⁵⁷Fe polarization-dependent synchrotron Mössbauer spectroscopy using a diamond phase plate and an iron borate nuclear Bragg monochromator

Energy-domain ⁵⁷Fe polarization-dependent synchrotron radiation Mössbauer spectroscopy was developed by using a diamond X-ray phase plate and an iron borate nuclear Bragg monochromator. The former controls the polarization of the incident synchrotron radiation X-rays and the latter filters the ⁵⁷Fe-Mössbauer radiation with a narrow bandwidth of ∼3.4 Γ₀ (Γ₀ ≃ 4.7 neV: natural linewidth of the ⁵⁷Fe nucleus) from the broadband synchrotron radiation. The developed nuclear diffraction optics allowed ⁵⁷Fe-Mössbauer studies to be performed with various polarization states, i.e. linear polarization, circular polarization and non-polarization. In this paper, the spectrometer system, beam characterization, performance-test experiments and a grazing-incidence Mössbauer measurement of an isotope-enriched (⁵⁷Fe: 95%) iron thin film are described.

1. Introduction

Mössbauer spectroscopy is a nuclear analytical technique based on the resonant recoil-free absorption and emission of γ-radiation by atomic nuclei bound in a solid, i.e. the Mössbauer effect (Mössbauer, 1958). The Mössbauer effect has been observed in approximately 100 nuclides of almost 50 elements. In particular, the most extensively studied isotope in Mössbauer spectroscopy is ⁵⁷Fe. ⁵⁷Fe-Mössbauer spectroscopy is a well established method for studying various iron-containing materials. Information on the local magnetic state, valence, electron density and electronic state anisotropy can be obtained through hyperfine interactions between the resonant nucleus and the surrounding electrons. In principle, the nuclear transition probability depends on the direction of the hyperfine magnetic field (H_hf) and the electronic field gradient at the resonant nucleus with respect to the polarization and the propagation vector of the incoming radiation. Hence, the Mössbauer studies using polarized radiation yield information not or barely obtainable using non-polarized radiation. For example, ⁵⁷Fe polarization-dependent Mössbauer spectroscopy allows a quick determination of the direction of H_hf at ⁵⁷Fe nuclei and gives a remarkable simplification of the spectral profile. The first study was conducted with a multi-line source (Frauenfelder et al., 1962). However, it is apparent that a well polarized single-line source is desirable to perform the Mössbauer study (Shtrikman, 1967; Shtrikman & Somekh, 1969). A large amount of work has already been undertaken to produce linearly or circularly polarized single-line ⁵⁷Fe-Mössbauer radiation, and a detailed review covering work up to 2006 has been given by Szymański (2006).

To perform a polarized ⁵⁷Fe-Mössbauer study, we can generally use two different photon sources, i.e. a conventional radioactive ⁵⁷Co source and a synchrotron radiation (SR) source. In the radioactive ⁵⁷Co source, the linearly or circularly polarized single-line ⁵⁷Fe-Mössbauer radiation is obtained by a filtering technique (Szymański et al., 1996; Jäschke et al., 1999); well polarized Mössbauer radiation is separated from allowed nuclear transitions by tuning the resonant velocity condition between the source and the absorber (polarizer). This technique can be easily implemented in laboratories. On the other hand, the strong SR source is the most suitable for performing practical and advanced polarized Mössbauer studies; the excellent beam properties of a well linearly polarized SR source (high brilliance, small beam size, short pulse, etc.) enable various applications for polarization-dependent Mössbauer spectroscopy in transmission and scattering geometry. Moreover, one can use a diamond phase plate to control the polarization state of SR X-rays (L'abbé et al., 2004).

