Fig. 2. Direct detection of the charge quadrupolar, structural and magnetic order parameters in BMRO.

a REXS experimental setup in the $\sigma \to {\pi }^{\prime }$ scattering channel. The ψ₀ (ψ₉₀) orientation corresponds to the configuration where the crystal c axis points perpendicular (within) the vertical scattering plane. b, c Energy dependence of the Q = (5, 5, 0) Bragg reflection with the ψ₀ and ψ₉₀ crystal orientations, at various temperatures. d Azimuthal dependence of the (5, 5, 0) reflection at E_q and at 20 K demonstrates the θ = x²−y² symmetry of the antiferroic quadrupolar $q_{\theta }^{\left[001\right]}$ order. The dashed (dotted) lines depict the calculated azimuthal dependence of the quadrupoles with xy,z² (xz,yz) symmetry. e Integrated intensity of the (5, 5, 0) peak at the magnetic resonance E_m and ψ₀ azimuth indicates the onset of the antiferroic $m_{xy}^{\left[001\right]}$ order of Re magnetic dipoles below 18 K. f, g Integrated intensity of the (5, 5, 0) and (5, 3, 0) peaks measured at E_q and off-resonance, respectively, to detect the antiferroic $q_{x^2-y^2}^{\left[001\right]}$ and $d_{x^2-y^2}^{\left[001\right]}$ orders. h The (10, 0, 0) peak measured at E_q resonance which is indicative of the ferroic $q_{z^2}^{\left[000\right]}$ order. i The γ splitting of the (10,0,0) reflection to reflect the ordering of $d_{z^2}^{\left[000\right]}$. The error bars correspond to the standard deviation.