- Open Access
Revealing charge anisotropies in metal compounds via high-purity x-ray polarimetry
Phys. Rev. Research 8, 023297 – Published 15 June, 2026
DOI: https://doi.org/10.1103/rj8d-86dj
Abstract
Linear polarization analysis of hard x-rays is employed to probe electronic anisotropies in metal-containing complexes with high selectivity. We use polarization-resolved nuclear forward scattering (PR-NFS) of synchrotron radiation at the 14.4 keV nuclear resonance of to determine electric field gradients (EFGs) in an iron(II) spin-crossover compound as they evolve during a temperature-dependent high-spin/low-spin transition. A pair of crossed Si(840) channel-cut crystals provides a high-purity x-ray polarimeter that suppresses the nonresonant background by nearly nine orders of magnitude and enables selective detection of nuclear resonant scattering. Using the spin-crossover complex as a model system, we determine the orientation of the EFG tensor in the high-spin and low-spin states and follow its reorientation across the gradual thermally driven spin transition. By choosing suitable sample orientations, the polarization selectivity enhances the signal of a high-spin minority fraction of a few percent at low temperature. It reveals that the high-spin EFG at 120 K is not randomly distributed and does not align with the dominant low-spin EFG when these high-spin centers form a minority phase embedded in a low-spin matrix. The combination of PR-NFS with dynamical NFS simulations and density-functional calculations thus provides a sensitive, element- and site-selective method to quantify electronic anisotropies and their changes across phase transitions in Mössbauer-active metal compounds.
Physics Subject Headings (PhySH)
Article Text
References (46)
- C. Kramer, A. Spinn, and K. R. Liedl, Charge anisotropy: Where atomic multipoles matter most, J. Chem. Theory Comput. 10, 4488 (2014).
- B. Nordén, A. Rodger, and T. Dafforn, Linear Dichroism and Circular Dichroism (The Royal Society of Chemistry, Cambridge, 2010).
- D. Che, D. B. Shapiro, R. M. Esquerra, and D. S. Kliger, Ultrasensitive time-resolved linear dichroism spectral measurements using near-crossed linear polarizers, Chem. Phys. Lett. 224, 145 (1994).
- J. Réhault, V. Zanirato, M. Olivucci, and J. Helbing, Linear dichroism amplification: Adapting a long-known technique for ultrasensitive femtosecond IR spectroscopy, J. Chem. Phys. 134, 124516 (2011).
- G. van der Laan, B. T. Thole, G. A. Sawatzky, J. B. Goedkoop, J. C. Fuggle, J.-M. Esteva, R. Karnatak, J. P. Remeika, and H. A. Dabkowska, Experimental proof of magnetic X-ray dichroism, Phys. Rev. B 34, 6529 (1986).
- G. Schütz, W. Wagner, W. Wilhelm, P. Kienle, R. Zeller, R. Frahm, and G. Materlik, Absorption of circularly polarized X-rays in iron, Phys. Rev. Lett. 58, 737 (1987).
- S. Lovesey and S. Collins, X-ray Scattering and Absorption by Magnetic Materials, Oxford Series on Synchrotron Radiation (Clarendon Press, Oxford, 1996).
- J. Stöhr and H. C. Siegmann, Magnetism (Springer, Berlin, 2006).
- K. Szymański, Polarized radiation in Mössbauer spectroscopy, Phys. Rep. 423, 295 (2006).
- T. Mitsui, Y. Imai, R. Masuda, M. Seto, and K. Mibu, polarization-dependent synchrotron Mössbauer-spectroscopy using a diamond phase plate and an iron borate nuclear Bragg-monochromator, J. Synchrotron Radiat. 22, 427 (2015).
- M. A. Andreeva, R. A. Baulin, O. V. Slinko, L. Häggström, V. E. Asadchikov, D. N. Karimov, B. S. Roshchin, D. A. Ponomarev, L. N. Romashev, A. I. Chumakov, D. Bessas, and R. Rüffer, Polarization selection in Mössbauer reflectivity for magnetic multilayer investigation, J. Phys.: Conf. Ser. 1389, 012016 (2019).