The use of a SR source for studying Mössbauer spectroscopy was proposed by Ruby (1974). Since then, a large number of experiments have been performed using a SR source. Generally, there are two kinds of measurement scheme for SR-based Mössbauer spectroscopy. One is the time-domain measurement using nuclear forward scattering (Hastings et al., 1991) and the other is the energy-domain measurement (Odeurs et al., 1998; L'abbé et al., 2000, 2001; Callens et al., 2002; Seto et al., 2009). In the former case a spectrum is recorded as a function of the time after the nuclear excitation by a short resonant synchrotron pulse. The hyperfine parameters are determined by analysis of the quantum beats, whose frequencies are characteristic of the hyperfine structure. Currently, this method is the most established measurement technique (see, for example, Gerdau & van Bürck, 1994; Smirnov, 1996). On the other hand, in the latter case, the nuclear ensemble in both an investigated sample and an oscillating single-line reference sample is collectively excited by the SR pulse. The delayed nuclear resonant scattering is recorded as a function of the velocity of the reference sample so that the energy-resolved spectrum is obtained (stroboscopic detection method). The scattering processes and the information extracted from the spectrum were critically compared between time-domain and energy-domain Mössbauer spectroscopy by Planckaert et al. (2009). Note that one can also use an `exo-interferometric' phase determination method, which enables reconstruction of the energy spectrum from the time-domain measurement (Sturhahn et al., 2004; Callens et al., 2005, 2007). However, the above-mentioned methods depend on the bunch operation modes of SR. It will considerably decrease the overall synchrotron beam time available for SR users. In particular, time-domain measurements require special bunch modes of SR having a rather long period (T > 100 ns for ⁵⁷Fe nuclei) between electron bunches in the storage ring. Unfortunately, such bunch modes are usually limited in SR facilities. Moreover, the energy-domain spectrum, obtained by the stroboscopic detection method, is strongly influenced by the finite experimental time window so that the data analysis is often difficult for users of conventional Mössbauer spectroscopy. However, as for the study of iron-containing materials, the SR user can perform conventional Mössbauer spectroscopy using almost perfect linearly polarized ⁵⁷Fe-Mössbauer radiation, which is filtered directly from a SR source by a nuclear Bragg monochromator. This method is operational in any bunch mode of SR, which leads to a dramatic increase in the available SR beam time. The principle is based on the nuclear Bragg reflection under the electrically forbidden condition of a single-crystal, which is due to the polarization dependence of nuclear resonance scattering in the presence of a hyperfine interaction (Trammell, 1961; Belyakov & Aivazyan, 1968, 1969; Smirnov et al., 1969; Mirzababaev et al., 1971). The so-called pure nuclear Bragg reflection from a ⁵⁷Fe-enriched crystal achieves an extremely high suppression of electronic scattering and filters ⁵⁷Fe-Mössbauer radiation from the SR source. An attempt at this type of measurement was started by Gerdau (Gerdau et al., 1985; Gerdau & Rüffer, 1986). Their experiment successfully showed a Mössbauer spectrum of a diffracted beam from an yttrium iron garnet crystal, using a stainless steel absorber as the analyzer in the energy domain. The theoretical aspects were also discussed by Belyakov (1987a,b). A breakthrough study of this method was performed by Smirnov et al. (1986). Their experiment clearly showed that a pure nuclear Bragg reflection of the ⁵⁷FeBO₃ crystal heated up to the Néel temperature in an external field could yield single-line 14.4 keV diffracted γ-radiation with an almost natural linewidth. The first single-line Mössbauer filtration of SR using a heated ⁵⁷FeBO₃ crystal was performed at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France (Chumakov et al., 1990), and finally Smirnov realised energy-domain Mössbauer spectroscopy using single-line ⁵⁷Fe-SR-Mössbauer radiation (Smirnov et al., 1997; Smirnov, 2000). The spectrum was measured by oscillating a sample along the incident ⁵⁷Fe-SR-Mössbauer radiation. Later, Doppler-shifted single-line ⁵⁷Fe-SR-Mössbauer radiation at a fixed beam position was successfully produced by oscillating a heated ⁵⁷FeBO₃ crystal in the plane of the crystal surface (Mitsui et al., 2007a, 2009; Potapkin et al., 2012). A detailed physical picture of single-line ⁵⁷Fe-SR-Mössbauer radiation was given by Smirnov et al. (2011). The first practical application using linearly polarized ⁵⁷Fe-SR-Mössbauer radiation was demonstrated by a study of the moment canting in an amorphous alloy (Pankhurst et al., 2001). To improve the polarized ⁵⁷Fe-SR-Mössbauer studies with a nuclear Bragg monochromator, we have recently developed a nuclear diffraction optics using a diamond phase plate and an iron borate nuclear Bragg monochromator to control the polarization states of the incident SR X-rays and/or the filtered ⁵⁷Fe-SR-Mössbauer radiation. This spectrometer allows us to perform SR-based ⁵⁷Fe-Mössbauer spectroscopy using a linearly polarized, a circularly polarized and even a non-polarized probe beam in the energy domain. In this paper we describe the technical details of the spectrometer system, beam characterization and performance-test experiments. As a demonstrative study, we introduce a grazing-incidence experiment to observe the circular dichroism on the specular nuclear resonant reflection from a thin layer of ⁵⁷Fe.

2. Diamond phase plate for ⁵⁷Fe-SR-Mössbauer radiation

In the developed device, a 750 µm-thick almost perfect diamond single-crystal has been used as a phase plate. A photograph of the crystal is shown in Fig. 1(a).

