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Polarised neutron diffraction measurements have been made on HoFeO$_3$ singlecrystals magnetised in both the [001] and [100] directions ($Pbnm$ setting).The polarisation dependencies of Bragg reflection intensities were measuredboth with a high field of H = 9 T parallel to [001] at T = 70 K and with thelower field H = 0.5 T parallel to [100] at T = 5, 15, 25~K. A Fourierprojection of magnetization induced parallel to [001], made using the $hk0$reflections measured in 9~T, indicates that almost all of it is due toalignment of Ho moments. Further analysis of the asymmetries of generalreflections in these data showed that although, at 70~K, 9~T applied parallelto [001] hardly perturbs the antiferromagnetic order of the Fe sublattices, itinduces significant antiferromagnetic order of the Ho sublattices in the$x\mhyphen y$ plane, with the antiferromagnetic components of moment having thesame order of magnitude as the induced ferromagnetic ones. Strong intensityasymmetries measured in the low temperature $\Gamma_2$ structure with a lowerfield, 0.5 T $\parallel$ [100] allowed the variation of the ordered componentsof the Ho and Fe moments to be followed. Their absolute orientations, in the180\degree\ domain stabilised by the field were determined relative to thedistorted perovskite structure,. This relationship fixes the sign of theDzyalshinski-Moriya (D-M) interaction which leads to the weak ferromagnetism.Our results indicate that the combination of strong y-axis anisotropy of the Homoments and Ho-Fe exchange interactions breaks the centrosymmetry of thestructure and could lead to ferroelectric polarization.

Single crystal polarized neutron diffraction study of the magnetic structure of HoFeO$_3$