# Nuclear Forward Scattering of Synchrotron Radiation by 99Ru

Dimitrios Bessas, D. G. Merkel, A.I. Chumakov, R. Rueffer, Raphaël P.

Hermann, Ilya Sergueev, Abdelfattah Mahmoud, B. Klobes, Michael A.

Mcguire, Moulay Tahar Sougrati, et al.

► To cite this version:

Dimitrios Bessas, D. G. Merkel, A.I. Chumakov, R. Rueffer, Raphaël P. Hermann, et al. Nuclear Forward Scattering of Synchrotron Radiation by 99Ru. Physical Review Letters, 2014, 113, pp.147601. 10.1103/PhysRevLett.113.147601. [hal-01091244]

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This is the accepted manuscript made available via CHORUS. The article has been published as:

Nuclear Forward Scattering of Synchrotron Radiation by
^{99}Ru

D. Bessas, D. G. Merkel, A. I. Chumakov, R. Rüffer, R. P. Hermann, I. Sergueev, A.

Mahmoud, B. Klobes, M. A. McGuire, M. T. Sougrati, and L. Stievano

Phys. Rev. Lett. **113**, 147601 — Published 3 October 2014

DOI: 10.1103/PhysRevLett.113.147601
Nuclear Forward Scattering by <sup>99</sup>Ru

D. Bessas,<sup>1,*</sup> D. G. Merkel,<sup>1</sup> A. I. Chumakov,<sup>1</sup> R. Rüffer,<sup>1</sup> R. P. Hermann,<sup>2,3</sup> I. Sergueev,<sup>4</sup>

A. Mahmoud,<sup>2</sup> B. Klobes,<sup>2</sup> M. A. McGuire,<sup>5</sup> M. T. Sougrati,<sup>6,7</sup> and L. Stievano<sup>6,7</sup>

<sup>1</sup>European Synchrotron Radiation Facility, F-38043, Grenoble, France

<sup>2</sup>Jülich Centre for Neutron Science, JCNS, and Peter Grünberg Institut PGI, JARA-FIT, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany

<sup>3</sup>Faculté des Sciences, Université de Liège, B-4000, Liège, Belgium

<sup>4</sup>Deutsches Elektronen-Synchrotron, D-22607 Hamburg, Germany

<sup>5</sup>Material Science and Technology Division, OakRidge National Laboratory, Oak Ridge, Tennessee 37831, USA

<sup>6</sup>Institute Charles Gerhard AIME UMR CNRS 5253, Université Montpellier 2, F-34095 Montpellier, France

<sup>7</sup>Réseau sur le Stockage Electrochimique de l'Energie (RS2E), FR CNRS 3459, France

We have measured nuclear forward scattering spectra utilizing the <sup>99</sup>Ru transition, 89.571(3) keV, with a notably mixed E2/M1 multipolarity. The extension of the standard evaluation routines to include mixed multipolarity allows us to extract electric and magnetic hyperfine interactions from <sup>99</sup>Ru containing compounds. This paves the way for several other high energy Mössbauer transitions, *E* ~ 90 keV. The high energy of such transitions allows for *operando* nuclear forward scattering studies in real devices.

PACS numbers: 63.20.dd, 76.80.+y, 41.85.Si, 75.50.Cc

Nuclear forward scattering of synchrotron radiation [1, 2] is nowadays a standard technique for obtaining information similar to that extracted from Mössbauer spectroscopy [3]. This technique is particularly useful when preparation of the radioactive source for Mössbauer spectroscopy is difficult, when the lifetime of the radioactive source is short, or when the experimental setup requires a collimated or a small-size beam.

Synchrotron radiation matching the energy difference between the nuclear ground state and an excited state impinges on the sample and leads to nuclear excitation. The excited state has a finite lifetime and the resonantly scattered photons are delayed with respect to non-resonantly scattered (prompt) photons. Both coherent nuclear forward scattering [4] and incoherent fluorescence are observed. The typical lifetime of excited states ranges between 0.2 and 200 ns and matches the bunch structure of the current synchrotron radiation facilities. Hence, the nuclear forward scattering can, in principle, be measured for any of the Mössbauer isotopes.