Figure 1 (a) Photograph of the diamond single-crystal plate. (b, c) Solid lines show the calculated angular dependence of degree of linear (PL) and circular (PC) polarizations for a perfect plane-wave X-ray at 14.4 keV. Blue dashed lines correspond to the phase difference δ. The phase plate is a 750 µm-thick C (111) crystal, used in the 220 symmetrical Laue case. (d, e) Calculated angular dependence of PL and PC for incident X-rays with three different angular divergences (ωh = 4.7′′, 7.5′′ and 15′′).

A diamond phase plate is an optical component to utilize the birefringence taking place in the vicinity of the Bragg condition in a perfect crystal (Hirano et al., 1991, 1995; Giles et al., 1994). The π- and the σ-polarization components of the incident X-rays have different phase velocities when they propagate through the crystal, which introduces a phase shift δ between them. If the diffraction plane is inclined by an angle of π/4 with respect to the electric field of the incident linearly polarized X-rays, the degree of linear polarization, P_L, and circular polarization, P_C, of the transmitted X-rays are proportional to cos(δ) and sin(δ), respectively. The phase shift δ is given as follows,

Here, r_e is the classical electron radius, λ is the wavelength, θ_B is the Bragg angle, V is the unit-cell volume, F_h is the structure factor, Δθ is the offset angle and t is the thickness of the crystal. The parameter Δθ is defined as Δθ = θ − θ_B, where θ is a glancing angle to the net plane. The X-ray transmission rate, T, at an incident angle far away from the Bragg condition is given by

where μ is a linear absorption coefficient.

In equation (1) the phase shift is controlled by the offset angle, Δθ, from the Bragg condition. Therefore, the crystal setting at δ = (n + 1)π acts as a half-wave plate, so that it rotates a polarization plane of linearly polarized X-rays by 90°. In other cases, the crystal setting at δ = (n + 1/2)π acts as a quarter-wave plate and then the linearly polarized X-rays are converted to circularly polarized X-rays. The phase shift, δ, is calculated for a symmetric C 220 reflection of the perfect plane-wave 100% linearly polarized 14.4 keV X-rays and t = (t₀ = 750 µm, θ_B = 19.94°), as a function of Δθ. Figs. 1(b) and 1(c) show the theoretical values of P_L and P_C, respectively.

One can see that the phase shift rapidly changes at close proximity to the Bragg condition and slowly changes in the region far away from the Bragg condition. The former case is not suitable for the production of high-quality polarized X-rays. Since, in real experiments, the finite angular divergence of the incident X-rays causes a degradation of the polarization state by way of the spread of δ, the polarization of transmitted X-rays is obtained by convoluting P_L(Δθ) or P_C(Δθ) with an angular distribution of the effective divergence of incident X-rays. In Figs. 1(b) and 1(c), the theoretical P_L and P_C values near the Bragg condition are extremely sensitive to Δθ. As a result, linearly polarized X-rays with finite angular divergence are converted to pseudo non-polarized X-rays (mixed polarization). This indicates that the diamond phase plate close to the Bragg condition works as a depolarizer (Bouchenoire et al., 2003; Ueji et al., 2005). On the other hand, the latter case, which is not sensitive to Δθ, is available for precise control of the polarization state of X-rays. Figs. 1(d) and 1(e) show the calculated angular dependence of P_L and P_C for incident X-rays with three different horizontal angular divergences, ω_h = 4.7′′, 7.5′′ and 15′′. In the calculations we have assumed that the vertical angular divergence, ω_v, is fixed to 3.0′′, whose values are comparable with a typical angular divergence of the undulator radiation at SPring-8. In Fig. 1(d), as the ω_h value increases from 4.7′′ to 15′′, P_L degrades rapidly and all calculated values are greater than −0.5. This is because the thickness of 750 µm is not thick enough to act as a half-wave plate for divergent X-rays with energy of 14.4 keV. In contrast, in Fig. 1(e), a maximum magnitude on P_C shows a considerably large value (|P_C|_max > 0.85) for ω_h values less than 7.5′′. The X-ray transmission rate, derived from equation (2), is estimated to be about 80%. These values are suitable for a quarter-wave plate: the C 220 phase plate, operating under the off-Bragg condition of Δθ ∼ ±8.0′′, can convert the linearly polarized 14.4 keV X-rays with ω_h = 4.7′′ to circularly polarized X-rays with P_C ≃ 0.9.

3. Optical system and experimental procedure

To perform energy-domain polarized ⁵⁷Fe-SR-Mössbauer spectroscopy a dedicated optical system has been designed and installed at the BL11XU beamline of SPring-8. It is composed of a high-resolution monochromator, a diamond phase plate and an iron borate nuclear Bragg monochromator. A photograph and a schematic view of the optical set-up are shown in Figs. 2(a) and 2(b), respectively.

