"Conical spin order with chiral quadrupole helix in CsCuCl3"
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Hiroki Ueda, Elizabeth Skoropata, Max Burian, Victor Ukleev, Gerard Sylvester Perren, Ludmila Leroy, Julien Zaccaro, and Urs Staub
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Abstract: Here we report a resonant x-ray diffraction (RXD) study at the Cu L3 edge on the multichiral system CsCuCl3, exhibiting helical magnetic order in a chiral crystal structure. RXD is a powerful technique to disentangle electronic degrees of freedom due to its sensitivity to electric monopoles (charge), magnetic dipoles (spin), and electric quadrupoles (orbital). We characterize electric quadrupole moments around Cu ascribed to the unoccupied Cu 3d orbital, whose quantization axis is off the basal plane. Detailed investigation of magnetic
reflections reveals additional sinusoidal modulations along the principal axis superimposed on the reported helical structure, i.e., a longitudinal conical (helical-butterfly) structure. The out-of-plane modulations imply
significant spin-orbit interaction despite S = 1/2 of Cu2+.
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Figure 3: Resonant diffraction profiles; (a), (c) around the (002) reflection, where (a) was measured for the left-handed crystal (P6522) while (c) was measured for the right-handed crystal (P6122), and (b) around the (001) reflection. Note that (a), (b) were taken from sample 1 with the (001) surface, whereas (c) was taken from sample 2 with the (119) surface. Solid or broken curves are pseudo-Voigt-peak fits.

Figure 4: Photon-energy dependence of the resonantly-allowed reflections around the Cu L3 edge while maintaining a given diffraction
condition; (a) (001) and (b) (002) forbidden reflections due to electric quadrupole moments from a left-handed (P6522) crystal (sample 1) with
the (001) surface, and (c) (1/3 1/3 +δ) and (d) (1/3 1/3 1+δ) magnetic reflections from sample 3 with the (110) surface. (c), (d) were taken
below TN. A green curve in (a) is a Lorentzian fit to correct the self-absorption (see main text).

Figure 5: FIG. 5. Resonant diffraction profiles of magnetic reflections measured below TN: (a) (1/3 1/3 +δ) [G = 0 + k1], (b) (1/3 1/3 –δ)
[G = 0 + k2], (c) (1/3 1/3 1+δ) [G = 0 + 2k3 + k1], (d) (1/3 1/3 1–δ) [G = 0 + 2k3 + k2], and (e) (0 0 1/2) [G = 0 + k3]. For comparison,
a profile measured above TN with the π polarization is shown in (e) by a black broken line. The inset of (a) shows the diffraction
geometry, where q (q	) is the wave vector of an incident (scattered) x-ray beam and τ is the scattering vector. (f) Temperature dependence
of the (1/3 1/3 1–δ) reflection from sample 2 with the (119) surface. Red curve in (f) represents the power-law fit [∝ (TN–T )α], where α
(= 0.48 ± 0.03) is the critical exponent and TN is fixed to 10.7 K.