Polar magnetization unveiled by polarized neutron diffraction

Polar magnetism is compulsory when magnetic ions occupy sites that are not centers of inversion symmetry. Such magnetism is known to be visible in neutron diffraction, the technique of choice for magnetic structure determinations. Experiments in which the diffracted neutron polarization is analyzed are not a novelty. Symmetry-informed simulations of polarized neutron diffraction (PND) amplitudes for room-temperature hematite (α-${\mathrm{Fe}}_2{\mathrm{O}}_3$) illustrate the wealth of information on offer in future experiments. Two magnetic motifs, distinguished by the orientation of their bulk ferromagnetism and delineated by magnetic space groups $C2/c$ and $C{2}^{\prime }/c^{\prime }$, are current front-runners for room-temperature hematite. Both motifs are endowed with polar magnetism and iron Dirac (magnetoelectric) multipoles. The technique of resonant x-ray Bragg diffraction has previously been used to expose Dirac multipoles in room-temperature hematite. For unspecified reasons, the authors of a recent PND study of hamatite do not mention the compulsory polar magnetism, the published observation of Dirac multipoles, or the direct confirmation of neutron scattering by Dirac multipoles [H. Thoma et al., Phys. Rev. X 11, 011060 (2021) .]. The authors omission of polar magnetism in fits to their extensive neutron diffraction patterns calls for a reassessment of the claim to have determined the absolute direction of the Dzyaloshinskii-Moriya interaction.

Figure 1

Depiction of an orbital anapole (toroidal dipole); author V. Scagnoli.

Figure 2

Radial integrals for the ferric ion ${\mathrm{Fe}}^{3+}\left(3d^5\right)$ displayed as a function of the magnitude of the reflection vector $\kappa =4\pi s$ with $s=sin\left(\theta \right)/\lambda \left({\AA }^{–1}\right)$, Bragg angle θ, and neutron wavelength λ. Also, $w=3a_{\mathrm{o}}\kappa$ where $a_{\mathrm{o}}$ is the Bohr radius. Blue and purple lines depict standard radial integrals $\langle j_0\left(\kappa \right)\rangle$ and $\langle j_2\left(\kappa \right)\rangle$ that occur in the axial dipole Eq. (4). Red, green, and blue curves are the radial integrals in the polar dipole Eq. (5). Two integrals ($g_1$) and ($j_0$) diverge in the forward direction of scattering and $w\left(g_1\right)$ and $w\left(j_0\right)$ are displayed. Calculations using Cowan's atomic code [16] and figure by G. van der Laan.