Frustration-driven unconventional magnetism in the Mn$^{2+}$ ($S=\frac{5}{2}$) based two-dimensional triangular-lattice antiferromagnet Ba$_{3}$MnTa$_{2}$O$_{9}$

A triple perovskite oxide Ba$_{3}$MnTa$_{2}$O$_{9}$ has been synthesized and its magnetic properties have been investigated through dc and ac magnetization, specific heat, electron spin resonance (ESR) measurements, and density functional theory (DFT) calculations. Mn$^{2+}$ ($S$ = 5/2) ions are the only magnetic species present in the material. These Mn$^{2+}$ ions constitute a quasi-two-dimensional triangular network in the crystallographic $ab$-plane. Magnetization and specific heat measurements reveal the absence of any long-range magnetic order down to 0.5\,K despite the presence of antiferromagnetic correlations between the magnetic ions, suggesting the presence of geometric frustration in the material. The entropy release is lower than the expected theoretical value of $Rln(6)$, further suggesting the presence of frustration. First-principles calculations using density functional theory (DFT) and atomistic spin dynamics (ASD) simulations further support this lack of static magnetic order even at low temperatures and identify the competing magnetic interactions along with the quasi-2D magnetic dimensionality as the underlying origin of such an unconventional magnetic behavior.