Figure 2 ^57Fe-SR-Mössbauer spectrometer installed at BL11XU of SPring-8. (a) External view and (b) nuclear diffraction optical system. SR: synchrotron radiation from the undulator of BL11XU; DM: double-crystal monochromator, Si 111 reflections; HRM: high energy resolution monochromator, nested-type channel-cut Si 511 × Si 975 reflections; S1: slit 1.0 mm (H) × 1.0 mm (V); DPP: diamond phase plate, C 220 reflection in Laue geometry; D1: PIN photodetector; NBM: nuclear Bragg monochromator, ^57FeBO3 111 reflection near the Néel point; Hex: external magnetic field, 150 Oe; S2: slit 1.0 mm (H) × 0.5 mm (V); D2: NaI(Tl) scintillation detector.

The experimental procedure is as follows. With reference to Fig. 2(b), the electron current of the SPring-8 storage ring is kept at 100 mA at 8.0 GeV. A liquid-nitrogen-cooled Si 111 double-crystal monochromator is used to handle the high heat load of undulator radiation (Shiwaku et al., 2004). Linearly σ-polarized (100%) SR X-rays with an energy bandwidth of 2.5 meV at the 14.4 keV nuclear resonance of ⁵⁷Fe are produced by a nested high-resolution monochromator consisting of asymmetric Si 511 and asymmetric Si 975 channel-cut crystals (Mitsui et al., 2001). The horizontal beam size is restricted by a slit, S₁. Behind S₁ the typical total flux is about 7.5 × 10⁹ photons s⁻¹, the beam size is 1.0 mm (H) × 0.4 mm (V) and horizontal and vertical angular divergences are estimated to be 4.7′′ and 3.0′′, respectively. The SR X-rays are incident onto the diamond phase plate, adjusting near the symmetric Laue 220 diffraction condition (θ_B = 19.94°). The scattering plane of the phase plate is set to be inclined by 45° from the vertical plane. Then, as described in §2, σ-polarized SR X-rays are converted to circular polarized or non-polarized SR X-rays by changing the parameter Δθ of the phase plate. The polarization-controlled SR X-rays are incident onto a ⁵⁷Fe-enriched (95%) iron borate nuclear Bragg monochromator, and 14.4 keV ⁵⁷Fe-SR-Mössbauer radiation is produced by the pure nuclear Bragg reflection of ⁵⁷FeBO₃ 111 (θ_B = 5.11°). Here, a static external field of 150 Oe is applied parallel to the crystal surface and perpendicular to the scattering plane to make the hyperfine field parallel to the scattering plane in the 111 plane. Then, the pure nuclear Bragg reflection of ⁵⁷FeBO₃ 111 is related to the Δm = ±1 nuclear transitions and its polarization state is in accord with the polarization factor in the nuclear resonance scattering amplitude (van Bürck et al., 1980; Siddons et al., 1989; Smirnov, 2000; Smirnov et al., 2011). In the antiferromagnetic pure nuclear Bragg reflection system of Fig. 2(b) the ⁵⁷FeBO₃ 111 nuclear Bragg monochromator produces strongly polarized ⁵⁷Fe-SR-Mössbauer radiation, whose polarization plane is rotated by 90° from that of incident X-rays; the σ-polarized incident SR beam is reflected as π-polarized ⁵⁷Fe-SR-Mössbauer radiation, while a circularly polarized (or non-polarized) SR beam is reflected as ⁵⁷Fe-SR-Mössbauer radiation with the same polarization state. Under that condition, the ⁵⁷Fe-SR-Mössbauer radiation is ultrafinely monochromated by heating the ⁵⁷FeBO₃ crystal up to near the Néel point (T_N = 348.8 K), whose energy bandwidth reaches about 3.4 Γ₀ (Mitsui et al., 2007b). Here Γ₀ (∼4.7 neV) is the natural linewidth of the ⁵⁷Fe nucleus. The resonance energy of iron borate is changed by the Doppler effect with the crystal oscillating parallel to the 111 plane in a sinusoidal velocity mode at 10 Hz. Behind S₂ the single-line ⁵⁷Fe-SR-Mössbauer radiation is counted by a NaI(Tl) scintillation detector. The typical total flux is about 1.0 × 10⁴ photons s⁻¹ and the beam size is 1.0 mm (H) × 0.4 mm (V). In Fig. 2(b), if a sample is placed at position A or B, the spectrum is obtained by counting the intensity of the pure nuclear Bragg reflection as a function of the velocity. Table 1 summarizes the available polarization states for ⁵⁷Fe-SR-Mössbauer spectroscopy; the design of the nuclear diffraction optics allows us to perform the ⁵⁷Fe-Mössbauer studies with various polarization states such as σ/π-linearly polarized, right/left circularly polarized and non-polarized SR X-rays. Here, we adopt a previously reported definition that the right circular polarization corresponds to a positive helicity (Δm = +1) photon emitted in the direction of H_hf at the ⁵⁷Fe nucleus, where m is the spin quantum number of the photon (Siddons et al., 1999).

