Hexagonal ${\mathrm{YMnO}}_3$ is an intensively studied representative of materials exhibiting the coexistence of magnetic and electric order, called multiferroicity. Nevertheless, a controversy about its antiferromagnetic order remains. Initial reports suggested space-group symmetry $P{6}_3{c}^{\prime }{m}^{\prime }$ with ${\mathrm{Mn}}^{3+}$ spins along the crystallographic $y$ axis and antiparallel orientation of corresponding spins in adjacent $xy$ planes. However, subsequent experiments increasingly supported $P{6}_3^{\prime }c{m}^{\prime }$ symmetry with spins aligned along the crystallographic $x$ axis and parallel orientation of corresponding spins in adjacent $xy$ planes. Despite accumulating evidence for this structure, a neutron polarimetry study revealed an order according to space-group symmetry $P{6}_3^{\prime }$, where the ${\mathrm{Mn}}^{3+}$ spins are rotated by ${11}^{\circ }$ from the $x$ toward the $y$ axis. Here we report experiments by optical second harmonic generation that point to $P{6}_3^{\prime }c{m}^{\prime }$ symmetry and no evidence for spin rotation within a noise-inflicted upper limit of $\lesssim 1^{\circ }$. We suggest that the discrepancy could be resolved by an expansion of the configurations measured by neutron polarimetry and the use of samples with enlarged domains to prevent domain-wall-related contributions.

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• Magnetic order
• Multiferroics
• Laser techniques
• Neutron diffraction