Magnetic excitations in the Kitaev material <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Na</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:msub> <mml:mi>IrO</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:mrow>

Inelastic neutron scattering experiments with a large set of comounted Na$_2$IrO$_3$ crystals reveal the low-energy magnon dispersion in this candidate material for Kitaev physics. The magnon gap amounts to 1.7(1) meV and can be interpreted similarly to the sister compound $α$-RuCl$_{3}$ to stem from the zone boundaries in the antiferromagnetic zigzag structure. The neutron experiments find no evidence for low-energy excitations with ferromagnetic character, which contrasts to the findings in $α$-RuCl$_{3}$. Our results are consistent with a recently proposed microscopic model that involves an antiferromagnetic Heisenberg nearest-neighbor exchange in Na$_2$IrO$_3$ in contrast to the ferromagnetic one considered for $α$-RuCl$_{3}$. Although the magnetic response shows the signatures of bond-directional anisotropy in both materials the different relative signs of Kitaev and Heisenberg interaction result in different deviations from the initial Kitaev model. Low-energy ferromagnetic fluctuations cannot be considered as a fingerprint of ferromagnetic Kitaev interaction.