functions $\ensuremath{\chi}(\mathit{k})$ show the maximum value. Except around the ${H}_{1}\ensuremath{-}{H}_{2}$ phase boundary, they are destabilized and show the intermediate phases in the neighborhood of the phase boundaries, where the relevant critical wave vector ${\mathit{k}}_{A}^{c}$ is not specified uniquely. The analogy between the paramagnetic phase diagram obtained here and the ordered ones derived by the simple spin wave theory suggests the possibility of the spin liquid state in the intermediate phase at $T=0.$ The first-order transition occurs between ${H}_{1}$ and ${H}_{2}$ phases, so the intermediate phase is not seen there. The dynamical spectrum function $F(\mathit{k},\ensuremath{\omega})$ is calculated in the form of Mori's continued fraction with the frequency moments. The dynamical aspects for the stable paramagnetic phases are also characterized by the critical wave vector ${\mathit{k}}_{A}^{c}.$ While the side peak or shoulder shape appears in $F({\mathit{k}}_{A}^{c},\ensuremath{\omega})$ at $T=\ensuremath{\infty},$ the line shape becomes considerably narrow when decreasing the temperature at ${\mathit{k}}_{A}^{c}.$ These behaviors are attributed to the spin flip-flop motion for the former case, and the quasicollective motion for the latter one. In the intermediate phase, at $T=\ensuremath{\infty}$ the line shape undergoes slow change versus the wave vector $\mathit{k}$ except for the drastic narrowing around $\mathit{k}\ensuremath{\simeq}0,$ due to the absence of the unique critical wave vector. It is found that the high-temperature dynamical aspect keeps there, even though the temperature is decreased, due to the frustration effect.