International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2013). Vol. D. ch. 1.11, pp. 269-283
https://doi.org/10.1107/97809553602060000910

Chapter 1.11. Tensorial properties of local crystal susceptibilities

V. E. Dmitrienko,a* A. Kirfelb and E. N. Ovchinnikovac

a A. V. Shubnikov Institute of Crystallography, Leninsky pr. 59, Moscow 119333, Russia,bSteinmann Institut der Universität Bonn, Poppelsdorfer Schloss, Bonn, D-53115, Germany, and cFaculty of Physics, M. V. Lomonosov Moscow State University, Leninskie Gory, Moscow 119991, Russia
Correspondence e-mail:  dmitrien@crys.ras.ru

References

First citation Altarelli, M. (2006). Resonant X-ray scattering: a theoretical introduction. Lecture Notes in Physics, Vol. 697, pp. 201–242. Heidelberg: Springer.Google Scholar
First citation Arenholz, E., van der Laan, G., Chopdekar, R. V. & Suzuki, Y. (2006). Anisotropic X-ray magnetic linear dichroism at the Fe L2,3 edges in Fe3O4. Phys. Rev. B, 74, 094407.Google Scholar
First citation Arima, T., Jung, J.-H., Matsubara, M., Kubota, M., He, J.-P., Kaneko, Y. & Tokura, Y. (2005). Resonant magnetochiral X-ray scattering in LaFeO3: observation of ordering of toroidal moments. J. Phys. Soc. Jpn, 74, 1419–1422.Google Scholar
First citation Authier, A. (2005). Dynamical Theory of X-ray Diffraction. Oxford University Press.Google Scholar
First citation Authier, A. (2008). In International Tables for Crystallography, Volume B, Reciprocal Space, edited by U. Shmueli, 3rd ed., pp. 626–646. Heidelberg: Springer.Google Scholar
First citation Barois, P., Gleeson, H., Huang, C. & Pindak, R. (2012). Application of X-ray resonant diffraction to structural studies of liquid crystals. Eur. Phys. J. Spec. Top. 208, 333–350.Google Scholar
First citation Beale, T. A. W., Beutier, G., Bland, S. R., Bombardi, A., Bouchenoire, L., Bunau, O., Di Matteo, S., Fernández-Rodríguez, J., Hamann-Borrero, J. E., Herrero-Martin, J., Jacques, V. L. R., Johnson, R. D., Juhin, A., Matsumura, T., Mazzoli, C., Mulders, A. M., Nakao, H., Okamoto, J., Partzsch, S., Princep, A. J., Scagnoli, V., Strempfer, J., Vecchini, C., Wakabayashi, Y., Walker, H. C., Wermeille, D. & Yamasaki, Y. (2012). REXS contribution to electronic ordering investigation in solids. Eur. Phys. J. Spec. Top. 208, 89–98.Google Scholar
First citation Belyakov, V. A. (1975). Diffraction of Mössbauer gamma-radiation in crystals. Sov. Phys. Usp. 18, 267–299.Google Scholar
First citation Belyakov, V. A. & Aivazyan, Y. M. (1969). Quadrupole diffraction maxima in Mossbauer scattering. JETP Lett. 9, 393.Google Scholar
First citation Belyakov, V. A. & Dmitrienko, V. E. (1985). The blue phase of liquid crystals. Sov. Phys. Usp. 28, 535–562.Google Scholar
First citation Belyakov, V. A. & Dmitrienko, V. E. (1989). Polarisation phenomena in X-ray optics. Sov. Phys. Usp. 32, 697–719.Google Scholar
First citation Berestetskii, V. B., Lifshitz, E. M. & Pitaevskii, L. P. (1982). Quantum Electrodynamics. Oxford: Pergamon Press.Google Scholar
First citation Bergevin, F. de & Brunel, M. (1972). Observation of magnetic superlattice peaks by X-ray diffraction on an antiferromagnetic NiO crystal. Phys. Lett. A, 39, 141–142.Google Scholar
First citation Bergevin, F. de & Brunel, M. (1981). Diffraction of X-rays by magnetic materials. I. General formulae and measurements on ferro- and ferrimagnetic compounds. Acta Cryst. A37, 314–324.Google Scholar
First citation Bernhoeft, N., Paixao, J. A., Detlefs, C., Wilkins, S. B., Javorsky, P., Blackburn, E. & Lander, G. H. (2012). Resonant X-ray scattering from UAs0.8Se0.2: multi-k configurations. Phys. Rev. B, 69, 174415.Google Scholar
