Tables for
Volume I
X-ray absorption spectroscopy and related techniques
Edited by C. T. Chantler, F. Boscherini and B. Bunker

International Tables for Crystallography (2023). Vol. I. Early view chapter

Control of X-ray polarization

Motohiro Suzukia*

aKwansei Gakuin University, 1 Gakuen Uegahara, Sanda, Hyogo 669-1330, Japan
Correspondence e-mail:

Synchrotron X-ray radiation is intrinsically polarized, with a nearly perfect degree of polarization. The polarized X-ray beam has been an essential probe for studying the anisotropy of crystal structures and electronic states, as well as the magnetic and chiral natures of matter. Absorption spectroscopy using circularly polarized X-rays offers a unique opportunity to investigate the origin of magnetic properties by X-ray magnetic circular dichroism (XMCD) effects with element sensitivity and orbital selectivity. This chapter describes techniques for controlling X-ray polarization states for X-ray absorption spectroscopy. A particular emphasis is placed on methods of generating circular polarization in XMCD spectroscopy experiments using crystal phase plates and special insertion devices.

Keywords: X-ray polarization; crystal phase plates; insertion devices; X-ray absorption spectroscopy.

1. Introduction

A polarized X-ray beam is a direct probe that is used to study the anisotropic nature of atomic structures and electronic states, as well as the magnetic properties of matter. In particular, the utilization of circularly polarized X-rays has significantly extended the power of absorption spectroscopy. X-ray magnetic circular dichroism (XMCD; Schütz et al., 1987[link]; Chen et al., 1990[link]) is a unique technique for exploring the microscopic origin of magnetism using the element and orbital specificities. In addition, polarization control and analysis are essential techniques for resonant/nonresonant X-ray scattering (Blume & Gibbs, 1988[link]; Murakami et al., 1998[link]). These polarization-dependent experiments require a high degree of polarization and full control of the X-ray polarization states.

In the 1980s, during the early development of polarization-dependent X-ray spectroscopy, researchers used bending-magnet radiation extracted from the upper or lower plane of the electron orbit as an elliptically polarized source. However, the X-ray beams obtained using this technique tended to be less intense and had a low degree of circular polarization PC with fixed helicity1. More sophisticated techniques were developed in order to yield full and highly efficient control of the X-ray polarization states. In particular, the ability to rapidly switch X-ray photon helicity has benefited from the detection of small dichroic effects in the hard X-ray region. This advance occurred immediately prior to the advent of third-generation synchrotron-radiation facilities. Crystal phase-plate optics were one such development, while another was the design of insertion devices that emit elliptically or circularly polarized X-rays. Both of these device designs have successfully been implemented at third-generation facilities. As a result, these developments have significantly improved the quality of data obtained from polarization-dependent X-ray spectroscopy and scattering experiments.

In this section, techniques for controlling X-ray polarization states for X-ray absorption spectroscopy are introduced. Particular emphasis is placed on methods of generating circular polarization in XMCD experiments using crystal phase plates and insertion devices.

2. Crystal phase plates

2.1. Principles

Crystal X-ray phase plates (Skalicky & Malgrange, 1972[link]; Annaka, 1982[link]; Golovchenko et al., 1986[link]; Mills, 1987[link]; Belyakov & Dmitrienko, 1989[link]; Hirano et al., 1991[link]) are the most popular optics components for polarization control in the hard X-ray region. This particular crystal optics setup has several advantages over helical undulators: (i) faster switching of photon helicities, (ii) a variety of polarization states (horizontal/vertical linear polarization is available in addition to right/left circular polarization), (iii) no depolarization effects from other optics components such as crystal monochromators and (iv) no influence on the electron orbit and X-ray beam path at other beamlines.