The typical bandwidth of conventional X-ray optics is in the eV range. As a result, every photon resonantly scattered is accompanied by between 10<sup>6</sup> and 10<sup>9</sup> photons that are not nucleary scattered, often overloading the detection scheme [5, 6]. In order to circumvent detection overload from non resonant quanta, monochromatization of the X-ray beam by high resolution monochromators with meV band-pass [7] is typically used. Such monochromators are usually made out of silicon. Efficient high resolution monochromatization for energies above 30 keV is restricted because of the physical properties of silicon, see Ref. [8], thus seriously limiting the number of high energy Mössbauer transitions studied using synchrotron radiation. Other approaches were suggested to circumvent the pitfalls of silicon monochromators and thus the problem of non resonant detection overload, such as sapphire backscattering monochromatization [9–12], and nuclear lighthouse effect [13]. However, these approaches seriously limit the sample environment.

It was previously shown that nuclear forward scattering around 70 keV can be carried out with medium resolution monochromatization of 30 [14] or even 100 meV [12]. The extension of this concept to higher energies in combination with an optimized detector system and the lower flux of synchrotron radiation above 80 keV highly reduces the need for sophisticated approaches to circumvent non resonant detection overload. In addition the high energy allows for *operando* measurements in real devices.

Although conventional Mössbauer spectroscopy can be applied to high energy Mössbauer transitions such as <sup>155</sup>Gd (60.0106(6) keV) and <sup>166</sup>Er (80.577(2) keV), Nuclear Forward Scattering with a collimated of small-size beam by <sup>156</sup>Gd (88.970(1) keV) and <sup>164</sup>Er (91.38(2) keV) may provide superior information related to hyperfine interactions on nanostructures and under extreme conditions, e.g., study of magnetic anisotropies in Gd nanostructures [15] and studies of partial amorphization of Er<sub>2</sub>O<sub>3</sub> under applied pressure [16]. Moreover, a study of a yet unexplored chemistry related to the novel electronic properties of hafnium compounds such as two dimensional hafnium honeycombs - similar to graphene - structure [17], hafnium carbides for use in extreme environments [18], and studies related to the applications of hafnium hydride in nuclear power plants [19] are now feasible by nuclear forward scattering on <sup>176</sup>Hf (88.349(24) keV).

In this letter, we report on nuclear forward scattering, NFS, of synchrotron radiation at energy as high as 90 keV using a conventional double crystal monochromator and a multielement Avalance Photo Diode, APD, detector. Using such a setup we measured (in two hours each) nuclear forward scattering spectra for <sup>99</sup>Ru-metal and <sup>99</sup>RuO<sub>2</sub> 99% enriched to <sup>99</sup>Ru and (in ten hours) spectra for SrRuO<sub>3</sub> [20, 21] with 12.7% <sup>99</sup>Ru natural abundance [22]. The related information, i.e., absolute values of recoil-free fraction (*f*<sub>LM</sub>), its temperature dependence and the related Debye temperature in <sup>99</sup>Ru-metal and the quadrupole splitting in <sup>99</sup>RuO<sub>2</sub> as well as the
hyperfine magnetic field in SrRuO$_3$ is extracted by extend-
ing the available routines including the mixture of E2 and M1
multipolarity.

$^{99}$Ru has a nuclear ground state with spin $I_g = 5/2$ and the first excited state with spin $I_e = 3/2$. The nuclear transition occurs via a combination of electric quadrupole, E2, and magnetic dipole, M1, radiation with a mixing ratio $\delta^2 = 2.7(6)$ [23]. The Mössbauer effect in $^{99}$Ru was first observed by Kistner *et al.*, [24]. Several groups [25–29] have worked on extracting hyperfine interaction parameters in Ru based compounds. The half life, only 16 days, of the used $^{99}$Rh radioactive source and the necessity to produce it using a particle accelerator limits the applicability of $^{99}$Ru Mössbauer spectroscopy. However, currently there is high demand for hyperfine interaction studies in Ru containing compounds with various applications, *i.e.* photocontrolled DNA binding in life sciences [30], energy harvesting using photovoltaic cells [31] and energy storage in lithium-ion batteries [32].

