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 $(3.9pm0.1)~mu_{mathrm{B}}/mathrm{f.u.}$, 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 $langle111rangle$ (magnetic space group $R[I]3c$). Surprisingly, below $T^{*}$, the moments tilt away from $langle111rangle$ 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.
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