The antiferromagnetic compound $\mathrm{Ba}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$ contains square cupola of corner-sharing ${\mathrm{CuO}}_4$ plaquettes, which were proposed to form effective quadrupolar order. To identify the magnetic structure, we have performed spherical neutron polarimetry measurements. Based on symmetry analysis and careful measurements, we conclude that the orientation of the ${\mathrm{Cu}}^{2+}$ spins form a noncollinear in-out structure with spins approximately perpendicular to the ${\mathrm{CuO}}_4$ motif. Strong Dzyaloshinskii-Moriya interaction naturally lends itself to explain this phenomenon. The identification of the ground-state magnetic structure should serve well for future theoretical and experimental studies into this and closely related compounds.

• Received 25 September 2017
• Revised 22 November 2017

DOI:https://doi.org/10.1103/PhysRevB.96.214436