Optical Activity (OA) which is a consequence of spatial dispersion is to be commonly described with a third rank tensor. Decomposing the latter tensor into irreducible representations invariant under the symmetry operations of the rotation group O(3) yields a pseudo-scalar, a polar vector and a pseudo-deviator. The pseudo-scalar term exists only for enantiomorphous systems that exhibit OA at optical wavelength. Unfortunately, OA associated with the pseudo-scalar term becomes vanishingly small in the X-ray range. Crystals which admit a pseudo-deviator as rotational invariant were shown to be those which exhibit X-ray natural circular dichroism (XNCD) [1].

Surprisingly, crystals in which the OA tensor has only an irreducible part that transforms as a polar vector in O(3) will exhibit neither enantiomorphism nor natural circular dichroism.

In 1905, Voigt was the first to try to detect the vector part of OA: his idea was that, in crystals of suitable symmetry, a linearly-polarised incident light could be reflected as an elliptically polarised light [2]. The first successful experiment was reported only in 1978, by Ivchenko et al. [3], who looked for OA at the exciton resonances in a hexagonal CdS crystal. In 1990, Graham and Raab [4] suggested that the most appropriate experiment to measure the vector part of OA in 6 mm crystals is circular dichroism in reflectivity when the optical c axis is perpendicular to the reflection plane and when the angle of incidence Q is close to 45°. Unfortunately, specular reflectivity of X-rays cannot be used for such measurements because the off-diagonal terms responsible for OA vanish at glancing angles. However, we suggested that the vector part of OA could still be measured in the X-ray resonant diffraction regime using circularly-polarised X-rays at Bragg angles near 45° for which the crystal will act as a linear polarimeter.

Our first experiment has been performed at beamline ID12 using a UHV compatible reflectometer/diffractometer featuring excellent mechanical reliability and a high reproducibility. For this challenging experiment we selected a high-quality ZnO single crystal with hexagonal symmetry (Würtzite structure). This crystal exhibits a strong (300) reflection characterised by a Bragg angle varying from 43.13° to 42.69° over the whole Zn K-edge XANES range (9655-9735 eV). A major experimental difficulty arose from the imperfect polarisation transfer function of the double crystal monochromator that resulted in the existence of an unwanted Stokes-Poincare component P2 (even though very small: 1.95% at 9.7 keV) which also changes the sign when the helicity of the incident photons is reversed.

The results of this delicate experiment are displayed in Figure 111. A typical Zn K-edge DANES (diffraction anomalous near edge structures) spectrum of our ZnO single crystal (c axis perpendicular to the scattering plane) is reproduced in Figure 111a. in which we plotted the integrated area below the (300) diffraction peak as a function of the incident photon energy. The circular dichroism spectra shown in Figure 111b. were obtained as a direct difference of the DANES spectra for left- and right-circularly polarised incident X-ray photons. Graham and Raab [4] pointed out that the sign of the circular dichroism should be reversed if the crystal were rotated by 180°, i.e. when the angle between the c axis of the crystal and reflection plane changed from +90° to –90°. This is precisely what we have observed, as illustrated by Figure 111b. Note that such a 180° rotation should leave the unwanted linear dichroism unchanged provided that the diffraction planes are perpendicular to the rotation axis. The sum of two circular dichroism spectra should reproduce the X-ray linear dichroism (XLD) due to the small P2 polarisation component in the monochromatic beam. As shown in Figure 111c. the spectral shape of this residual signal perfectly reproduces the XLD spectrum measured simultaneously in the total fluorescence yield detection mode.

Fig. 111: XNCD in the Zn K-edge DANES spectra of ZnO (300) single crystal: a) A polarisation averaged DANES spectrum. b) circular dichroism DANES spectra for two orientations of the crystal. c) Comparison of the residual signal with XLD spectrum.

 

This is the first example of X-ray circular dichroism measured in the DANES regime using a non-centrosymmetric single crystal. This experiment clearly establishes the possibility to unravel the vector part of optical activity in the X-ray range. We have also shown that the effective operator responsible for the vector part of OA can be assigned to the vector product L x L– L x L n, in which L and L are time-reversal odd operators associated with the orbital angular momentum and the orbital anapole respectively, whereas n is a true time-reversal even electric dipole. This observation is consistent with the pyroelectric properties of zincite crystals. Given that ZnO belongs to a very important class of semiconducting materials, we expect this pioneering experiment to open a completely new field of applications for X-ray optical activity.

 

References

[1] J. Goulon et al., J. Exp.Theor. Phys. 97, 402 (2003).
[2] W. Voigt, Ann. Phys.(Leipzig) 18, 651 (1905).
[3] E.L. Ivchenko et al., Sol. State Comm. 28, 345 (1978).
[4] E.B. Graham and R.E. Raab, Proc. R. Soc. A 430, 593 (1990).

Principal publication and authors

J. Goulon (a), N. Jaouen (a), A. Rogalev (a), F. Wilhelm (a), C. Goulon-Ginet (a), C. Brouder (b), Y. Joly (c), E.N. Ovchinnikova (d) and V.E. Dmitrienko (e), J. Phys.: Condens. Matter 19, 156201 (2007).
(a) ESRF
(b) Institut de Minéralogie et de Physique des Milieux Condensés, Universités Paris-VI et VII (France)
(c) Institut Néel, CNRS, Associé à l’Université J Fourier, Grenoble (France)
(d) Physics Department of Moscow State University (Russia)
(e) Institute of Crystallography, Moscow (Russia)