Phase diagram of theJ1−J2−J3Heisenberg model on the honeycomb lattice: A series expansion study

Abstract

We study magnetically-ordered phases and their phase boundaries in the ${J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ Heisenberg models on the honeycomb lattice using series expansions around N\'eel and different colinear and noncolinear magnetic states. An Ising anisotropy ($\ensuremath{\lambda}={J}_{\ensuremath{\perp}}/{J}_{z}\ensuremath{\ne}1$) is introduced and ground-state energy and magnetization order parameter are calculated as a power series expansion in $\ensuremath{\lambda}$. Series extrapolation methods are used to study properties for the Heisenberg model ($\ensuremath{\lambda}=1$). We find that at large ${J}_{3}$ ($>0.6$) there is a first-order transition between N\'eel and columnar states, in agreement with the classical answer. For ${J}_{3}=0$, we find that the N\'eel phase extends beyond the region of classical stability. We also find that spiral phases are stabilized over large parameter regions, although their spiral angles can be substantially renormalized with respect to the classical values. Our study also shows a magnetically disordered region at intermediate ${J}_{2}/{J}_{1}$ and ${J}_{3}/{J}_{1}$ values.