The experiment was carried out at the nuclear resonance
beamline ID18 [33] of the European Synchrotron Radiation
Facility. The storage ring was operating in 16-bunch mode
providing 176 ns interbunch spacing. The optical elements
in the experimental setup were: a compound refractive lense
[34], CRL, for collimation comprised of 115 cylindrical holes
of 1 mm diameter in beryllium, with 50% transmission at
90 keV, and a Si (3 3 3) double crystal monochromator, see
Fig. 1a. The internal conversion, with coefficient 1.50(3)
[35], converts the delayed resonant quanta to delayed inco-
herent Ru K<sub>a</sub> fluorescence at 19.214 keV which is easier to
detect [36]. The nuclear transition energy, E<sub>0</sub>, for the <sup>99</sup>Ru
first excited state was determined by measuring the delayed
K<sub>a</sub> fluorescence coming from a <sup>99</sup>Ru-metal sample placed
3 mm away from a 100 mm<sup>2</sup>, 100 &mu;m thick, APD; see Fig.
1a. The estimated efficiency of the Si APD used for 19 keV
is ~ 10%. The energy resolution of the Si (3 3 3) double
crystal monochromator measured by the delayed Ru K<sub>a</sub> fluo-
orescence is shown in Fig. 1b. This energy resolution is de-
fined by the angular spread of the beam after CRL. A typical
angular spread is given by the full width at half maximum,
3.6(1) &mu;rad, of a Gaussian function fitted to the experimen-
tal data. The angular acceptance of the Si (3 3 3) monochro-
mator is 0.53 &mu;rad. Thus, the monochromator accepts only
~ 15% of the beam. The time spectra of the nuclear forward
scattering were recorded by using a 10-element array consist-
ing of 30 &mu;m thick, 3 mm diameter Si APD with time resolu-
tion of ~ 0.5 ns. All detection elements are inclined and dis-
placed vertically with respect to each other in order to cover
the full beam heigth, 0.5 mm, and to equally distribute the ra-
diation load. The thickness of each element along the beam
was ~ 2.5 mm resulting in a detection efficiency of ~ 10%
at 89 keV. The photon flux detected by each APD in this de-
tection scheme was less than 2 &middot; 10<sup>6</sup> photons/s at 70 mA stor-
age ring current, far from the saturation regime. The detected
background of 0.03 Hz, measured 20 eV away from the res-
onant energy is uniformly distributed in time, see Fig.2. A
slight increase around 2 ns could be attributed to scattering of

<figure><img src="image_2.png" /></figure>

FIG. 1: (a) The experimental setup consisted of three undulators (U), two pair of slits, a compound refractive lense (CRL) for collimation, a Si (3 3 3) double crystal monochromator (HHLM), a Sn absorber (see text), the sample (S) in a helium cryostat, a Si APD for measuring the Ru K<sub>a</sub> fluorescence (INC) and the 10-element Si APD for measuring the nuclear forward scattering (FWD). (b) The energy resolution of the Si (3 3 3) double crystal monochromator measured by the delayed Ru K<sub>a</sub> fluorescence. The angular spread of the beam after CRL is also shown (upper tics). The line is a fit with a Gaussian function to the experimental data with 3.6(1) µrad full width at half maximum.

the beam in the detector housing. A similar detector is pre-
sented in Ref. [37].

The double crystal monochromator allows transmission for
radiation related both to the third harmonic - Si (3 3 3) -
with energy of 89.6 keV, and the first harmonic - Si (1 1 1)
- with energy of 29.8 keV. The coexistence of the first and
third harmonic gave us the opportunity to calibrate the energy
scale using the Sn K-edge (29.2004(2) keV [38]). The res-
onance energy for the ⁹⁹Ru first excited state was found to
be 89.571(3) keV, in excellent agreement with the tabulated
value, 89.57(6) keV [39]. In order to avoid detector overload
in the forward direction, the 29.8 keV radiation was filtered
out by a 200 µm Sn foil [40]. The small fraction of low en-
ergy radiation passing through the Sn foil is further absorbed
by the ruthenium containing sample, 3.5 mg/mm² of ⁹⁹Ru.

