Short range order in the quantum XXZ honeycomb lattice material BaCo$_2$(PO$_4$)$_2$

We present observations of highly frustrated quasi two-dimensional (2D) magnetic correlations in the honeycomb lattice layers of the S$_{eff}$ = 1/2 compound $gamma$-BaCo$_2$(PO$_4$)$_2$ ($gamma$-BCPO). Specific heat shows a broad peak comprised of two weak kink features at $T_{N1} sim$ 6 K and $T_{N2} sim$ 3.5 K, the relative weights of which can be modified by sample annealing. Neutron powder diffraction measurements reveal short range quasi-2D order that is established below $T_{N1}$ and $T_{N2}$, at which two separate, incompatible, short range magnetic orders onset: commensurate antiferromagnetic correlations with correlation length $xi_c = 60pm2$ AA ($T_{N1}$) and in quasi-2D helical domains with $xi_h = 350 pm 11$ AA ($T_{N2}$). The ac magnetic susceptibility response lacks frequency dependence, ruling out spin freezing. Inelastic neutron scattering data on $gamma$-BCPO is compared with linear spin wave theory, and two separate parameter regions of the XXZ $J_1$-$J_2$-$J_3$ model with ferromagnetic nearest-neighbor exchange $J_1$ are favored, both near regions of high classical degeneracy. High energy coherent excitations ($sim 10$ meV) persist up to at least 40 K, suggesting strong in-plane correlations persist above $T_N$. These data show that $gamma$-BCPO is a rare highly frustrated, quasi-2D S$_{eff}$ = 1/2 honeycomb lattice material which resists long range magnetic order and spin freezing.