The Kitaev model, a spin-1/2 two-dimensional (2D) honeycomb lattice that theoretically achieves a QSL ground state, has been a tantalizing goal in condensed matter physics. While the model has been realized in several 3d, 4d, and 5d transition metal compounds, many of these materials fail to exhibit the QSL state due to non-Kitaev interactions, such as Heisenberg exchanges [1,2]. This is where NCTO, a 3d cobalt-based material, enters the scene.

Initially, NCTO showed promise as a Kitaev QSL candidate, with evidence suggesting a field-induced QSL state. However, the magnetic structure of its ground state remained a subject of debate [3-5]. Various experimental methods, including single-crystal and powder neutron diffraction, nuclear magnetic resonance, and electrical polarization measurements, have been employed to uncover its secrets, but an undisputed conclusion had yet to be reached.

Our research aimed to resolve this ambiguity by investigating the magnetic order of NCTO single crystals using neutron scattering and muon-spin rotation and relaxation (μSR) techniques. These methods allowed us to probe both the long-range and short-range magnetic orders, as well as the spin dynamics, providing a comprehensive view of the material's magnetic behavior.

Neutron scattering experiments revealed that the magnetic ground state of NCTO is characterized by a multi-domain zigzag antiferromagnetic (AFM) order, rather than a multi-k structure. By measuring the temperature- and magnetic-field dependence of the magnetic reflections at specific points (M and M1), we observed distinct behaviors that supported the multi-domain scenario. The modulation of magnetic domains induced two additional transitions at lower temperatures (TF and T*), which were also reflected in the μSR data.

The μSR technique provided further evidence of the multi-domain structure and highlighted the presence of strong quantum fluctuations in NCTO. The temperature-dependent muon-spin relaxation rates and the static magnetic volume fraction (~90%) confirmed the homogeneous nature of the magnetic order. The relatively large and temperature-independent muon-spin relaxation rate in the AFM state suggested that quantum fluctuations play a significant role in NCTO's magnetic behavior.

One of the most intriguing aspects of NCTO is the presence of strong quantum fluctuations, even in its nearly fully ordered magnetic state. These fluctuations, enhanced by applied magnetic fields, were evidenced by the broadening of the spin-wave excitation spectra and the temperature-independent muon-spin relaxation rates. Such behavior is indicative of the underlying Kitaev interactions, which contribute to the dynamic quantum fluctuations observed in NCTO.

Our findings provide crucial experimental evidence supporting the Heisenberg-Kitaev model in NCTO, where the coexistence of static magnetic order and dynamic quantum fluctuations suggests a highly frustrated magnetic structure. This complex interplay between different exchange interactions offers new insights into the nature of QSL states and highlights the potential of NCTO as a platform for exploring Kitaev physics.

The discovery of a multi-domain zigzag AFM order with strong quantum fluctuations in NCTO opens up several exciting avenues for future research. Investigating the effects of higher magnetic fields and exploring other potential Kitaev QSL candidates in the cobalt-based family could further our understanding of these fascinating materials. Moreover, advanced theoretical models that incorporate the observed quantum fluctuations and domain structures could provide a more detailed picture of the magnetic interactions at play.

Reference:

[1] Takagi, H., Takayama, T., Jackeli, G., Khaliullin, G. & Nagler, S. E. Concept and realization of Kitaev quantum spin liquids. Nat. Rev. Phys. 1, 264-280 (2019).

[2] Lin, G., et al. Field-induced quantum spin disordered state in spin-1/2 honeycomb magnet Na₂Co₂TeO₆. Nat. Commun. 12, 5559 (2021).

[3] Bera, A. K., Yusuf, S. M., Kumar, A. & Ritter, C. Zigzag antiferromagnetic ground state with anisotropic correlation lengths in the quasi-two-dimensional honeycomb lattice compound Na₂Co₂TeO₆. Phys. Rev. B. 95, 094424 (2017).

[4] Yao, W., et al. Magnetic ground state of the Kitaev Na₂Co₂TeO₆ spin liquid candidate. Phys. Rev. Res. 5, L022045 (2023).

[5] Chen, W., et al. Spin-orbit phase behavior of Na₂Co₂TeO₆ at low temperatures. Phys. Rev. B. 103, L180404 (2021).