Two-dimensional quantum spin-1/2 Heisenberg model with competing interactions

Abstract

We study the quantum spin-1/2 Heisenberg model in two dimensions, interacting through a nearest-neighbor antiferromagnetic exchange ($J$) and a ferromagnetic dipolar-like interaction ($J_d$), using double-time Green's function, decoupled within the random phase approximation (RPA). We obtain the dependence of $k_B{T}_c/J_d$ as a function of frustration parameter $\delta$, where $T_c$ is the ferromagnetic (F) transition temperature and $\delta$ is the ratio between the strengths of the exchange and dipolar interaction (i.e., $\delta =J/J_d$). The transition temperature between the F and paramagnetic phases decreases with $\delta$, as expected, but goes to zero at a finite value of this parameter, namely $\delta ={\delta }_c=\pi /8$. At T=0 (quantum phase transition), we analyze the critical parameter ${\delta }_c(p)$ for the general case of an exchange interaction in the form $J_{ij}=J_d/r_{ij}^p$, where ferromagnetic and antiferromagnetic phases are present.

arXiv comment4 pages, 1 figure

References in corpus (6)

• Absence of spontaneous magnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactions
• Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions
• Aging in a Two-Dimensional Ising Model with Dipolar Interactions
• Slow dynamics in a 2D Ising model with competing interactions
• Violation of the Fluctuation-Dissipation Theorem in a Two-Dimensional Ising Model with Dipolar Interactions
• Dipolar random field Ising model: an application to garnet films

Cited by in corpus (1)

• Two- and three-dimensional magnetic correlations in the spin-1/2 square-lattice system Zn2VO(PO4)2