Non-linear spin wave theory in the strong easy-axis limit of the triangular XXZ model

Abstract

Motivated by recent experimental studies, we investigate the spectrum of the nearest-neighbour triangular XXZ model within the $1/S$ expansion, in the limit in which the exchange couplings present a strong easy-axis anisotropy $J_{xy}/J_{zz}\ll 1$. We show that in the limit in which $1/S\to 0$ and $J_{xy}\to 0$ at fixed $V=J_{zz}/(S{J}_{xy})$, the triangular spin model can be reduced to an effective boson model with quartic interactions on the honeycomb lattice. This effective model interpolates between a spin-wave ($V\to 0$) and a strong-coupling limit ($V\to \infty$) and encodes in a simple framework the regimes discussed by Kleine~\emph{et al.}~[Z. Phys. B Condens. Matter~{\bf 86}, 405 (1992);~{\bf 87}, 103 (1992)]. For zero field, the classical ground state of the model presents an accidental degeneracy, which can be traced to a simple symmetry of the classical energy. The model thus offers a transparent realization of a theory with quantum order-by-disorder and a pseudo-Goldstone mode. We analyze the spectrum at zero magnetic field by calculating the self-energy at one-loop order. In the calculation, we introduce a self-consistent renormalization of the energy scale and of the pseudo-Goldstone energy gap; the latter renormalization is essential to remove infrared divergences in the on-shell corrections to the energy dispersion. Finally, we discuss qualitatively the structure of the one-loop corrections in comparison with the spectrum observed experimentally in K${}_2$Co(SeO${}_3$)${}_2$.

28 pages, 13 figures

References in corpus (1)

• Dynamics and thermodynamics of the S = 5/2 almost Heisenberg triangular lattice antiferromagnet K2Mn(SeO3)2