The Kitaev candidate material ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ is proposed to be proximate to a quantum spin liquid state but a suitable spin model and the nature of its ground states are still under debate. Our high-frequency/high-field electron spin resonance spectroscopy studies of ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ single crystals under in-plane and out-of-plane magnetic fields elucidate the ground state by investigating its low-energy spin wave excitations. Several excitation modes are observed in the low-field phase and in the phases induced by $B\parallel a^{*}$. In addition, the spectra exhibit a frequency-independent feature at the phase boundary connected to the putative quantum phase transition. For magnetic fields applied along the $c$ axis, the observation of three distinct spin wave modes in the antiferromagnetic (AFM) ground state reveals a previously unresolved splitting of the zero-field excitation gap into $\mathrm{\Delta }=211\mathrm{GHz}$ and ${\mathrm{\Delta }}_2=237\mathrm{GHz}$. The softening of one of these modes evidences a field-induced phase transition at $B_{\mathrm{c}1}=4.7\mathrm{T}$, which is corroborated by a clear anomaly in the isothermal magnetization. Spin wave calculations based on the extended Heisenberg-Kitaev model exclude a zigzag ground state of the AFM phase. A triple-$\mathbf{q}$ spin configuration correctly predicts two spin wave modes but fails to reproduce the softening mode. Our analysis shows that the triple-$\mathbf{q}$ ground state model of ${\mathrm{Na}}_2{\mathrm{Co}}_2{\mathrm{TeO}}_6$ is incomplete and suggests the relevance of interlayer interactions.

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• Frustrated magnetism
• Magnetism
• Magnons
• Electron spin resonance
• Kitaev-Heisenberg model