We predict that an interplay between isotropic and anisotropic exchange interactions in a honeycomb lattice structure can lead to topological edge conduction when the anisotropic interaction is at least twice the strength of the isotropic interaction. For materials like ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, such a strong anisotropic exchange interaction simultaneously induces a zigzag type of antiferromagnetic order that breaks the time-reversal symmetry of the topological edge conductor. We show that the electronic transport in such topological conductors will exhibit a quantized Hall conductance without any external magnetic field when the Fermi energy lies within a particular energy range.

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• Exchange interaction
• Magnetic order
• Quantum Hall effect
• Quantum transport
• Spintronics
• Topological phase transition
• Topological materials