Table 1
Available polarization states for ⁵⁷Fe-SR-Mössbauer spectroscopy

Polarization state for the incident beam	C 220 phase plate (offset angle)	Position A B
Horizontal linear polarization (σ)	Without	○ ×
Vertical linear polarization (π)	Without	× ○
Circular polarization (right/left)	Δθ = ±8.0′′	○ ○
Non-polarization (mixed polarization)	Δθ = 0	○ ○

4. Beam characterization and performance-test experiments

The performance of the developed spectrometer was evaluated in detail. Firstly, to check the quality of the diamond phase plate [behind the HRM in Fig. 2(b)], a rocking curve of the C 220 Laue symmetric reflection and the Δθ angle dependence of the P_L value were measured with the 14.4 keV incident SR X-rays. The experimental set-up is shown in Fig. 3(a). There are some techniques for the characterization of X-ray polarization (see, for example, Siddons et al., 1989, 1990; Finkelstein et al., 1994; Shen et al., 1995; Shen & Finkelstein, 1995; Shen, 1996, 2000). However, in this study a simple polarimeter was used to measure the P_L value of the SR X-rays; it consisted of a scatterer (polyimide film) and two NaI(Tl) scintillation detectors (Hayakawa et al., 1998; Suzuki, 2004). The detectors D₂ and D₃ counted the vertical (I_y) and horizontal (I_x) components of the scattered X-ray intensities, respectively. Because of the polarization dependence of the X-ray scattering, the P_L value was determined by

The results are shown in the upper part of Fig. 3(b). The rocking curve shows a sharp single-peak profile (solid circles) with a narrow full width at half-maximum of 3.65′′, whose value is in good agreement with the theoretical one (3.63′′). It implies that the diamond phase plate has an ideal crystal perfection, which enables the precise phase control of the transmitted SR X-rays via the offset angle Δθ. Indeed, the measured P_L values (open circles) are in good agreement with the theoretical curve (solid line). Hence, as shown in the calculated Δθ-angle dependence of the P_C value (dashed line), we can expect that the σ-polarized SR X-rays are converted into the circular polarization at Δθ = ±8 or the non-polarization condition at Δθ = 0.

Figure 3 (a) Experimental set-up for characterization of the C 220 phase plate. S1: slit 1.0 mm (H) × 0.5 mm (V); S2, S3: slits 1.0 mm (H) × 1.0 mm (V); D1: PIN photodetectors; D2, D3: NaI(Tl) detectors. (b) Experimental results. The solid and open circles show a rocking curve of the C 220 reflection and the offset-angle dependence of the measured PL, respectively. The black solid and blue dashed lines are the theoretical curves of PL and PC, respectively. Solid triangles show the offset-angle dependence of the measured peak intensity ratio of the ^57FeBO3 111 reflection near the Néel temperature. (c) SR Mössbauer absorption spectra of a 2.5 µm-thick stainless steel foil (^57Fe 90%) measured at three different offset angles (Δθ = 0, 8.0′′ and −8.0′′). Solid lines are guides for the eye.

Secondly, the Bragg peak intensity of ⁵⁷FeBO₃ 111, I_NBR, was measured by changing the offset angle. The typical intensity was about 8.0 × 10³ counts s⁻¹ at Δθ = ±8′′ and about 5.0 × 10³ counts s⁻¹ at Δθ = 0. The measured intensity curve (solid inverted triangle) is shown in the lower part of Fig. 3(b), which is normalized by a Bragg peak intensity obtained without the phase plate, I₀. For the circular polarization conditions (Δθ = ±8′′), the I_NBR/I₀ value is about 0.8, which is in good agreement with the calculated X-ray transmission rate of the 750 µm-thick diamond. On the other hand, for the non-polarization condition (Δθ = 0), the I_NBR/I₀ value decreases to about 0.5, whose physical origin is due to the anomalous absorption caused by the X-ray dynamical diffraction of an almost perfect diamond crystal (Batterman & Cole, 1964).