First citation Blume, M. (1985). Magnetic scattering of X-rays. J. Appl. Phys. 57, 3615–3618.Google Scholar
First citation Blume, M. (1994). Resonant X-ray diffraction and polarization analysis at the iron K-edge. In Resonant Anomalous X-ray Scattering. Theory and Applications, edited by G. Materlik, C. J. Sparks & K. Fischer, pp. 91–97. Amsterdam: North-Holland.Google Scholar
First citation Brouder, C. (1990). Angular dependence of X-ray absorption spectra. J. Phys. Condens. Matter, 2, 701–738.Google Scholar
First citation Brunel, M. & de Bergevin, F. (1981). Diffraction of X-rays by magnetic materials. II. Measurements on antiferromagnetic Fe2O3. Acta Cryst. A37, 324–331.Google Scholar
First citation Carra, P. & Thole, B. T. (1994). Anisotropic X-ray anomalous diffraction and forbidden reflections. Rev. Mod. Phys. 66, 1509–1515.Google Scholar
First citation Carra, P., Thole, B. T., Altarelli, M. & Wang, X. (1993). X-ray circular dichroism and local magnetic fields. Phys. Rev. Lett. 70, 694–697.Google Scholar
First citation Champeney, D. C. (1979). The scattering of Mössbauer radiation by condensed matter. Rep. Prog. Phys. 42, 1017–1054.Google Scholar
First citation Chen, C. T., Sette, F., Ma, Y. & Modesti, S. (1990). Soft X-ray magnetic circular dichroism at the L2,3 edges of nickel. Phys. Rev. B, 42, 7363–7265.Google Scholar
First citation Collins, S. & Bombardi, A. (2010). Resonant X-ray scattering and absorption. In Magnetism and Synchrotron Radiation, edited by E. Beaurepaire, H. Bulou, F. Scheurer & K. Jean-Paul. Springer Proceedings in Physics, Vol. 133, pp. 223–262. Berlin, Heidelberg: Springer.Google Scholar
First citation Collins, S., Lovesey, S. & Balcar, E. (2007). Dichroism and resonant diffraction in X-ray scattering by complex materials. J. Phys. Condens. Matter, 19, 213201.Google Scholar
First citation Collins, S. P., Laundy, D., Dmitrienko, V., Mannix, D. & Thompson, P. (2003). Temperature-dependent forbidden resonant X-ray scattering in zinc oxide. Phys. Rev. B, 68, 064110.Google Scholar
First citation Collins, S. P., Laundy, D., Tang, C. C. & Cernik, R. J. (1995). Magnetic X-ray powder diffraction from antiferromagnetic uranium oxide. J. Phys. Condens. Matter, 7, L223–L229.Google Scholar
First citation Cracknell, A. P. (1975). Group Theory in Solid-State Physics. London: Taylor and Francis Ltd.Google Scholar
First citation Crooker, P. P. (2001). Blue phases. In Chirality in Liquid Crystals, edited by H.-S. Kitzerow & C. Bahr, pp. 186–222. New York: Springer.Google Scholar
First citation Dawson, B. (1975). Studies of atomic charge density by X-ray and neutron diffraction – a perspective. In Advances in Structure Research by Diffraction Methods, Vol. 6, edited by W. Hoppe & R. Mason. Oxford: Pergamon Press.Google Scholar
First citation Detlefs, C., Sanchez del Rio, M. & Mazzoli, C. (2012). X-ray polarization: general formalism and polarization analysis. Eur. Phys. J. Spec. Top. 208, 359–371.Google Scholar
First citation Di Matteo, S., Joly, Y. & Natoli, C. R. (2005). Detection of electromagnetic multipoles by X-ray spectroscopies. Phys. Rev. B, 72, 144406.Google Scholar
First citation Dmitrienko, V. E. (1983). Forbidden reflections due to anisotropic X-ray susceptibility of crystals. Acta Cryst. A39, 29–35.Google Scholar
First citation Dmitrienko, V. E. (1984). Anisotropy of X-ray susceptibility and Bragg reflections in cubic crystals. Acta Cryst. A40, 89–95.Google Scholar