The recorded time distribution of the delayed Ru K<sub>a</sub> fluo-
rescence reveals an exponential decay; see Fig. 2a. Fitting the
data with a simple exponential function, I(t) = I<sub>0</sub>e<sup>-t/t<sub>0</sub></sup> + c,
yields a lifetime, t<sub>0</sub>, of the excited state of 28.8(3) ns. The
lifetime extracted herein is in agreement with the reported
value of 29(1) ns [41] measured using the delayed coinci-
<figure><img src="image_3.png" /><figcaption>FIG. 2: (a) The time distribution of the delayed incoherent Ru Kα fluorescence obtained on $^{99}$Ru-metal. (b) The nuclear forward scattering obtained on $^{99}$Ru-metal at 5 and 80 K (2 h each), the spectra obtained on $^{99}$RuO$_2$ at 5 and 60 K (2 h each), respectively, the spectra obtained on SrRuO$_3$ at 5 K (10 h) and a measurement of the background, 20 eV, away from resonance (0.5 h). Solid lines show the fit of the experimental data (see text). The arrow between 5 and 80 K at the $^{99}$Ru-metal data highlights the stretching in the dynamical beats due to the reduction in effective thickness.</figcaption></figure>

dence technique.

The nuclear forward spectrum recorded by $^{99}$Ru-metal at 5 and 80 K with ~ 0.5 Hz countrate indicates a pronounced structure; see Fig. 2b. The beat pattern broadens and shifts in time when the temperature increases. In $^{99}$Ru-metal no electric or magnetic hyperfine splitting is present [42]. In this

case the nuclear forward scattering intensity is given by Kagan et al., [43]. In order to extract the recoil-free fraction from the obtained spectrum the unitless effective thickness, $\xi$, of the sample is used:

$$ \xi = \frac{1}{4} L \sigma_0 f_{LM} \frac{\beta}{V_{Ru}} \quad (1) $$

where L is the geometric sample thickness, $\sigma_0$ is the nuclear resonant absorption cross section, $f_{LM}$ is the recoil free fraction, known as Lamb-Mössbauer factor, $\beta$ is the isotopic enrichment, $V_{Ru}$ is the volume per Ru atom. Pronounced beating, i.e., dynamical beats, is observed when $\xi$ is large. The spectra for $^{99}$Ru-metal shown in Fig. 2b were fitted between 5 and 150 ns and the obtained $\xi$ is 10.01(9) and 7.35(6) at 5 and 80 K, respectively. The $f_{LM}$ and the Debye temperature is extracted by fitting a Debye model to the obtained values of the effective thickness [12]. The obtained $f_{LM}$ are 0.19(1) and 0.14(1) at 5 and 80 K, respectively and the obtained Debye temperature is 466(50) K. The Debye temperature extracted herein is in good agreement with the Debye temperature, 495(24) K, extracted from X-ray diffraction on Ru [44, 45].

The mixing of electric quadrupole and magnetic dipole multipolarity of the nuclear transition is not included in the available fitting routines [46, 47] and, as a result, they cannot be used to analyse our measurements on $^{99}$RuO$_2$ and SrRuO$_3$. Thus, we had to modify [48] the available routines for extracting the quadrupole splitting and the magnetic hyperfine field in paramagnetic $^{99}$RuO$_2$ and ferromagnetic SrRuO$_3$, respectively. The fit of the data was performed with an algorithm [14] developed on the basis of the Fourier transformation of the energy spectrum to nuclear forward scattering [43] and extended for the case of large effective thickness. The mixing of E2 and M1 multipolarities was included with a fixed ratio $\delta^2(E2/M1) = 2.7$ [23]. The ratio of the nuclear quadrupole moments of the ground, $Q_g$, and excited state, $Q_e$, were fixed to $Q_e/Q_g = 2.93$ [49]. The nuclear magnetic moments of the ground state, $\mu_g = -0.641\mu_n$, and of the excited state, $\mu_e = -0.284\mu_n$, were also fixed. The spectra were treated using an isotropic distribution of the hyperfine interactions.