Thirdly, the energy bandwidth of the ⁵⁷Fe-SR-Mössbauer radiation was examined at three different offset-angle conditions (Δθ = 0 and ±8′′) by measuring the absorption spectra of a 2.5 µm-thick 90% ⁵⁷Fe-enriched stainless steel foil placed at position B in Fig. 2(b). The measured spectra are shown in Fig. 3(c). At a glance, we can see that all the spectra exhibit clear single-line absorption profiles with almost the same energy bandwidth. The results prove that the nuclear Bragg monochromator can filter the Doppler-shifted single-line ⁵⁷Fe-Mössbauer radiation from broadband SR X-rays with different polarization states.

Finally, we characterized the controlled polarization states of the incident SR X-rays and the reflected ⁵⁷Fe-SR-Mössbauer radiation. The experiment was performed using the nuclear diffraction optics of Fig. 2(b) with and without the C 220 phase plate. The linear polarizations and non-polarization were evaluated from the absorption spectra of a 2 µm-thick 90% ⁵⁷Fe-enriched iron foil. In both cases the foil was magnetized perpendicular to the scattering plane by applying an external field (H_ex) of 5.2 kOe. Then, as is shown in Fig. 4(a), H_hf at the ⁵⁷Fe nuclei was aligned antiparallel to H_ex. The room-temperature Mössbauer spectra were measured for the iron foil placed at positions A or B in Fig. 2(b). The measured spectra are shown in Figs. 4(c) and 4(d), respectively. In the upper part of Fig. 4(c) the spectrum, measured without the phase plate, shows a symmetric spectral profile with four absorption lines (first, third, fourth, sixth) of Δm = ±1 nuclear transitions. This is due to the pure σ-polarization of incident SR X-rays at position A. In contrast, as shown in the upper part of Fig. 4(d), the spectrum, measured without the phase plate, shows a symmetric spectral profile with two absorption lines (second, fifth) of Δm = 0 nuclear transitions. The result clearly shows that the ⁵⁷Fe-SR-Mössbauer radiation has pure π-polarization at position B (Mitsui et al., 2007a). On the other hand, in the lower part of Figs. 4(c) and 4(d), the spectra, measured with the phase plate at Δθ = 0, exhibit a similar spectral profile with six absorption lines. The results prove that the incident SR X-rays and the ⁵⁷Fe-SR-Mössbauer radiation have the non-polarization state, like a conventional ⁵⁷Co Mössbauer source. The right and left circular polarizations and their P_C values were evaluated from the absorption spectra of a 15 µm-thick non-enriched iron foil. H_hf of the iron foil was arranged as much as possible to be parallel to the beam direction (k); as shown in Fig. 4(b), the foil in an external field of 5.2 kOe (H_ex ∥ k) was magnetized in its plane so that H_hf was aligned almost parallel (φ = 12°) to the beam direction, because it is usually difficult to magnetically polarize an iron foil perpendicular to the foil plane. In Fig. 2(b) the offset angle of the phase plate was adjusted to circular polarization conditions (Δθ = ±8′′) and the room-temperature Mössbauer spectra were measured for the iron foil placed at position A or B. The results are shown in Figs. 4(e) and 4(f), respectively. In the upper part of Figs. 4(e) and 4(f) the spectra, measured with the phase plate at Δθ = +8′′, show almost the same asymmetric profile with two main absorption lines (first, fourth) of Δm = +1 nuclear transitions. The results provide clear evidence that the incident SR X-rays and the ⁵⁷Fe-SR-Mössbauer radiation have right circular polarization. Note that the traces of the other lines (second, third, fifth, sixth) come from incomplete polarization and incomplete alignment of H_hf in the iron foil. As discussed in §2, one can switch the helicity of the circularly polarized incident beam by offset-angle reversal. Indeed, as shown in the lower part of Figs. 4(e) and 4(f), the spectra, measured with the phase plate at Δθ = −8′′, exhibit the reversed asymmetric profile with two main absorption lines (third, sixth) of Δm = −1 nuclear transitions. The results prove that the incident SR X-rays and the ⁵⁷Fe-SR-Mössbauer radiation have left circular polarization.

Figure 4 ^57Fe polarization-dependent SR-Mössbauer spectroscopy of magnetized iron foils. (a) Linearly (σ, π) or non-polarized (NP) beams are incident on a 2 µm-thick 90% ^57Fe-enriched iron foil, whose Hhf is aligned perpendicular to the beam direction and the scattering plane; hi (i = σ, π) is the magnetic unit vector of the incident beam. (b) The circularly (right, left) polarized beam is incident on a 15 µm-thick non-enriched iron foil, whose Hhf forms an angle φ (= 12°) with the beam direction. ^57Fe-Mössbauer spectra measured for (c) σ-polarized and non-polarized SR X-rays at Hex ⊥ hσ, (d) π-polarized and non-polarized ^57Fe-SR-Mössbauer radiation at Hex ∥ hπ, (e) for right and left circularly polarized SR X-rays at k ∥ Hex and (f) right and left circularly polarized ^57Fe-SR-Mössbauer radiation at k ∥ Hex. Solid lines correspond to calculation. Note that the spectra are measured for the iron foil placed before (c, e) and after (d, f) the nuclear Bragg monochromator.

