Short range order in the quantum XXZ honeycomb lattice material γ-BaCo2(PO4)2

γ-BaCo₂(PO₄)₂ (γ-BCPO) is a honeycomb-lattice compound with quasi-two-dimensional structure exhibiting short-range ordered (SRO) frustrated magnetism. We have studied hydrothermally synthesized γ-BCPO samples via magnetometry (Χ_ac), specific heat (C_p), x ray and inelastic neutron scattering (INS) experiments. Χ_ac and C_p showed a broad anomaly at ∼ 5 K, with two weak kink features in C_p at T_N1 ∼ 6 K and T_N2 ∼ 3.5 K. Collinear antiferromagnetic SRO with ordering wavevector |k_c| = 0.5 and correlation length ξ_c = 60 Å and quasi-2D helical SRO with |k_h| = 0.25 and ξ_h = 253 Å form below T_N1 and T_N2 respectively. Our INS data compares well with linear spin wave theory for two separate parameter regimes of the XXZ J₁-J₂-J₃ model with near neighbor ferromagnetic exchange, J₁. Competing further interactions, J₂ and J₃ place γ-BCPO near regions of high classical degeneracy such as the highly frustrated point, J₁/2 = -J₂ = J₃. Our analysis suggests that γ-BCPO balances near the edge of competing classical phases of the XXZ J₁-J₂-J₃ model, implying that frustration and quantum fluctuations may account for its inability to form a long range order state.