The beats in the NFS spectra of $^{99}$RuO$_2$ are due to a combination of the dynamical beats related to the large effective thickness and the quantum beats related to the quadrupole interaction which merge into hybrid beats [50]. By using the routine we developed we fitted the data with only two free parameters the quadrupole splitting, $eQ_eV_{zz}/2$, and the effective thickness. The obtained quadrupole splitting, 5.93(15) $\Gamma_0$ or 0.44(1) mm/s, agrees with that obtained by Mössbauer spectroscopy, 0.5(1) mm/s [42]. The $f_{LM}$ and the Debye temperature are extracted similarly to the $^{99}$Ru-metal case. The obtained Lamb-Mössbauer factor is 0.24(1) and 0.22(1) at 5 and 60 K, respectively, and the extracted Debye temperature is 535(60) K. This value is slightly lower than the Debye temperature measured previously using calorimetry [51], 610(10) K at 10 K.
The shape of the nuclear forward scattering spectrum of SrRuO₃ is defined by the magnetic hyperfine splitting. The obtained countrate was low, 0.04 Hz, and comparable with the background countrate. The low countrate is due to the low ⁹⁹Ru natural isotopic abundance. Magnetic splitting of the excited and the ground state for the E2/M1 mixed multipolarity allows for 18 transitions. Due to the numerous transitions distinct peaks appear in the nuclear forward spectrum. A similar effect was observed for the ¹⁸¹Ta nuclear transition [52]. In the case of SrRuO₃, the clearly seen peak at 60 ns; see Fig. 2b; allows us to precisely extract a hyperfine magnetic field of 33.9(5) T at 5 K. This value is in agreement with the result, 33.0(4) T at 4 K, determined by Mössbauer spectroscopy measurements [53, 54].

In conclusion, we have studied the nuclear forward scattering by the 89.571(3) keV in several ⁹⁹Ru containing reference materials, i.e., ⁹⁹Ru-metal, ⁹⁹RuO₂ and SrRuO₃. Moreover, we have modified the available fitting routines for extracting electric and magnetic hyperfine interaction in mixed multipolarity transitions. The typical countrate observed on ⁹⁹Ru enriched sample is ~ 0.5 Hz and allows us to acquire reasonable statistics in two hours. Measurements on non ⁹⁹Ru enriched samples are currently challenging. The observed countrate can be increased in the future by at least an order of magnitude by optimization and upgrading the optics and the detector. Under such conditions measurements on non enriched samples will be feasible. By taking advantage of the high penetration depth of the radiation at 89 keV [55] as well as of the simplicity of the experimental setup *operando* hyperfine interaction studies on real devices are now feasible. Our study opens a new field of research not only on ruthenium compounds with a variety of application, i.e. photocontrolled DNA binding in life sciences [30], energy harvesting using photovoltaic cells [31], energy storage in lithium-ion batteries [32], and ruthenium catalyst systems [56], but also on isotopes which have similar nuclear transition energies, ¹⁷⁶Hf (88.349(24) keV), ¹⁵⁶Gd (88.970(1) keV), and ¹⁶⁴Er (91.38(2) keV). Despite the expectedly low $f_{LM}$ in organometallic compounds, feasibility measurements on ruthenium nitrosyls already exist in literature [57] using conventional Mössbauer spectroscopy.
The European Synchrotron Radiation Facility is acknowledged for provision of synchrotron radiation beam time at the Nuclear Resonance beamline ID18. R.H. acknowledges the Helmholtz Association of German Research for funding (VH NG-407). A. M. acknowledges the Forschungszentrum Jülich for an international post-doc fellowship. We are grateful to Prof. F. E. Wagner for providing the $^{99}$Ru isotope. Dr. M. Sathiya and Prof. J.-M. Tarascon are gratefully acknowledged for the $^{99}$RuO$_2$ sample preparation. M. A. M acknowledges support from the Materials Sciences and Engineering Division, Office of Basic Energy Sciences, US Department of Energy (SrRuO$_3$ synthesis and characterization). We thank Mr. J.-P. Celse for technical assistance and Dr. Brian C. Sales for helpful discussions.

* Electronic address: bessas@esrf.fr

[1] J. B. Hastings, D. P. Siddons, U. van Bürck, R. Hollatz, and U. Bergmann, Phys. Rev. Lett. 66, 770 (1991).

[2] U. van Bürck, D. P. Siddons, J. B. Hastings, U. Bergmann, and R. Hollatz, Phys. Rev. B 46, 6207 (1992).

[3] P. Gütlich, E. Bill, and A. X. Trautwein, Mössbauer spectroscopy and Transition Metal Chemistry: Fundamentals and Applications (Springer, 2011).

[4] A. Q. R. Baron, A. I. Chumakov, H. F. Grünsteudel, H. Grünsteudel, L. Niesen, and R. Rüffer, Phys. Rev. Lett. 77, 4808 (1996).

[5] A. Q. Baron, Hyperfine Interact. 125, 29 (2000).

[6] E. Gerdau, Hyperfine Interact. 90, 301 (1994).