First citation Dmitrienko, V. E., Ishida, K., Kirfel, A. & Ovchinnikova, E. N. (2005). Polarization anisotropy of X-ray atomic factors and `forbidden' resonant reflections. Acta Cryst. A61, 481–493.Google Scholar
First citation Eichhorn, K. & Kirfel, A. (1988). Genaue Strukturuntersuchung mit Synchrotron Strahlung. II. Anisotropie der anomalen Dispersion in Cuprit, Cu2O. Z. Kristallogr. 185, 56–58.Google Scholar
First citation Erskine, J. L. & Stern, E. A. (1975). Calculation of the M23 magneto-optical absorption spectrum of ferromagnetic nickel. Phys. Rev. B, 12, 5016–5024.Google Scholar
First citation Finkelstein, K. D. & Dmitrienko, V. E. (2012). Resonant scattering techniques. In Characterization of Materials, edited by E. N. Kaufmann, pp. 1–15. New Jersey: John Wiley & Sons, Inc.Google Scholar
First citation García, J. & Subías, G. (2004). The Verwey transition – a new perspective. J. Phys. Condens. Matter, 16, R145–R178.Google Scholar
First citation García, J., Subías, G., Proietti, M. G., Renevier, H., Joly, Y., Hodeau, J. L., Blasco, J., Sánchez, M. C. & Bérar, J. F. (2000). Resonant forbidden reflections in magnetite. Phys. Rev. Lett. 85, 578–581.Google Scholar
First citation Gibbs, D., Harshmann, D. R., Isaacs, E. D., McWhan, D. B., Mills, D. & Vettier, C. (1988). Polarization and resonance properties of magnetic X-ray scattering in holmium. Phys. Rev. Lett. 61, 1241–1244.Google Scholar
First citation Gleeson, H. & Hirst, L. (2006). Resonant X-ray scattering: a tool for structure elucidation in liquid crystals. Chem. Phys. Chem. 7, 321–328.Google Scholar
First citation Goulon, J., Jaouen, N., Rogalev, A., Wilhelm, F., Goulon-Ginet, C., Brouder, C., Joly, Y., Ovchinnikova, E. N. & Dmitrienko, V. E. (2007). Vector part of optical activity probed with X-rays in hexagonal ZnO. J. Phys. Condens. Matter, 19, 156201.Google Scholar
First citation Goulon, J., Rogalev, A., Wilhelm, F., Goulon-Ginet, C. & Carra, P. (2002). X-ray magnetochiral dichroism: a new spectroscopic probe of parity nonconserving magnetic solids. Phys. Rev. Lett. 88, 237401.Google Scholar
First citation Goulon, J., Rogalev, A., Wilhelm, F., Goulon-Ginet, C., Carra, P., Marri, I. & Brouder, C. (2003). X-ray optical activity: application of sum rules. J. Exp. Theor. Phys. 97, 402–431.Google Scholar
First citation Gukasov, A. & Brown, P. J. (2010). Determination of atomic site susceptibility tensors from neutron diffraction data on polycrystalline samples. J. Phys. Condens. Matter, 22, 502201.Google Scholar
First citation Hagiwara, K., Kanazawa, M., Horie, K., Kokubun, J. & Ishida, K. (1999). Measurements of ATS scattering from magnetite near the Fe K-absorption edge in the temperature range 290 K–80 K. J. Phys. Soc. Jpn, 68, 1592–1597.Google Scholar
First citation Hahn, Th. (2005). Editor. International Tables for Crystallography, Volume A, Space-Group Symmetry, 5th ed. Heidelberg: Springer.Google Scholar
First citation Hannon, J. P., Trammell, G. T., Blume, M. & Gibbs, D. (1988). X-ray resonance exchange scattering. Phys. Rev. Lett. 61, 1245–1248.Google Scholar
First citation Hart, M. & Rodriques, A. R. D. (1981). Optical activity and the Faraday effect at X-ray frequencies. Philos. Mag. B, 43, 321–332.Google Scholar
First citation Hill, J. P. & McMorrow, D. F. (1996). Resonant exchange scattering: polarization dependence and correlation function. Acta Cryst. A52, 236–244.Google Scholar
First citation Hodeau, J.-L., Favre-Nicolin, V., Bos, S., Renevier, H., Lorenzo, E. & Bérar, J.-F. (2001). Resonant diffraction. Chem. Rev. 101, 1843–1867.Google Scholar
