  We report the low-temperature properties of phase-pure single crystals of the
half-Heusler compound CuMnSb grown by means of optical float-zoning. The
magnetization, specific heat, electrical resistivity, and Hall effect of our
single crystals exhibit an antiferromagnetic transition at $T_{\mathrm{N}} =
55~\mathrm{K}$ and a second anomaly at a temperature $T^{*} \approx
34~\mathrm{K}$. Powder and single-crystal neutron diffraction establish an
ordered magnetic moment of $(3.9\pm0.1)~\mu_{\mathrm{B}}/\mathrm{f.u.}$,
consistent with the effective moment inferred from the Curie-Weiss dependence
of the susceptibility. Below $T_{\mathrm{N}}$, the Mn sublattice displays
commensurate type-II antiferromagnetic order with propagation vectors and
magnetic moments along $\langle111\rangle$ (magnetic space group $R[I]3c$).
Surprisingly, below $T^{*}$, the moments tilt away from $\langle111\rangle$ by
a finite angle $\delta \approx 11^{\circ}$, forming a canted antiferromagnetic
structure without uniform magnetization consistent with magnetic space group
$C[B]c$. Our results establish that type-II antiferromagnetism is not the
zero-temperature magnetic ground state of CuMnSb as may be expected of the
face-centered cubic Mn sublattice.
