[en] We investigate the intrinsic magnon spin current in a noncollinear antiferromagnetic insulator. We introduce a definition of the magnon spin current in a noncollinear antiferromagnet and find that it is in general nonconserved, but for certain symmetries and spin polarizations the averaged effect of nonconserving terms can vanish. We formulate a general linear response theory for magnons in noncollinear antiferromagnets subject to a temperature gradient and analyze the effect of symmetries on the response tensor. We apply this theory to single-layer potassium iron jarosite ${\mathrm{KFe}}_3{\left(\mathrm{OH}\right)}_6{\left({\mathrm{SO}}_4\right)}_2$ and predict a measurable spin current response.

[en] Topological antiferromagnetic (AFM) spintronics is an emerging field of research, which involves the topological electronic states coupled to the AFM order parameter known as the Néel vector. The control of these states is envisioned through manipulation of the Néel vector by spin-orbit torques driven by electric currents. In this work, we present a different approach favorable for low-power AFM spintronics, where the control of the topological states in a two-dimensional material, such as graphene, is performed via the proximity effect by the voltage induced switching of the Néel vector in an adjacent magnetoelectric AFM insulator, such as chromia. Mediated by the symmetry protected boundary magnetization and the induced Rashba-type spin-orbit coupling at the interface between graphene and chromia, the emergent topological phases in graphene can be controlled by the Néel vector. Using density functional theory and tight-binding Hamiltonian approaches, we model a $\mathrm{graphene}/{\mathrm{Cr}}_2{\mathrm{O}}_3$ (0001) interface and demonstrate nontrivial band gap openings in the graphene Dirac bands asymmetric between the $K$ and $K^{\text{'}}$ valleys. This gives rise to an unconventional quantum anomalous Hall effect (QAHE) with a quantized value of $2e^2/h$ and an additional steplike feature at a value close to $e^2/2h$, and the emergence of the spin-polarized valley Hall effect (VHE). Additionally, depending on the Néel vector orientation, we predict the appearance and transformation of different topological phases in graphene across the 180° AFM domain wall, involving the QAHE, the valley-polarized QAHE, and the quantum VHE, and the emergence of the chiral edge states along the domain wall. These topological properties are controlled by voltage through magnetoelectric switching of the AFM insulator with no need for spin-orbit torques.