Precise magnetic structures of $R{\mathrm{Mn}}_2{\mathrm{O}}_5$, with $R=\mathrm{Y},\mathrm{Ho},\mathrm{Bi}$ in the commensurate and/or ferroelectric regime, have been determined by single-crystal neutron diffraction. For each system, the integrated intensities of a large number of independent magnetic Bragg reflections have been measured, allowing unconstrained least-squares refinement of the structures. The analysis confirms the previously reported magnetic configuration in the $ab$ plane, in particular, the existence of zigzag antiferromagnetic chains. For the Y and Ho compounds, additional weak magnetic components parallel to the $c$ axis were detected, which are modulated in phase quadrature with the $a\text{−}b$ components. This component is extremely small in the $\mathrm{Bi}{\mathrm{Mn}}_2{\mathrm{O}}_5$ sample, therefore supporting symmetric exchange as the principal mechanism inducing ferroelectricity. For $\mathrm{Ho}{\mathrm{Mn}}_2{\mathrm{O}}_5$, a magnetic ordering of the Ho moments was observed, which is consistent with a superexchange interaction through the oxygens. For all three compounds, the point symmetry in the magnetically ordered state is $m2m$, allowing the polar $b$ axis found experimentally.

• Received 10 October 2007

DOI:https://doi.org/10.1103/PhysRevB.77.134434