Susceptibility anisotropy and absence of ferroelectric order in the Kitaev spin liquid candidate Na${}_2$Co${}_2$TeO${}_6$

We report the magnetic, magnetodielectric, and electric polarization properties of single crystals of the Co-based Kitaev Spin Liquid (KSL) candidate Na${}_2$Co${}_2$TeO${}_6$ (NCTO). The sample shows magnetic transitions at 26 K, 16 K, and 5 K, consistent with the literature. The magnetic measurements along and perpendicular to the Co-honeycomb planes show a strong anisotropy in susceptibility and in Curie-Weiss (C-W) temperatures. The experimental anisotropic C-W temperatures of NCTO qualitatively match with the theoretical C-W temperatures, calculated using the HKTF model [C. Kim $\mathit{\text{et}}\mathit{\text{al.}}$, J. Phys.: Condens. Matter $\mathbf{\text{34}}$, 045802 (2021)]. We find from our temperature- and field-dependent dielectric and pyroelectric ($I_p$) current studies ($H\parallel ab$ and $E\perp ab$) that our single crystal NCTO samples do not have a finite electric polarization below 100 K. These $I_p$ studies confirm the absence of a magnetoelectric coupling and electric polarization properties in the title compound and suggest that the zig-zag AFM structure is more favorable than the triple-$Q$ structure with AFM Kitaev interactions.