Resonant x-ray scattering investigation of the multipolar ordering in ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$

We have performed a resonant x-ray scattering (RXS) study near the $\text{Co}K$ edge on a single crystal of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$. In the magnetically ordered phase a new class of weak reflections appears at the magnetic propagation vector $\vec{\tau }\simeq \left(\frac{1}{3},\frac{1}{3},\frac{1}{3}\right)$. These new reflections allow direct access to the dipolar-quadrupolar $E_1{E}_2$ scattering channel. The theoretical possibility of observing isolated $E_1{E}_2$ electromagnetic multipoles has attracted a lot of interest in recent years. Unfortunately in many systems of interest, parity even and parity odd tensor contributions occur at the same positions in reciprocal space. We demonstrate that in ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ it is possible to completely separate the parity even from the parity odd terms. The possibility of observing such terms even in globally centrosymmetric systems using RXS has been investigated theoretically; ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ allows a symmetry based separation of this contribution.

Figure 1

(Color online) Schematic of the unit cell of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$. The trigonal prisms are shown in light blue (dark gray) and the octahedra in yellow (light gray). The magnetic moments are also drawn.

Figure 2

(Color online) The intensity versus photon-energy dependence around the $\text{Co}K$ absorption edge of an $E_1{E}_1$ (top) and an $E_1{E}_2$ (bottom) magnetic reflection. The data were collected in the $\sigma \pi$ channel.

Figure 3

(Color online) Comparison of the temperature dependence of two reflections due to different scattering processes. The lines are a guide for the eye. While the general behavior is similar, the intensity of the $E_1{E}_2$ reflection (circles) increases more slowly immediately below the ordering temperature than the signal due to $E_1{E}_1$ (squares).

Figure 4

(Color online) Theoretical and experimental azimuthal dependence of three magnetic reflections at the $\text{Co}K$ absorption edge. In the first panel a $E_1{E}_1$ reflection is reported, whereas the central and bottom panels show reflections resulting from the $E_1{E}_2$ interference together with the model predictions. The amplitude is the only free parameter in the fit.