Berezinskii-Kosterlitz-Thouless region and magnetization plateaus in easy-axis triangular weak-dimer antiferromagnet K$_2$Co$_2$(SeO$_3$)$_3$

We investigate the magnetic phase diagram of the bilayer triangular antiferromagnet K$_2$Co$_2$(SeO$_3$)$_3$, revealing a rich interplay among geometric frustration, bilayer coupling, and symmetry-driven phenomena. High-field magnetization measurements show fractional magnetization plateaus at 1/3, 1/2, 2/3, and 5/6 of the saturation magnetization. To elucidate the experimental magnetic phase diagram at low fields, we propose that K$_2$Co$_2$(SeO$_3$)$_3$ can be described as an easy-axis triangular weak-dimer antiferromagnet. We emphasize the critical role of the emergent $U(1) \otimes S_3$ symmetry, where $S_3 = \mathbb{Z}_3 \otimes \mathbb{Z}_2^d$, in determining the magnetic phases at low fields. The remarkable agreement between the experimental and theoretical phase diagrams suggests that the phase transitions are governed by this symmetry. Notably, our combined experimental and theoretical results identify a Berezinskii-Kosterlitz-Thouless (BKT) phase region at finite fields. These findings provide new insights into the phase structure of frustrated magnets and establish K$_2$Co$_2$(SeO$_3$)$_3$ as a compelling platform for exploring unconventional quantum phenomena in $U(1) \otimes S_3$ systems.