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We report the results of magnetization and specific heat measurements ofBa$_2$CoTeO$_6$ composed of two subsystems A and B, which are magneticallydescribed as an $S\,{=}\,1/2$ triangular-lattice Heisenberg-likeantiferromagnet and a $J_1-J_2$ honeycomb-lattice Ising-like antiferromagnet,respectively. These two subsystems were found to be approximately decoupled.Ba$_2$CoTeO$_6$ undergoes magnetic phase transitions at $T_{\rm N1}\,{=}\,12.0$K and $T_{\rm N2}\,{=}\,3.0$ K, which can be interpreted as the orderings ofsubsystems B and A, respectively. Subsystem A exhibits a magnetization plateauat one-third of the saturation magnetization for the magnetic field $H$perpendicular to the $c$ axis owing to the quantum order-by-disorder, whereasfor $H\,{\parallel}\,c$, subsystem B shows three-step metamagnetic transitionswith magnetization plateaus at zero, one-third and one-half of the saturationmagnetization. The analysis of the magnetization process for subsystem B showsthat the classical ground states at these plateaus are infinitely degeneratewithin the Ising model.

physical review. b./physical review. b

Field-driven successive phase transitions in quasi-two-dimensional  frustrated antiferromagnet Ba$_2$CoTeO$_6$ and highly degenerate classical  ground states