Conical spin order with chiral quadrupole helix in CsCuCl3

Here we report a resonant x-ray diffraction (RXD) study at the Cu L3 edge on the multi-chiral 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 Cu. † Present address: SwissFEL, Paul Scherrer Institute, 5232 Villigen-PSI, Switzerland. * To whom correspondence should be addressed: hiroki.ueda@psi.ch and urs.staub@psi.ch Magnetism and associated functionalities in non-centrosymmetric materials have attracted significant interest in the field of condensed matter physics. These interests lie, for example, in symmetry-protected spin textures, such as skyrmion lattices [Mühlbauer1] and chiral soliton lattices [Togawa1], and in non-reciprocal responses of quantum (quasi-)particles [Tokura1]. The low crystal symmetry is essential to stabilize a complex magnetic ground state with enriched properties due to additional interactions absent in centrosymmetric materials [Dzyaloshinsky1,Moriya1]. On the other hand, the low symmetry adds complexity in solving the magnetic ground state. Resonant x-ray diffraction (RXD) has been used to explore complex electronic ordered states, e.g., charge, magnetic, or orbital modulations, of which some show chiral orders [Gibbs1,Murakami1,Lang1,Tanaka1]. RXD is based on the anisotropic scattering of xrays at an atomic resonance, with contributions that are described by tensors up to the secondrank multipole moments 〈TQ K〉 (–K ≤ Q ≤ K), electric monopole (K = 0), magnetic dipole (K = 1), and electric quadrupole (K = 2) [Matteo1]. Here we restrict our interpretation to the electric dipole-electric dipole channel of scatterings, generally most relevant in RXD. An electric monopole corresponds to a charge (spherical electron density), a magnetic dipole corresponds to a magnetic moment, and an electric quadrupole corresponds to an aspheric electron density due to partial electron occupancy of orbital(s) and/or covalency. Therefore,