We present a comprehensive study of single crystals of Na2Co2TeO6, a putative Kitaev honeycomb magnet, focusing on its low-temperature phase behaviors. A new thermal phase transition is identified at 31.0 K, below which the system develops a two-dimensional (2D) long-range magnetic order. This order precedes the well-known 3D order below 26.7 K, and is likely driven by strongly anisotropic interactions. Surprisingly, excitations from the 3D order do not support the orders commonly accepted zigzag nature, and are instead consistent with a triple-q description. The 3D order exerts a fundamental feedback on high-energy excitations that likely involve orbital degrees of freedom, and it remains highly frustrated until a much lower temperature is reached. These findings render Na2Co2TeO6 a spin-orbit entangled frustrated magnet that hosts very rich physics.
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