- B. Marx, K. S. Schulze, I. Uschmann, T. Kämpfer, R. Lötzsch, O. Wehrhan, W. Wagner, C. Detlefs, T. Roth, J. Härtwig, E. Förster, T. Stöhlker, and G. G. Paulus, High-precision X-ray polarimetry, Phys. Rev. Lett. 110, 254801 (2013).
- B. Marx-Glowna, I. Uschmann, K. S. Schulze, H. Marschner, H.-C. Wille, K. Schlage, T. Stöhlker, R. Röhlsberger, and G. G. Paulus, Advanced X-ray polarimeter design for nuclear resonant scattering, J. Synchrotron Radiat. 28, 120 (2021).
- K. S. Schulze, Fundamental limitations of the polarization purity of X-rays, APL Photon. 3, 126106 (2018).
- D. P. Siddons, M. Hart, Y. Amemiya, and J. B. Hastings, X-ray optical activity and the Faraday effect in cobalt and its compounds, Phys. Rev. Lett. 64, 1967 (1990).
- M. Hart, D. P. Siddons, Y. Amemiya, and V. Stojanoff, Tunable X‐ray polarimeters for synchrotron radiation sources, Rev. Sci. Instrum. 62, 2540 (1991).
- A. T. Schmitt, Y. Joly, K. S. Schulze, B. Marx-Glowna, I. Uschmann, B. Grabiger, H. Bernhardt, R. Loetzsch, A. Juhin, J. Debray, H.-C. Wille, H. Yavas, G. G. Paulus, and R. Röhlsberger, Disentangling X-ray dichroism and birefringence via high-purity polarimetry, Optica 8, 56 (2021).
- T. S. Toellner, E. E. Alp, W. Sturhahn, T. M. Mooney, X. Zhang, M. Ando, Y. Yoda, and S. Kikuta, Polarizer/analyzer filter for nuclear resonant scattering of synchrotron radiation, Appl. Phys. Lett. 67, 1993 (1995).
- D. Siddons, J. Hastings, U. Bergmann, F. Sette, and M. Krisch, Mössbauer spectroscopy using synchrotron radiation: Overcoming detector limitations, Nucl. Instrum. Methods Phys. Res. Sect. B 103, 371 (1995).
- R. Röhlsberger, E. Gerdau, R. Rüffer, W. Sturhahn, T. Toellner, A. Chumakov, and E. Alp, X-ray optics for -resolved spectroscopy, Nucl. Instrum. Methods Phys. Res. Sect. A 394, 251 (1997).
- E. Alp, W. Sturhahn, and T. Toellner, Polarizer–analyzer optics, Hyperfine Interact. 125, 45 (2000).
- K. P. Heeg, H.-C. Wille, K. Schlage, T. Guryeva, D. Schumacher, I. Uschmann, K. S. Schulze, B. Marx, T. Kämpfer, G. G. Paulus, R. Röhlsberger, and J. Evers, Vacuum-assisted generation and control of atomic coherences at X-Ray energies, Phys. Rev. Lett. 111, 073601 (2013).
- J. Haber, K. S. Schulze, K. Schlage, R. Loetzsch, L. Bocklage, T. Gurieva, H. Bernhardt, H.-C. Wille, R. Rüffer, I. Uschmann, G. G. Paulus, and R. Röhlsberger, Collective strong coupling of X-rays and nuclei in a nuclear optical lattice, Nat. Photon. 10, 445 (2016).
- B. Marx-Glowna, B. Grabiger, R. Lötzsch, I. Uschmann, A. T. Schmitt, K. S. Schulze, A. Last, T. Roth, S. Antipov, H.-P. Schlenvoigt, I. Sergueev, O. Leupold, R. Röhlsberger, and G. G. Paulus, Scanning high-sensitive X-ray polarization microscopy, New J. Phys. 24, 053051 (2022).
- R. Röhlsberger, Nuclear Condensed Matter Physics with Synchrotron Radiation, Springer Tracts in Modern Physics (Springer-Verlag, Berlin, 2004), Vol. 208.