The polarization state conversion is based on X-ray bi­refringence due to dynamical multiple diffraction (Batterman & Cole, 1964[link]; Ishikawa & Kohra, 1991[link]), which occurs under conditions close to the diffraction conditions of a so-called perfect crystal, such as silicon, germanium or diamond. Extensive studies employing several different materials and geometries (reflection, transmission, Bragg, Laue and so on) have concluded that the use of a light element in transmission Laue or transmission Bragg geometry is the most efficient method of controlling the X-ray polarization states (Hirano et al., 1993[link]). As synthetic diamond crystals are the most suitable material for this technique, they are typically employed (Sumiya & Tamasaku, 2012[link]).

A crystal phase plate functions as a quarter-wave plate that converts horizontally polarized X-rays from a bending magnet or planar undulator to circularly polarized rays. Fig. 1[link] shows a typical scheme of a crystal X-ray phase plate in transmission geometry using a symmetric Laue reflection. A diamond crystal in (111) orientation is mounted on a rotation stage with the axis tilted by 45° such that the (220) diffraction plane is also tilted. An incident electromagnetic wave with horizontal polarization can be decomposed into σ and π polarization components with respect to the diffraction plane, which have the same amplitude and are oscillating in phase. The diffracted X-ray beam is monitored in order to determine the Bragg condition of the (220) reflection. The transmitted beam (forward diffraction) is used as a variably polarized X-ray.

[Figure 1]

Figure 1

Schematic of a crystal X-ray phase plate in transmission Laue geometry.

According to the dynamical theory of diffraction, the phase retardation between the σ and π components generated by a crystal of thickness t is given by (Giles et al., 1994[link]) [\delta = -{{\pi} \over {2}} \left[ {{r_{\rm e}^{2}{\rm Re}(F_{h}F_{\bar{h}})} \over {\pi^{2}V^{2}}} {{\lambda^3\sin 2\theta_{\rm B}} \over {\Delta\theta}} \right] {{t} \over {\cos\theta}} = -{{\pi} \over {2}} {{At} \over {\Delta\theta}},\eqno (1)]where re is the classical electron radius, Fh and [F_{\bar{h}}] are the structure factors of the hkl and hkl reflections, respectively, V is the unit-cell volume, λ is the X-ray wavelength, θB is the Bragg angle and [A = r_{\rm e}^{2}{\rm Re}(F_{h}F_{\bar{h}})\lambda^{3}\sin 2\theta_{\rm B}/{\pi^{2}V^{2}}\cos\theta]. Further, note that δ is a function of the angular offset Δθ = θθB. Fig. 2[link] plots δ versus Δθ for values calculated for a diamond crystal with t = 0.5 mm at a photon energy of 7.0 keV, where At = 80.4 arcsec. The incoming horizontal polarization can be converted to circular polarization with positive helicity at Δθ = At, at which the crystal generates a retardation of δ = −π/2. The helicity of the circular polarization can be reversed by changing the sign of the offset angle, i.e. Δθ = −At. The crystal angular motion required to reverse the helicity is very small, typically being a few tens of arcseconds (∼0.01°). Note that fast switching of photon helicities has previously been achieved at 100 Hz through the use of a piezo actuator (Hirano et al., 1992[link]) and at frequencies of up to 2 kHz using a galvano scanner (Suzuki et al., 2003[link]).

[Figure 2]

Figure 2

Phase shift δ and degree of circular polarization PC as functions of the offset angle Δθ calculated for a diamond crystal with 0.5 mm thickness at 7.0 keV. For these plots, the energy band width ΔE/E = 1.3 × 10−4 of a Si(111) monochromator is assumed. δ and PC will be impacted by the energy and angular spread of the radiation incoming on the crystal, both of which will reduce PC from ideal values.

The crystal can also function as a half-wave plate, rotating the linear polarization direction from horizontal to vertical. This rotation is achieved by tuning the offset angle to Δθ = ±At/2 so as to yield a phase shift of δ = ∓π. This feature is particularly useful for examining the polarization dependence of the X-ray absorption fine structure (XAFS) at a liquid surface and for polarized hard X-ray photoemission spectroscopy (HAXPES). It should be noted that with the use of a crystal half-wave plate, the degree of vertical polarization, PL = (IHIV)/(IH + IV), where IH and IV are the intensities of the horizontal and vertical polarization components, respectively, is typically not very high ([|P_{\rm L}|\,\lesssim \,80\%]) due to the beam divergence and energy spread.

