  Magnetization measurements on single-crystal cubic SrCuTe$_2$O$_6$ with an
applied magnetic field of along three inequivalent high symmetry directions
$[100]$, $[110]$, and $[111]$ reveal weak magnetic anisotropy. The fits of the
magnetic susceptibility to the result from a quantum Monte Carlo simulation on
the Heisenberg spin-chain model, where the chain is formed via the dominant
third-nearest-neighbor exchange interaction $J_3$, yield the intra-chain
interaction $(J_3/k_B)$ between 50.12(7) K for the applied field along $[110]$
and 52.5(2) K along $[100]$ with about the same $g$-factor of 2.2.
Single-crystal neutron diffraction unveils the transition to the magnetic
ordered state as evidenced by the onset of the magnetic Bragg intensity at
$T_\textrm{N1}=5.25(9)$ K with no anomaly of the second transition at
$T_\textrm{N2}$ reported previously. Based on irreducible representation theory
and magnetic space group analysis of powder and single-crystal neutron
diffraction data, the magnetic structure in the Shubnikov space group $P4_132$,
where the Cu$^{2+}$~$S=1/2$ spins antiferromagnetically align in the direction
perpendicular to the spin chain, is proposed. The measured ordered moment of
$0.52(6)~\mu_B$, which represents 48% reduction from the expected value of
$1~\mu_B$, suggests the remaining influence of frustration resulting from the
$J_1$ and $J_2$ bonds.
