Nuclear resonant scattering from 193Ir as a probe of the electronic and magnetic properties of iridates

The high brilliance of modern synchrotron radiation sources facilitates experiments with high-energy x-rays across a range of disciplines, including the study of the electronic and magnetic correlations using elastic and inelastic scattering techniques. Here we report on Nuclear Resonance Scattering at the 73 keV nuclear level in 193Ir. The transitions between the hyperfine split levels show an untypically high E2/M1 multi-polarity mixing ratio combined with an increased sensitivity to certain changes in the hyperfine field direction compared to non-mixing transitions. The method opens a new way for probing local magnetic and electronic properties of correlated materials containing iridium and provides novel insights into anisotropic magnetism in iridates. In particular, unexpected out-of-plane components of magnetic hyperfine fields and non-zero electric field gradients in Sr2IrO4 have been detected and attributed to the strong spin-orbit interaction in this iridate. Due to the high, 62% natural abundance of the 193Ir isotope, no isotopic enrichment of the samples is required, qualifying the method for a broad range of applications.


Sensitivity of NRS to the Direction of Magnetic Hyperfine Fields in Iridates
Nuclear multipole transitions are excited selectively, depending on the direction of the γ radiation with respect to the quantization axis defined by the hyperfine fields, and on the change ∆m of the magnetic quantum numbers of the hyperfine levels involved in the transition. Synchrotron radiation is polarized, in the standard notation it's called σ polarization. This gives additional information in NFS since γ radiation from nuclear transitions is polarized, as well, rendering NFS sensitive to the orientation of hyperfine fields 1 . For instance, if B h f is parallel to the wave vector k, the eigenpolarizations of the nuclear transitions are left and right circular, resp., and a two line beating pattern with reduced quantum beat contrast is observed, see Fig. S1 first row, in this case M1/E2 and pure M1 radiation show the same behaviour.
For magnetic hyperfine fields in the plane orthogonal to the beam direction the linear eigenpolarizations are σ and π. When the hyperfine field is aligned parallel to the σ -polarization of synchrotron radiation, in case of pure M1 transitions, only the ∆m = ±1 transitions are excited, which results in a 4 line beating pattern 1 . For the mixed M1/E2 transitions of 193 Ir one gets an unexpected 2 line beating pattern, see Fig. S1, 2nd row. This is due to the E2/M1 mixing parameter, which has a value of -0.577 2 for 193 Ir. This value is "accidentally" close to − 1/3 which leads to a cancelling of specific M1 and E2 transition amplitudes.
In case of a hyperfine field aligned perpendicular to the σ -polarization and the k vector of synchrotron radiation, there is no such cancelling of transitions and the mixed M1/E2 transitions exhibit a 4 line beating pattern, see Fig. S1, 3rd row. Fig. S2 shows NFS energy and time spectra for different orientations of the magnetic hyperfine field relative to the wavevector and σ polarization of the exciting radiation for antiferromagnetic ordering. As compared to the pure M1 transition, where alignment of B h f parallel to k and parallel to the σ polarization yield the same time patterns (Ref. 1 and Fig. S3), for mixed M1/E2 transitions these two field geometries can be distinguished. This benefit from the mixed M1/E2 transition is shown in Fig. S3 in more detail. There is an angular dependence on the hyperfine field direction, if in antiferromagnetic spin arrangement the magnetization is rotated in the k − σ plane, Fig. S3 middle column. In the pure M1 case, shown for the 57 Fe resonance in the right column, the different orientations exhibit exactly the same quantum beat pattern. Hence, one essential feature of NFS at the 73 keV resonance in 193 Ir is the pronounced sensitivity to the tilt of the hyperfine fields from the basal plane (plane determined by σ -and π-polarization of the synchrotron radiation in the experimental setup).

Design of the Two-Crystal Silicon X-ray Filter
In order to prevent the detector from overloading the photon intensity has to be reduced to a certain level. This is achieved by decreasing the bandwidth around the nuclear resonant photon energy using a medium resolution monochromator or x-ray filter. The design of the x-ray filter is similar to that implemented for the NRS studies at the 67 keV resonance in 61 Ni 3 . The device includes two Si crystals with asymmetric Bragg reflections (Table1 and Fig. S4). A tight fixation does induce a curvature of the crystals, the effect is significant even for thick crystals, as mentioned in Ref. 3 . In the present work the crystals were placed onto the holders, without squeezing, thus, the mounting prevented curvature of the crystals.

Fast APD Detector Array
The coherent NRS has been detected by a multi-element array detector built by ATIM Radiocommunications (France) 4 with 16 fast, 30 µm thin APDs S5344 from Hamamatsu Photonics (Fig. S5). For an overview on APD detectors see e.g. 5 . The diameter of each APD was 3 mm and the whole beam was accepted by the detector. The single APDs have been stacked and inclined to an angle of about 3 o relative to the incident beam in order to increase detection efficiency for 73 keV photons to about 9%.  The crucible was cooled inside the furnace to near room temperature in around 6 hours before being removed from the furnace. The crystals were removed from the matrix by sonication in warm water and were further cleaned in ethanol.

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All crystals exhibit the form of platelets with (0 0 1) planes being parallel to the largest surface areas. The thickness of the crystals was about 30-70 µm and the lateral size was about 2x3 mm 2 .
The orientation of the crystals was carried out using Raman spectroscopy with a 532 nm laser. Particularly, the Raman signal intensity from the B 2g mode (380 cm −1 ) was measured owing to that it is maximal if the polarization of the incident laser beam is parallel to the [1 1 0] direction in Sr 2 IrO 4 (Fig. S6). Assembling the sample stack under the microscope, each crystal was carefully pushed by tweezers along optical axis and the change of the focus distance was measured. Knowing the length of each crystal and change of focus depth, the deviation angle from ideally parallel crystal stacking was estimated to be about 2 to 8 o . The crystals have been stacked along the beam so that the (0 0 1) plane in Sr 2 IrO 4 was perpendicular to the incident beam