The P_C values of the incident beam were determined by a fit of the spectra. The theoretical treatment has been described by Szymański et al. (1996): in the case of incomplete polarization, the spectrum can be fitted with a linear combination of the functions N_RS_R(φ) + N_LS_L(φ), where S_R(φ) and S_L(φ) are the spectra measured with complete right and left circular polarization, φ is the angle between the ⁵⁷Fe nuclear moment and the beam direction, N_R and N_L are proportional to the number of photons for each polarization. Figs. 4(e) and 4(f) show the results of curve fitting (solid lines) calculated in the same manner as previously reported (Szymański et al., 1996). From the estimated coefficients N_R and N_L we have determined the degree of right and left circular polarization, P_C = (N_R − N_L)/(N_R + N_L), to be about ±0.91, in good agreement with the theoretical values as expected in §2.

In this performance-test study the experimental results have clearly demonstrated that the developed spectrometer allows us to perform conventional energy-domain Mössbauer spectroscopy using a polarization-controlled SR probe beam. Certainly, this device can realise the advanced polarization-dependent ⁵⁷Fe-SR-Mössbauer experiments, which was impossible before. However, the user should note that the energy bandwidth of ⁵⁷Fe-SR-Mössbauer radiation is still several times larger than that of a radioactive ⁵⁷Co source. We think that this problem should be improved in future studies.

5. Grazing-incidence experiment with circularly polarized ⁵⁷Fe-SR-Mössbauer radiation

High-brilliance SR is extremely suitable for grazing-incidence Mössbauer spectroscopy, which is an effective tool for investigation of hyperfine interactions near the surface (see, for example, Bernstein & Campbell, 1963; Wagner, 1968; Frost et al., 1985; Andreeva et al., 1991, 1994; Irkaev et al., 1993). In the early SR-based Mössbauer studies, grazing-incidence anti­reflection (GIAR) multilayer films were intensively studied with regard to the principle of nuclear resonant filtering of SR (Hannon et al., 1979, 1985a,b,c,d; Gerdau et al., 1990; Andreeva et al., 1991). Since then, a number of thin film and multilayer systems have been studied by the time-domain measurement (see, for example, Röhlsberger et al., 1993; Chumakov et al., 1993, 1999; Toellner et al., 1995; Niesen et al., 1998; Nagy et al., 1999, 2000; Röhlsberger et al., 2001). The optical properties of a thin film containing a Mössbauer isotope and selected applications have been reviewed by Röhlsberger (1999). Subsequently, the energy-domain measurement of a thin film under grazing-incidence conditions was also performed using the stroboscopic detection method (Bottyán et al., 2003; Deák et al., 2006). These methods are complementary, having their own features and advantages. At present, Mössbauer spectroscopy with single-line ⁵⁷Fe-SR-Mössbauer radiation is also a potential candidate for developing the grazing-incidence studies (Mitsui et al., 2012a; Potapkin et al., 2012; Mibu et al., 2013). Generally, SR-based grazing-incidence Mössbauer spectroscopy has been performed with a linearly polarized beam. However, a previous work (L'abbé et al., 2004) has demonstrated that the circularly polarized beam is useful for a layer-selective magnetization measurement of a magnetic thin film. Therefore, as a pilot study, we performed a grazing-incidence experiment with circularly polarized ⁵⁷Fe-SR-Mössbauer radiation to observe the dichroism effect (Gonser & Fischer, 1981, 1985) of the specular nuclear resonant reflection from a thin layer of ⁵⁷Fe. In this experiment we prepared a 100 nm-thick 95% ⁵⁷Fe-enriched iron thin film, which was grown using an MBE machine on an MgO(001) substrate. The sample had dimensions of 5 × 30 × 0.5 mm (width × length × thickness).

