Successive topological phase transitions in two distinct spin-flop phases on the honeycomb lattice

The Kitaev magnets with bond-dependent interactions have garnered considerable attention in recent years for their ability to harbor exotic phases and nontrivial excitations. The topological magnons, which are indicated by nonzero Chern number and thermal Hall conductivity, are proposed to partially explain thermal Hall measurements in real materials. Hitherto, topological magnons have been extensively explored when the magnetic field is normal to the honeycomb plane, but their topological characteristics are less studied in the presence of in-plane magnetic field. Here, we study two distinct in-plane field induced spin-flop phases in the $\Gamma$-$\Gamma'$ model, both of which are off-diagonal couplings that have intimate relation to the Kitaev interaction. The two spin-flop phases are distinguished by their out-of-plane spin components which can be either antiparallel or parallel, thus dubbing antiferromagnetic (AFM) or ferromagnetic (FM) spin-flop phases, respectively. We map out topological phase diagrams for both phases, revealing a rich pattern of the Chern number over exchange parameters and magnetic field. We analytically calculate the boundaries of topological phase transitions when the magnetic field is along the $a$ and $b$ directions. We find that the thermal Hall conductivity and its derivative display contrasting behaviors when crossing different topological phase transitions. The striking difference of the two phases lies in that when the magnetic field is along the $b$ direction, topological magnons are totally absent in the AFM spin-flop phase, while they can survive in the FM analogue in certain parameter regions.