Quartz-based flat-crystal resonant inelastic x-ray scattering spectrometer with sub-10 meV energy resolution

Continued improvement of the energy resolution of resonant inelastic x-ray scattering (RIXS) spectrometers is crucial for fulfilling the potential of this technique in the study of electron dynamics in materials of fundamental and technological importance. In particular, RIXS is the only alternative tool to inelastic neutron scattering capable of providing fully momentum resolved information on dynamic spin structures of magnetic materials, but is limited to systems whose magnetic excitation energy scales are comparable to the energy resolution. The state-of-the-art spherical diced crystal analyzer optics provides energy resolution as good as 25 meV but has already reached its theoretical limit. Here, we demonstrate a novel sub-10 meV RIXS spectrometer based on flat-crystal optics at the Ir-L3 absorption edge (11.215 keV) that achieves an analyzer energy resolution of 3.9 meV, very close to the theoretical value of 3.7 meV. In addition, the new spectrometer allows efficient polarization analysis without loss of energy resolution. The performance of the instrument is demonstrated using longitudinal acoustical and optical phonons in diamond, and magnon in Sr3Ir2O7. The novel sub-10 meV RIXS spectrometer thus provides a window into magnetic materials with small energy scales.


Supplementary Figures
Supplementary Figure 1| Installed flat-crystal RIXS spectrometer. The flat-crystal analyzer system is installed on a 6-circle RIXS spectrometer at the sector 27-ID-B at the advanced photon source (APS). Plexiglass box is filled with a helium atmosphere to improve thermal stability and reduce air scattering and absorption. The center of the Montel mirror is located at a distance of 200 mm from the sample as designed. The center of the C-crystal is positioned at around 500 mm downstream to a collision with the Montel mirror and the existing RIXS spectrometer. The A-crystal is placed at a distance of about 1000 mm from the C-crystal to secure a proper space for the detector which is positioned below the C-cryatal and collects the reflected beam from the Acrystal. In this figure, the polarizer (P-crystal) is not shown.

Supplementary Tables
Supplementary Table 1| Configuration

Supplementary Notes Supplementary Note 1| Simulations
In designing the flat-crystal analyzer system, care was taken to maximize the incident solid-angle acceptance for scattered radiation emanating from the sample, while optimizing the throughput for all optical components (crystals, multilayer mirror), maintaining the best energy resolution and provide efficient polarization analysis without sacrificing any resolution. This was accomplished by carefully selecting suitable crystal reflection and asymmetry angles. Mathematica 11" computing environment, using subroutines that implement pertinent dynamical diffraction formulas. An example is shown below in Supplementary Fig. 2.

Multilayer Mirror
The incident radiation was modelled as a double-Gaussian, representing the energy band pass of the high-resolution monochromator along the energy axis and the emittance of the multilayer mirror along the angular axis. In the present case, two successive double-bounce, monolithic Si(844) channel-cut crystals were employed as high-resolution monochromator. The resulting energy bandpass is 8.9 meV, determined by a simulation based on dynamic diffraction theor. The multilayer mirror was designed to collimate incident scattered radiation to within 100 µrad in the vertical plane 3 .
Comparing measurements with simulations, an actual emittance of 92 µrad was determined. The incident beam is shown in Supplementary Fig. 2a.

Supplementary Note 3| Collimator Crystal
For the collimator (C-crystal), a low-order, asymmetric Si reflection was chosen in order to be able to match its angular acceptance to the emittance of the preceding multilayer mirror, while maximizing the degree of collimation and the throughput. An asymmetric Si(111) crystal with an angle of 8.95º between its surface and the diffraction planes, corresponding to an asymmetry factor of b=-0.0642, provided a well matched acceptance of 95 µrad. With the prevailing b-factor, a degree of collimation by 15.6-times was reached, resulting in an angular emission of 6 µrad. The acceptance of the C-crystal is shown in Supplementary Fig. 2b., resulting in the combined acceptance shown in Supplementary Fig. 2c, when merged with the incident beam. The asymmetric transformation leads to an emission from the C-crystal shown in Supplementary Fig. 2d, where the angular extension is now reduced 15.6-times (note the contracted angular scale in Supplementary Fig. 2c), while conditions along the energy axis are unaffected.

Supplementary Note 4| Analyzer Crystal
In order to attain the best energy-resolution, a crystal reflection at near-backscattering conditions at the incident energy associated with the Ir L3 absorption edge, 11.215 keV was required. While the more commonly used Si(844) reflection has an intrinsic angular width of 17.4 µrad, corresponding to and intrinsic energy width of 14.6 meV, the availability of near-ideal crystals of α-quartz allowed for a choice of even higher resolution. Quartz(309) has an intrinsic angular width of 11.5 µrad, however, at a Bragg angle of 88.6º, much closer to back-scattering than Si(844), this angular width corresponds to an intrinsic energy width of only 3.7 meV. Moreover, the angular acceptance is more than adequate to accommodate the full beam from the collimator, thus, a symmetric quartz(309) crystal was implemented as the analyzer (A-crystal).
Supplementary Fig. 2e shows the acceptance of the A-crystal in blue, crossing the emission from the collimator and resulting in the A-crystal emission shown in Supplementary Fig. 2f with an intrinsic energy width of 3.9 meV.

Supplementary Note 5| Polarizer Crystal
For the polarizer (P-crystal) to function it needs to have a Bragg angle of close to 45º.
At an energy of 11.215 keV, Si(444) has a Bragg angle of 44.8 º, and is therefore suitable as a polarizer. However, with an angular acceptance of the symmetric Si(444) reflection of only 4.8 µrad, an asymmetric crystal with a b-factor of at least -0.6 is desirable to capture the full beam from the analyzer. Nevertheless, due to availability reason, a symmetric Si(844) crystal was used as a polarizer in the present initial implementation of the spectrometer. The polarizer acceptance is shown in Supplementary Fig. 2g and the resultant emittance is shown in Supplementary Fig. 2h.

Supplementary Note 6| Rocking Curve and Incident Energy Scans.
Rocking curve scans are a useful tool for judging the quality and strain-free mount of a crystal. In simulating rocking curve scans, the acceptance of the crystal in question is translated along the angular axis, traversing the emittance of the preceding optical system. For every point a convolution of acceptance and emittance is performed. Supplementary Fig. 3a, 3b, and 3c show angular rocking curve scans obtained for the C-crystal, A-crystal, and P-crystal polarizer, respectively. For an incident energy scan in Supplementary Fig. 3d , the incident beam profile is translated along the energy axis, keeping the acceptance of the Montel mirror and successive reflectivities static.