Theory of the anomalous spin dynamics of spin-$\frac{1}{2}$ triangular lattice Heisenberg antiferromagnet and its application to Ba$_3$CoSb$_2$O$_9$

Abstract

Although it is well accepted that the spin-$\frac{1}{2}$ triangular lattice Heisenberg antiferromagnet(TLHAF) has a long range ordered ground state, a thorough understanding of its spin dynamics is still missing. While the linear spin wave theory(LSWT) predicts three branches of magnon mode in the magnetic Brillouin zone(MBZ), the 1/S expansion at the next order is found to break down in a large portion of the MBZ centered around the M point, leaving the fate of the magnon modes there undecided. Recent neutron scattering measurement on Ba$_3$CoSb$_2$O$_9$, an ideal realization of the spin-$\frac{1}{2}$ TLHAF, provides a surprising answer to this issue. Two, rather than three branches of magnon mode are observed around the M point, whose dispersion are strongly renormalized with respect to the LSWT prediction and exhibit pronounced roton-like minimum at the M point. This is accompanied by a strong spin fluctuation continuum at higher energy, inside which two strong and broad spectral peaks of unknown origin are observed. In this work, we propose a simple picture for these spectral anomalies by invoking the resonating valence bond(RVB) physics in the description of the ground state of the system. We find that the roton-like minimum in the magnon dispersion can be explained by the coupling between the collective spin fluctuation and the continuum of Dirac spinon excitation moving in a $π$-flux background. We also propose that the two broad peaks in the continuum can be understood respectively as the Landau damped third magnon mode and the Landau damped longitudinal mode. Such a picture can be verified by studying the polarization character of the various spectral features.