We report a comprehensive study of the structural and magnetic properties of the two-dimensional $S=\frac{5}{2}$ frustrated triangular-lattice antiferromagnet ${\mathrm{Ba}}_3{\mathrm{MnTa}}_2{\mathrm{O}}_9$ using x-ray diffraction, magnetization, electron spin resonance, and heat-capacity measurements on a polycrystalline sample, combined with density-functional band-structure calculations. The magnetic susceptibility and heat-capacity data reveal the onset of antiferromagnetic long-range order at $T_{\mathrm{N}}\simeq 2.6\mathrm{K}$, which is in sharp contrast with the recent report by Mondal et al. [Phys. Rev. B 112, 155153 (2025)] who did not observe magnetic order in this material. The nearest-neighbor exchange coupling $J/k_{\mathrm{B}}\simeq 0.85\mathrm{K}$ is obtained from Monte Carlo fits to the experimental susceptibility data. Combined with the ab initio estimate of the interlayer coupling, this $J/k_{\mathrm{B}}$ value leads to $T_{\mathrm{N}}\simeq 2.7\mathrm{K}$ in a perfect agreement with the experiment. Magnetic isotherms reveal a field-induced transition below $T_{\mathrm{N}}$. The complex $H\text{−}T$ phase diagram features multiple phases as a consequence of magnetic frustration and anisotropy present in the system.

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• Antiferromagnetism
• Exchange interaction
• Frustrated magnetism
• Magnetic phase transitions
• Antiferromagnets
• Triangular lattice
• Density functional calculations
• Electron spin resonance
• Magnetization measurements
• Specific heat measurements