  Trillium lattices formed by corner-shared triangular units are the platform
for magnetic frustration in three dimensions. Herein, we report structural and
magnetic properties of the Cr-based double trillium lattice material
KBaCr$_2$(PO$_4$)$_3$ studied by x-ray diffraction, magnetization, heat
capacity, thermal conductivity, and $^{31}$P nuclear magnetic resonance (NMR)
measurements complemented by density-functional band-structure calculations.
Heat capacity and $^{31}$P NMR measurements reveal the magnetic transition at
$T_{\rm N1} \simeq 13.5$ K in zero field followed by another transition at
$T_{\rm N2} \simeq 7$ K in weak applied fields. The NMR sublattice
magnetization confirms that the transition at $T_{\rm N1}$ is 3D in nature. The
$^{31}$P spin-lattice relaxation rate in the ordered state follows the $T^3$
behavior indicative of the two-magnon Raman process. The spin lattice of
KBaCr$_2$(PO$_4$)$_3$ comprises two crystallographically nonequivalent
ferromagnetic sublattices that are coupled antiferromagnetically, thus
eliminating frustration in this trillium network.