2.2. Performance

PC is determined using δ and the transmitted amplitudes of the σ and π polarizations, Eσ and Eπ, respectively, according to [P_{\rm C} = -{{2E_{\sigma}E_{\pi}} \over {|E_{\sigma}|^{2}+|E_{\pi}|^{2}}}\sin\delta. \eqno (2)]For a perfect horizontally polarized beam incident on the phase-plate crystal with the 45° tilted diffraction plane, Eσ ≃ Eπ and thus PC ≃ −sinδ. The transmittance of the crystal in a symmetric Laue geometry is given by [T = \exp(-\mu t/\cos\theta),]where μ is the linear absorption coefficient of diamond. The figure of merit is then given by [P_{\rm C}^{2}T].

The polarization conversion efficiency is maximized for a parallel and monochromatic incident X-ray beam. The combination of a modern undulator source and a Si(111) double-crystal monochromator yields a desirable X-ray beam for a crystal phase plate that allows excellent performance. A high PC (>0.95) and a reasonable T (0.25–0.5) can practically be obtained using a diamond crystal with t equal to a few hundred micrometres at photon energies of 5–10 keV. Fig. 3[link] shows the calculated performance for diamond phase plates with different t values and geometries. In practical use, the available X-ray energy range for a diamond phase plate is between 3.3 and 20 keV. The lowest energy limit is determined by the small lattice constant of diamond and the absorption losses, although a high-quality thin diamond crystal of 50 µm thickness is currently available. Ultrathin silicon crystals can be used as phase plates to cover X-ray energies between 2.4 and 3.2 keV (Bouchenoire et al., 2012[link]). The use of phase plates in this energy range is of great advantage over the use of helical undulators since the degree of circular polarization produced by a helical undulator is degraded by the Si(111) monochromator working as a linear polarizer around 2.8 keV, at which the Bragg angle is close to 45°. The higher energy side is primarily determined by the size of the available crystals. The use of a diamond phase plate at higher X-ray energies requires a thicker crystal. The effects of the degradation induced by the energy spread and angular divergence are stronger at higher energies, and a thicker crystal is required in order to eliminate this influence. To improve the polarization conversion efficiency and the controllability of the polarization states, a method involving the combination of multiple diamond crystals has been proposed (Okitsu et al., 2002[link]).

[Figure 3]

Figure 3

Calculated performance of diamond phase plates for different crystal thicknesses t and geometries: t = 0.1 mm for (111) Laue diffraction (thin solid line) and t = 0.5 and 1.5 mm for (220) Laue diffraction (thick solid and dashed lines, respectively). (a) Degree of circular polarization PC, (b) transmittance T and (c) figure of merit [P^2_{\rm C} T] as functions of X-ray energy. The calculation assumes a relative band width ΔE/E = 1.3 × 10−4, corresponding to a Si(111) monochromator.

2.3. Application to XMCD spectroscopy

Giles and coworkers performed the first XMCD measurements using a diamond phase plate with a polychromator in the energy-dispersive mode (Giles et al., 1994[link]). The angle of the crystal phase plate was essentially fixed, but was optimized so as to yield appropriate phase retardation for divergent and polychromatic X-ray beams to cover the X-ray absorption edge simultaneously. This skilfully established setup enabled energy-dispersive XMCD measurements, which are particularly useful for both time-resolved XMCD analyses and XMCD spectroscopy conducted under high pressure using a diamond anvil cell (Torchio et al., 2014[link]).

