Antiferromagnetic spin canting and Magnetoelectric Multipoles in h-YMnO$_3$

Hexagonal YMnO$_{3}$ is a prototype antiferromagnet which exhibits multiferroic behavior with the ferroelectric and magnetic transitions occurring at different temperatures. We observe an out-of-plane canting of the Mn$^{3+}$ magnetic moments using resonant X-ray diffraction (RXD) in a single crystal of this material. These canted moments result in the symmetry-forbidden (0,0,1) magnetic Bragg reflection, which is observed at the Mn $L_{2,3}$ absorption edges. We also observe an unexpected difference in the RXD spectral shapes at different temperatures. Using ab initio calculations, we explore the possibility that this behavior arises due to the interference between scattering from the canted magnetic moments and parity-odd atomic multipoles on the Mn$^{3+}$ ions.