Page 23 - ILL Annual Report 2019

SCIENTIFIC HIGHLIGHTS
20-21
Basis-forbidden Bragg spots in diamond-type structures have been painstakingly investigated for almost a century because they offer valuable information about the valence–electron distribution (the (2, 2, 2) reflection was studied by W.H. Bragg, 1921). Participating electrons possess opposing parities because sites in the primitive cell are related by point inversion. Equivalent magnetic Bragg spots yield unique information on Dirac multipoles; the same type of information cannot be derived from NMR, NQR or muon spin-rotation experiments, for example.
Some Bragg spots in the diffraction pattern of SmAl2 are fundamentally the same as those observed in diffraction by Hg1201 [3]. Specifically, spots indexed by Miller indices obeying H + K + L = 4n + 2, with n as an integer, are due to Al nuclei alone. Consequently, below the magnetic phase transition a magnetic contribution
to a Bragg spot indexed by this condition must use unpaired electrons with opposite parities, e.g. Dirac multipoles created with Sm 4f and 5d electrons. The magnetic contribution in question was identified using polarisation analysis on the instrument D3. The motif of magnetic dipoles inferred from our diffraction patterns is displayed in figure 2.
Figure 1
Ferro-motif of Dirac quadrupoles in the Cu–O plane for Hg1201 in the pseudo-gap phase [3]. Arrows indicate spin (S) directions in Dirac quadrupoles 〈H 20 〉 ∝ 〈3Sz nz − S • n〉 and 〈H 2 〉′∝ 〈Sx nx − Sy ny〉, together with their response to space (n) or time inversion.
The basis is {(1, −1, 0), (1, 1, 0), (0, 0, 1)} with respect to the tetragonal parent P4/mmm labelled (x, y, z), and lobes of 〈H 2 〉′ are orientated at 45 ° with respect to cell edges.
Figure 2
Magnetic dipoles for magnetisation parallel to [1, 1, 0] in SmAl2 using a magnetic space-group Imm'a' (#74.559). Cubic parent cell outlined in black, and orthorhombic magnetic cell (ξ, η, ζ) with ξ = (1/2, 1/2, 0), η = (1/2, −1/2, 0),
ζ = (0, 0, −1) outlined in yellow. Green arrows are axial dipoles (L + 2S) parallel to the ξ axis, while blue and red arrows that lie along the η axis denote anapoles related by point inversion.
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