In another energy-scanning mode, a crystal phase plate is combined with a silicon double-crystal monochromator (Hirano & Maruyama, 1997[link]). The angle of the phase plate crystal is tuned to follow the X-ray energy scanning at every energy point of the spectrum and therefore magnetic extended X-ray absorption fine-structure (EXAFS) measurements over a wide energy range have become feasible (Suzuki et al., 2001[link]). In the energy-scanning mode, the helicity-modulation (lock-in detection) technique can be employed to significantly improve the signal-to-noise ratio of the XMCD measurements (Suzuki et al., 1998[link]). XMCD signals as small as ∼10−5, which correspond to a paramagnetic moment of ∼10−4μB per atom in bulk gold, have been detected using this technique (Suzuki et al., 2012[link]). In addition to the XMCD applications, diamond X-ray phase plates have facilitated the development of polarization-dependent HAXPES (Ueda et al., 2008[link]; Ouardi et al., 2011[link]).

3. Helical undulators and special insertion devices

Another principal technique to obtain circularly polarized X-rays is the use of specially designed insertion devices. Helical undulators generate brilliant and intense circular polarization in a wide energy range between the soft and hard X-ray regions (Rogalev & Wilhelm, 2015[link]). These devices are particularly useful for XMCD spectroscopy in the soft X-ray region below 2 keV, where efficient phase-plate optics are not available. Note that in the initial XMCD experiments conducted at second-generation synchrotron-radiation facilities, elliptical multipole wigglers (Yamamoto et al., 1989[link]) were used. These devices provide elliptical polarization with a moderate degree of circular polarization over a wide energy range from the soft to the extremely hard X-ray region. For higher brilliance, many kinds of undulator devices equipped with polarization-state control functionality have since been developed (Elleaume, 1994[link]; Hara et al., 1998[link]; Kimura et al., 1998[link]). Among them, the most popular device is the APPLE-II helical undulator (Sasaki et al., 1993[link]), which in principle can provide photons in any polarization state. Thus, APPLE-II undulators have been used as standard insertion devices on many beamlines, which exploit the resultant polarization properties.

The helicities of all of the insertion devices mentioned above can in principle be switched using the mechanical motion of magnetic arrays in a technique known as a phasing operation. However, the switching speed cannot exceed a maximum value of 0.1 Hz (Agui et al., 2001[link]). In order to increase the permissible switching speed, an elliptical multipole wiggler equipped with electromagnets is employed, which facilitates photon-helicity switching at 22 Hz (Sánchez-Hanke et al., 2009[link]). Another method of rapidly switching helicity is based on twin helical undulators combined with five kicker magnets, which facilitate helicity switching with a frequency of up to 10 Hz (Shirasawa et al., 2004[link]). Further, segmented cross undulators with electromagnet phase shifters have been developed which enable helicity switching at up to 30 Hz (Yamamoto et al., 2014[link]). Finally, a helicity-modulation technique with lock-in detection has been performed in which these devices were used to improve the XMCD measurement accuracy in the soft X-ray region (Muro et al., 2005[link]; Sánchez-Hanke et al., 2009[link]).

4. Summary and outlook

Crystal phase plates and helical undulators are established devices for the generation and control of circularly polarized X-rays, and are in practical use at several synchrotron-radiation facilities worldwide. For further development and applications of the crystal phase plate, which are urgently required, it is essential that the available X-ray energy range be extended below 3 keV and above 20 keV; this extension would be helpful for intensive studies of 4d and 5f systems. In addition, helicity switching in the kilohertz range has not yet been applied in practical XMCD measurements. Faster polarization switching will provide effective reduction of 1/f noise (where f is the frequency) using a lock-in technique. In situ or time-evolution XMCD spectroscopy in the millisecond regime would then be feasible. Moreover, polarization control of X-ray free-electron lasers (Suzuki et al., 2014[link]; Nuhn et al., 2013[link]) may facilitate the spectroscopic investigation of ultrafast phenomena involving changes in the electronic and magnetic structures of matter, which occur on picosecond to femto­second time scales.


The author would like to thank Takashi Tanaka of RIKEN SPring-8 Center for his helpful comments on the development of insertion devices.


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