[7] T. Toellner, Hyperfine Interact. 125, 3 (2000).

[8] Y. V. Shvyd'ko, X-Ray Optics: High Energy-Resolution Applications (Springer, 2004).

[9] H.-C. Wille, R. P. Hermann, I. Sergueev, U. Pelzer, A. Möchel, T. Claudio, J. Perbon, R. Rüffer, A. Said, and Y. Shvyd'ko, EPL 91, 62001 (2010).

[10] H.-C. Wille, Y. V. Shvyd'ko, E. E. Alp, H. D. Rüter, O. Leupold, I. Sergueev, R. Rüffer, A. Barla, and J. P. Sanchez, Europhys. Lett. 74, 170 (2006).

[11] B. Klobes, A. Desmedt, I. Sergueev, K. Schmalzl, and R. P. Hermann, EPL 103, 36001 (2013).

[12] R. E. Simon, I. Sergueev, J. Persson, C. A. McCammon, F. Hatert, and R. P. Hermann, EPL 104, 17006 (2013).

[13] R. Röhlsberger, T. S. Toellner, W. Sturhahn, K. W. Quast, E. E. Alp, A. Bernhard, E. Burkel, O. Leupold, and E. Gerdau, Phys. Rev. Lett. 84, 1007 (2000).

[14] I. Sergueev, A. I. Chumakov, T. H. D. Beaume-Dang, R. Rüffer, C. Strohm, and U. van Bürck, Phys. Rev. Lett. 99, 097601 (2007).

[15] C.-J. Hsu, S. V. Prikhodko, C.-Y. Wang, L.-J. Chen, and G. P. Carman, Journal of Applied Physics 111, 111 (2012).

[16] X. Ren, X. Yan, P. Wang, Y. Li, S. Wang, F. Peng, L. Xiong, J. Liu, and D. He, High Pressure Research 34, 70 (2014).

[17] L. Li, Y. Wang, S. Xie, X.-B. Li, Y.-Q. Wang, R. Wu, H. Sun, S. Zhang, and H.-J. Gao, Nano Letters 13, 4671 (2013).

[18] Q. Zeng, J. Peng, A. R. Oganov, Q. Zhu, C. Xie, X. Zhang, D. Dong, L. Zhang, and L. Cheng, Phys. Rev. B 88, 214107 (2013).

[19] K. Konashi and M. Yamawaki, Advances in Applied Ceramics 111, 106 (2012).

[20] A. Callaghan, C. W. Moeller, and R. Ward, Inorg. Chem. 5, 1572 (1966).

[21] J. M. Longo, P. M. Raccah, and J. B. Goodenough, J. Appl. Phys. 39, 1327 (1968).

[22] SrRuO$_3$ was synthesized by heating a mixture of SrCO$_3$ and Ru powders at 1000°C. X-ray diffraction confirmed that the product was single phase SrRuO$_3$ (space group Pnma), and magnetization measurements showed the expected Curie temperature near 160 K.

[23] O. C. Kistner, Phys. Rev. 144, 1022 (1966).

[24] O. Kistner, S. Monaro, and R. Segnan, Phys. Lett. 5, 299 (1963).

[25] T. C. Gibb, R. Greatrex, N. N. Greenwood, and P. Kaspi, J. Chem. Soc. D pp. 319–320 (1971).

[26] M. De Marco, D. Graf, J. Rijssenbeek, R. J. Cava, D. Z. Wang, Y. Tu, Z. F. Ren, J. H. Wang, M. Haka, S. Toorongian, et al., Phys. Rev. B 60, 7570 (1999).

[27] W. Potzel, F. Wagner, R. Mössbauer, G. Kaindl, and H. Seltzer, Z. Phys. 241, 179 (1971).

[28] D. C. Foyt, M. Good, J. Cosgrove, and R. Collins, J. Inorg. Nucl. Chem. 37, 1913 (1975).

[29] Y. Kobayashi, J. Phys.: Conf. Ser. 217, 012023 (2010).

[30] F. Barragán, P. López-Senín, L. Salassa, S. Betanzos-Lara, A. Habtemariam, V. Moreno, P. J. Sadler, and V. Marchán, J. Am. Chem. Soc. 133, 14098 (2011).

[31] T. Kinoshita, J. T. Dy, S. Uchida, T. Kubo, and H. Segawa, Nat. Photon. 7, 535 (2013).