The experimental set-up is shown in Fig. 5(a). The iron thin film, ⁵⁷Fe(100 nm)/MgO(001), was placed behind the ⁵⁷FeBO₃ 111 nuclear Bragg monochromator. The magnetic moment (hyperfine field) was aligned antiparallel (parallel) to the beam direction by applying an external magnetic field (H_ex = 600 Oe) in the film plane. Note that an epitaxial Fe/MgO(001) film was magnetically saturated by a weak external field of several hundred Oe in the film plane (Zhan et al., 2009). The room-temperature specular nuclear resonant reflection spectra were measured at a low grazing angle condition of 0.3°. Then the ⁵⁷Fe-enriched iron thin film acted as a GIAR film: the electron scattering was sufficiently suppressed and only the nuclear resonant scattering contributed to the specular reflection because the critical angle of the nuclear resonant scattering was greater than that of the electron scattering (φ_e = 0.22°). As a result, the specular nuclear resonant reflection occurred when the energy of the incident beam was close to the allowed nuclear transition's resonant energy of the ⁵⁷Fe nuclei (Isaenko et al., 1994). The X-ray background level was reduced by a restrictive slit (S) in front of a NaI(Tl) detector (D). The spectrum was measured with non-polarized (Δθ = 0) and right (Δθ = +8′′) circularly polarized ⁵⁷Fe-SR-Mössbauer radiation. In both cases a statistically sufficient spectrum was obtained with a short measurement time of 15 min. Fig. 5(b) shows the signal-to-background ratios (SBR) of the measured specular reflectivity spectra. In the upper part of Fig. 5(b) the spectrum, measured in the non-polarization state, shows a symmetric spectral profile with four resonance peaks of Δm = ±1 nuclear transitions. The result means that the net magnetization of the iron thin film is sufficiently saturated by a H_ex of 600 Oe. In contrast, as shown in the lower part of Fig. 5(b), the spectrum, measured with right circular polarization, clearly shows an asymmetric spectral profile with two main resonance peaks of Δm = +1 nuclear transitions. The result proves that the magnetic moment (hyperfine field) of ⁵⁷Fe in the thin film is aligned antiparallel (parallel) to the beam direction. As a remarkable effect, it shows a large enhancement in the SBR, whose value is almost twice as large as that of the non-polarized beam incidence case. This result gives clear evidence of circular dichroism on the specular nuclear resonant reflection from a thin layer of ⁵⁷Fe: in Fig. 5(a) the right circularly polarized beam excites only the Δm = +1 nuclear transitions with full beam flux. However, in the case of the non-polarized (mixed polarization) beam incidence the Δm = +1 nuclear transitions are excited by one half of the beam flux, with right circular polarization, and the other half, with the opposite helicity, excites the Δm = −1 nuclear transitions.

Figure 5 Grazing-incidence ^57Fe-SR-Mössbauer spectroscopy of a ^57Fe 95%-enriched ^57Fe(100 nm)/MgO(001) film. (a) Experimental set-up. NBM: nuclear Bragg monochromator; S: slit 0.5 mm (V) × 1.0 mm (H); D: NaI(Tl) detector. (b) Reflectivity spectra of the magnetized iron thin film at a grazing angle of 0.3°. Upper and lower parts correspond to the spectrum measured with the non-polarized and right circularly polarized ^57Fe-SR-Mössbauer radiation, respectively. The magnetic moment (hyperfine field) of the iron thin film has been aligned antiparallel (parallel) to the beam direction by applying an external magnetic field (Hex = 600 Oe) in the film plane.

In this study the developed spectrometer has been successfully applied to grazing-incidence ⁵⁷Fe-SR-Mössbauer spectroscopy. Polarization-controlled high-brilliance ⁵⁷Fe-SR-Mössbauer radiation enables the measurement of the specular nuclear resonant reflection spectrum in a short data collection time. In particular, the circularly polarized beam gives an energy-domain Mössbauer spectrum with a high signal-to-background ratio and a high sensitivity to the direction of H_hf. The simple optical system is very suitable for applied research under special conditions, such as low temperatures, high magnetic fields, in situ studies with various gas environments and non-equilibrium spin Hall conditions (Mibu et al., 2015). In the near future these advantages will give unique insights into the magnetic states at the surface and interface of various functional magnetic thin films.

6. Conclusion

A new SR-based Mössbauer spectrometer using a diamond phase plate and an iron borate nuclear Bragg monochromator has been developed at the BL11XU beamline of SPring-8. It can easily realise energy-domain ⁵⁷Fe-SR-Mössbauer studies with various polarization states, i.e. linear polarization, circular polarization and non-polarization. Its outstanding potential has been demonstrated by a grazing-incidence Mössbauer study of an iron thin film. As a special advantage the measurement is possible even in multi-bunch mode of SR. We believe that the developed spectrometer provides new possibilities for the application of polarized ⁵⁷Fe-SR-Mössbauer spectroscopy, including Mössbauer polarimeter (Pfannes & Gonser, 1974), γ-ray diffraction (Belyakov, 1975), ultrahigh-pressure experiments (Nasu, 1994), small-angle scattering (Shvyd'ko et al., 1996) and Rayleigh scattering of ⁵⁷Fe-SR-Mössbauer radiation (Masuda et al., 2008; Mitsui et al., 2012b).