- P. Gütlich, A. Hauser, and H. Spiering, Thermal and optical switching of iron(II) complexes, Angew. Chem. Int. Ed. Engl. 33, 2024 (1994).
- O. Kahn and C. J. Martinez, Spin-transition polymers: From molecular materials toward memory devices, Science 279, 44 (1998).
- P. Gütlich and H. A. Goodwin, Spin crossover—An overall perspective, in Spin Crossover in Transition Metal Compounds I, edited by P. Gütlich and H. Goodwin (Springer, Berlin, 2004), pp. 1–47.
- M. Halcrow, Spin-Crossover Materials: Properties and Applications (Wiley, Chichester, 2013).
- T. G. Gopakumar, F. Matino, H. Naggert, A. Bannwarth, F. Tuczek, and R. Berndt, Electron-induced spin crossover of single molecules in a bilayer on gold, Angew. Chem. Int. Ed. 51, 6262 (2012).
- E. Ruiz, Charge transport properties of spin crossover systems, Phys. Chem. Chem. Phys. 16, 14 (2014).
- N. Baadji and S. Sanvito, Giant resistance change across the phase transition in spin-crossover molecules, Phys. Rev. Lett. 108, 217201 (2012).
- J.-F. Létard, G. Chastanet, O. Nguyen, S. Marcén, M. Marchivie, P. Guionneau, D. Chasseau, and P. Gütlich, Spin crossover properties of the complex—Phases I and II, Monatsh. Chem. 134, 165 (2003).
- W. Nicolazzi and A. Bousseksou, Thermodynamical aspects of the spin crossover phenomenon, C. R. Chim. 21, 1060 (2018).
- http://photon-science.desy.de/facilities/petra_iii/beamlines/p01_dynamics/index_eng.html.
- S. Rackwitz, I. Faus, M. Schmitz, H. Kelm, H.-J. Krüger, K. K. Andersson, H.-P. Hersleth, K. Achterhold, K. Schlage, H.-C. Wille, V. Schünemann, and J. A. Wolny, A new sample environment for cryogenic nuclear resonance scattering experiments on single crystals and microsamples at P01, PETRA III, Hyperfine Interact. 226, 673 (2014).
- M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, et al., Gaussian 09 Revision E.01, Gaussian Inc., Wallingford, CT, 2009.
- W. Sturhahn, CONUSS and PHOENIX: Evaluation of nuclear resonant scattering data, Hyperfine Interact. 125, 149 (2000).
- CONUSS is free software. It can be obtained via the software site http://www.nrixs.com.
- DFT calculations were performed using Gaussian09 [37] with the functional B3LYP and the basis CEP-31G. We used a model molecule (shown in Fig. 3) with one of the rings of biphenyl replaced with hydrogen in order to approximate the molecule with symmetry (compare with Fig. 5).
- L. Scherthan, Polarimetrie mit resonanter Kernstreuung, Diploma Thesis, Technische Universität Kaiserslautern, Fachbereich Physik, 2016.
- M. Gerharz, W. Hippler, B. Marx-Glowna, S. Sadashivaiah, K. S. Schulze, I. Uschmann, R. Lötzsch, K. Schlage, S. Velten, D. Lentrodt, et al., Single-shot sorting of Mössbauer time-domain data at X-ray free electron lasers, arXiv:2509.15833.
- J.-F. Létard, P. Guionneau, L. Rabardel, J. A. K. Howard, A. E. Goeta, D. Chasseau, and O. Kahn, Structural, magnetic, and photomagnetic studies of a mononuclear iron(ii) derivative exhibiting an exceptionally abrupt spin transition. Light-induced thermal hysteresis phenomenon, Inorg. Chem. 37, 4432 (1998).
- J. Hannon and G. Trammell, Coherent -ray optics, Hyperfine Interact. 123, 127 (1999).
- D. Siddons, U. Bergmann, and J. Hastings, Polarization effects in resonant nuclear scattering, Hyperfine Interact. 123, 681 (1999).
- H. P. Gunnlaugsson, Spreadsheet based analysis of Mössbauer spectra, Hyperfine Interact. 237, 79 (2016).