Page 45 - ILLS Annual Report 2018

SCIENTIFIC HIGHLIGHTS
42-43
corresponding to the M point of the Brillouin zone. This wave vector characterises a number of non-collinear multi-k magnetic structures predicted theoretically [2], and the observed extinction rule points to the octahedral structure. One particularity of this structure is that it is energetically degenerate with numerous coplanar and collinear magnetic structures. Indeed, subsequent neutron diffraction measurements performed at WISH, ISIS (UK) showed evidence of the coplanar ‘hexagonal’ magnetic structure illustrated in figure 1.
The measured spin-wave spectra shown in figure 2a are well reproduced by linear spin wave theory (figure 2b) using exchange between third-nearest neighbours only (J3 in figure 1), with all other interactions being at least one order of magnitude smaller. The intensity of these spin-wave excitations shows an unusual energy dependence, see figure 3, which can be explained by a small symmetric exchange anisotropy, less than 1 % of J3. This anisotropy creates a finite energy gap for one of the acoustic spin- wave branches leaving the other modes gapless, resulting in the strong spectral change. The presence of this weak exchange anisotropy also explains the selection of the coplanar hexagonal magnetic structure rather than the non-coplanar octahedral structure predicted for the isotropic Heisenberg case.
A particularity of the multi-k hexagonal structure we
observe in vesignieite is that it consists of three essentially decoupled lattices. In such a ‘decoupled’ multi-k structure, disordering one of the sites will have no effect on the magnetic order or magnetic excitations. This is exactly what happens in vesignieite. Orbital disorder on only one of the Cu sites, which occurs because of an inability to arrange the orbitals with threefold rotational symmetry around the kagome triangles, does not destroy the magnetic order. This effect is consistent with the observed multi-k magnetic structure, since the global trigonal symmetry of the P3121 space group of vesignieite is restored by the ‘deselection’ of different arms of the star of k in adjacent kagome layers.
Our results, in addition to being the first experimental observation of symmetric exchange anisotropy in a powder sample using inelastic neutron scattering, have implications well beyond kagome systems since the hexagonal structure of vesignieite can be thought of as three interlocked, skewed, square lattices.
Figure 2
a) Dynamic susceptibility of vesignieite at a temperature of T = 1.6 K measured on IN5 with Ei = 8.0 meV.
b) Calculated spin-wave dispersion using a J3-only model. Dashed white lines indicate the magnetic Bragg peak positions.
Figure 3
a) Dynamic susceptibility of vesignieite at T = 1.6 K measured on IN5 with
Ei = 1.9 meV.
b) Energy scan at constant Q = 0.65 ± 0.1 Å (symbols), plotted with spin-wave calculations for the hexagonal magnetic structure using isotropic exchange (green curve) and symmetric exchange anisotropy (blue curve).
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