Development of short and long-range magnetic order in the double perovskite based frustrated triangular lattice antiferromagnet Ba $$_{2}$$ 2 MnTeO $$_{6}$$ 6

Frustrated magnets based on oxide double perovskites offer a viable ground wherein competing magnetic interactions, macroscopic ground state degeneracy and complex interplay between emergent degrees of freedom can lead to correlated quantum phenomena with exotic excitations highly relevant for potential technological applications. By local-probe muon spin relaxation ( $$\mu$$ SR) and complementary thermodynamic measurements accompanied by first-principles calculations, we here demonstrate novel electronic structure and magnetic phases of Ba $$_{2}$$ MnTeO $$_{6}$$ , where Mn $$^{2+}$$ ions with S = 5/2 spins constitute a perfect triangular lattice. Magnetization results evidence the presence of strong antiferromagnetic interactions between Mn $$^{2+}$$ spins and a phase transition at $$T_{N}$$ = 20 K. Below $$T_{N}$$ , the specific heat data show antiferromagnetic magnon excitations with a gap of 1.4 K, which is due to magnetic anisotropy. $$\mu$$ SR reveals the presence of static internal fields in the ordered state and short-range spin correlations high above $$T_{N}$$ . It further unveils critical slowing-down of spin dynamics at $$T_{N}$$ and the persistence of spin dynamics even in the magnetically ordered state. Theoretical studies infer that Heisenberg interactions govern the inter- and intra-layer spin-frustration in this compound. Our results establish that the combined effect of a weak third-nearest-neighbour ferromagnetic inter-layer interaction (owing to double-exchange) and intra-layer interactions stabilizes a three-dimensional magnetic ordering in this frustrated magnet.