Bond dependent spin-orbital exchange and quantum order-by-disorder in CoTiO3

There has been a great deal of interest in bond-dependent anisotropic couplings in strong spin-orbit coupled magnets - especially on iridates and ruthenates - that has brought new physics into focus. Recent theoretical work has proposed that such couplings can be significant in certain cobalt magnets where the spin-orbit coupling is sub-dominant [1]. Here we report on CoTiO3, an insulating ABC stacked honeycomb easy plane magnet that orders into a structure with ferromagnetic layers stacked antiferromagnetically with a spin wave spectrum that is known to host Dirac magnons [2]. Our high resolution inelastic neutron scattering data clearly shows the presence of a magnon gap of about 1meV that must arise through the presence of bond-dependent exchange couplings [3]. The spectral gap also provides strong evidence for the existence of a quantum order-by-disorder mechanism − a very rare phenomenon that selects the long-ranged ordered magnetic structure through the effect of quantum fluctuations - that, in this material, crucially involves virtual crystal field excitations. The same couplings that lead to the spectral gap also cause the Dirac magnons to wind around one another in a double helix structure and we show that the experimental data is consistent with this scenario. We also show the presence of dispersive exciton modes with Dirac nodes. All the key features of the experiment are explicable through a multi-boson theory with spin-orbital exchange couplings.
[1] H. Liu and G. Khaliullin, Phys. Rev. B 97, 014407 (2018); R. Sano, Y. Kato, and Y. Motome, Phys. Rev. B 97, 014408 (2018).
[2] B. Yuan, I. Khait, G.-J. Shu, F. C. Chou, M. B. Stone, J. P. Clancy, A. Paramekanti, and Y.-J. Kim, Phys. Rev. X 10, 011062 (2020).
[3] M. Elliot, P. A. McClarty, D. Prabhakaran, R. D. Johnson, H. C. Walker, P. Manuel, and R. Coldea, arXiv:2007.04199.