Spin waves in the Kitaev quantum magnet Na₂Co₂TeO₆: Successes and failures of the triple-q model

The Kitaev candidate Na₂Co₂TeO₆ is proposed to be proximate to a quantum spin liquid state and exhibits signatures of a quantum phase transition revealed as a quantum critical endpoint in our previous works [1,2]. However, a suitable spin model and the nature of its ground states are still under debate. Our high-frequency/high-field electron spin resonance studies of Na₂Co₂TeO₆ single crystals elucidate the ground state by investigating its low-energy spin wave excitations [3]. Several excitation modes and a feature at the phase boundary connected to the putative quantum phase transition are observed for in-plane magnetic fields. For out-of-plane magnetic fields, 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 Δ₁= 211 GHz and Δ₂ = 237 GHz. The softening of one of these modes evidences a field-induced phase transition at B_c1 = 4.7 T. Our spin wave calculations based on the extended Heisenberg-Kitaev model exclude a zigzag ground state of the AFM phase. A triple-q spin configuration correctly predicts two spin wave modes but fails to reproduce the softening mode. Our analysis shows that the triple-q ground state model of Na₂Co₂TeO₆ needs to be expanded and suggests the relevance of interlayer interactions.

[1] Arneth et al., PRB 2024: doi.org/10.1103/PhysRevB.110.L140402

[2] Arneth et al., PRM 2025: doi.org/10.1103/gxyn-xqdv

[3] Bischof et al., PRB 2025: doi.org/10.1103/qk2w-hx49