Quantum effect of triple-perovskite antiferromagnets with triangular lattices, A₃MB₂O₉ (A = Ba, Ca, and Sr; M = Co, Ni, and Mn; B = Sb, Nb)

As a typical two-dimensional frustrated quantum magnet, the triangular-lattice antiferromagnet exhibits a series of exotic states from the complicated interplay of the lattice, spin, electron, and orbit with quantum and thermal fluctuations. From the ground state of a triangular-lattice Heisenberg antiferromagnet with coplanar 120^\circ ordering, a series of magnetization anomalies can manifest under a magnetic field, such as the 1/3 magnetization plateau (Ms/3) and umbrella-shaped phase. This Ms/3 plateau state is recognized as an up-up-down structure stabilized by the quantum effect. By surveying theoretical research and experimental measurements on triangular-lattice antiferromagnets, this review article describes the current understanding of the magnetic properties of triple-perovskite antiferromagnets A_3MB_2O_9(A = Ba, Ca, and Sr; M = Co, Ni, and Mn; B = Sb, Nb). Through examining both the bulk properties and spin dynamics, fascinating insights into the quantum effect on the triangular lattice are discussed.