[32] M. Sathiya, G. Rousse, K. Ramesha, C. P. Laisa, H. Vezin, M. T. Sougrati, M.-L. Doublet, D. Foix, D. Gonbeau, W. Walker, et al., Nat. Mater. 12, 827 (2013).

[33] R. Rüffer and A. I. Chumakov, Hyperfine Interact. 97-98, 589 (1996).

[34] A. Snigirev, V. Kohn, I. Snigireva, and B. Lengeler, Nature 384, 49 (1996).

[35] T. Kibédi, T. Burrows, M. Trzhaskovskaya, P. Davidson, and C. N. Jr., Nucl. Instrum. and Methods Phys. Res., Sect A 589, 202 (2008).

[36] M. Seto, R. Masuda, S. Higashitaniguchi, S. Kitao, Y. Kobayashi, C. Inaba, T. Mitsui, and Y. Yoda, Phys. Rev. Lett. 102, 217602 (2009).

[37] A. Q. R. Baron, S. Kishimoto, J. Morse, and J.-M. Rigal, J. Synchrotron Rad. 13, 131 (2006).

[38] S. Kraft, J. Stümpel, P. Becker, and U. Kuetgens, Rev. of Sci. Instrum. 67, 681 (1996).

[39] E. Browne and J. Tuli, Nucl. Data Sheets 112, 275 (2011).

[40] The transmission of the 29.8 and the 89.6 kev radiation is 0.2% and 72%, respectively.

[41] O. C. Kistner, S. Monaro, and A. Schwarzschild, Phys. Rev. 137, B23 (1965).

[42] G. Kaindl, W. Potzel, F. Wagner, U. Zahn, and R. Mössbauer, Z. Physik 226, 103 (1969).

[43] Y. Kagan, A. M. Afanas'ev, and V. G. Kohn, J. Phys. C 12, 615 (1979).

[44] D. Singh and Y. P. Varshni, Acta Cryst. A 38, 854 (1982).

[45] M. Shankar Narayana, N. Gopi Krishna, and D. B. Sirdeshmukh, Acta Cryst. A 57, 217 (2001).

[46] Y. Shvyd'ko, Hyperfine Interact. 125, 173 (2000).

[47] W. Sturhahn, Hyperfine Interact. 125, 149 (2000).

[48] Supplementary material is available, which includes Refs. [43, 58–60].

[49] O. C. Kistner and A. H. Lumpkin, Phys. Rev. C 13, 1132 (1976).

[50] Y. V. Shvyd'ko, U. van Bürck, W. Potzel, P. Schindelmann, E. Gerdau, O. Leupold, J. Metge, H. D. Rüter, and G. V.
Smirnov, Phys. Rev. B **57**, 3552 (1998).

[51] B. C. Passenheim and D. C. McCollum, *J. Chem. Phys.* **51**, 320 (1969).

[52] O. Leupold, A. Chumakov, E. Alp, W. Sturhahn, and A. Baron, *Hyperfine Interact.* **123-124**, 611 (1999).

[53] M. DeMarco, G. Cao, J. E. Crow, D. Coffey, S. Toorongian, M. Haka, and J. Fridmann, *Phys. Rev. B* **62**, 14297 (2000).

[54] T. C. Gibb, R. Greatrex, N. N. Greenwood, D. C. Puxley, and K. G. Snowdon, *J. Solid State Chem.* **11**, 17 (1974).

[55] At 89 keV, 2 mm of steel has 50% transmission.

[56] I. Clausen, C.A. and M. Good, in *Mössbauer Effect Methodology*, edited by I. Gruverman and C. Seidel (Springer US, 1976), pp. 93–118.

[57] M. S. Goodman, M. J. DeMarco, M. S. Haka, S. A. Toorongian, and J. Fridmann, *J. Chem. Soc., Dalton Trans.* pp. 117–120 (2002).

[58] M. Blume and O. C. Kistner, *Phys. Rev.* **171**, 417 (1968).

[59] D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, *Quantum Theory of Angular Momentum* (World Scientific, 1988).

[60] R. Steffen and K. Alder, in *The Electromagnetic Interaction in Nuclear Spectroscopy*, edited by W. Hamilton (North-Holland, Amsterdam, 1975), pp. 505–583.