First citation International Tables for Crystallography (2004). Volume C, Mathematical, Physical and Chemical Tables, 3rd ed., edited by E. Prince. Dordrecht: Kluwer.Google Scholar
First citation International Tables for Crystallography (2008). Volume B, Reciprocal Space, 3rd ed., edited by U. Shmueli. Heidelberg: Springer.Google Scholar
First citation Ishii, K., Kuzushita, K., Murakami, Y., Haga, Y., Yamamoto, E. & Onuki, Y. (2006). Resonant magnetic X-ray scattering study of UPd2Al3. J. Phys. Soc. Jpn, 75S, 102–104.Google Scholar
First citation Ji, S., Song, C., Koo, J., Lee, K.-B., Park, Y. J., Kim, J. Y., Park, J.-H., Shin, H. J., Rhyee, J. S., Oh, B. H. & Cho, B. K. (2003). Interference of magnetic and ATS reflections in resonant X-ray scattering of GdB4. Phys. Rev. Lett. 91, 257205.Google Scholar
First citation Joly, Y., Di Matteo, S. & Bunau, O. (2012). Resonant X-ray diffraction: basic theoretical principles. Eur. Phys. J. Spec. Top. 208, 21–38.Google Scholar
First citation Kim, M. G., Kreyssig, A., Lee, Y. B., McQueeney, R. J., Harmon, B. N. & Goldman, A. I. (2011). Fe K-edge X-ray resonant magnetic scattering from Ba(Fe1−xCox)2As2 superconductors. Phys. Rev. B, 83, 134522.Google Scholar
First citation Kirfel, A. & Morgenroth, W. (1993). Anisotropy of anomalous scattering in X-ray diffraction. III. `Forbidden' axial reflections in space groups up to orthorhombic symmetry. Acta Cryst. A49, 35–45.Google Scholar
First citation Kirfel, A. & Petcov, A. (1991). Anisotropy of anomalous dispersion. An application to partial structure determination. Z. Kristallogr. 195, 1–15.Google Scholar
First citation Kirfel, A. & Petcov, A. (1992). Anisotropy of anomalous scattering in X-ray diffraction. II. Combining polarization-dependent transmission and diffraction, and an application to partial-structure analysis. Acta Cryst. A48, 247–259.Google Scholar
First citation Kirfel, A., Petcov, A. & Eichhorn, K. (1991). Anisotropy of anomalous dispersion in X-ray diffraction. Acta Cryst. A47, 180–195.Google Scholar
First citation Kokubun, J., Sawai, H., Uehara, M., Momozawa, N., Ishida, K., Kirfel, A., Vedrinskii, R. V., Novikovskii, N., Novakovich, A. A. & Dmitrienko, V. E. (2010). Pure dipole–quadrupole resonant scattering induced by the p–d hybridization of atomic orbitals in anatase TiO2. Phys. Rev. B, 82, 205206.Google Scholar
First citation Kolpakov, A. V., Bushuev, V. A. & Kuz'min, R. N. (1978). Dielectric permittivity in the X-ray region. Sov. Phys. Usp. 21, 959–977.Google Scholar
First citation Laan, G. van der, Arenholz, E., Chopdekar, R. V. & Suzuki, Y. (2008). Influence of crystal field on anisotropic X-ray magnetic linear dichroism at the Co2+ L2,3 edges. Phys. Rev. B, 77, 064407.Google Scholar
First citation Laan, G. van der, Thole, B. T., Sawatzky, G., Goedkoop, J. B., Fuggle, J. C., Esteva, J.-M., Karnatak, R., Remeika, J. P. & Dabkowska, H. A. (1986). Experimental proof of magnetic X-ray dichroism. Phys. Rev. B, 34, 6529–6531.Google Scholar
First citation Lander, G. H. (2012). Resonant elastic X-ray scattering from 5f systems. Eur. Phys. J. Spec. Top. 208, 129–132.Google Scholar
First citation Lovesey, S. W., Balcar, E., Knight, K. S. & Fernández-Rodríguez, J. (2005). Electronic properties of crystalline materials observed in X-ray diffraction. Phys. Rep. 411, 233–289.Google Scholar
First citation Lovesey, S. W. & Collins, S. P. (1996). X-ray Scattering and Absorption by Magnetic Materials. Oxford: Clarendon Press.Google Scholar
First citation Lovesey, S. W., Detlefs, C. & Rodríguez-Fernández, A. (2012). Neptunium multipoles and resonant X-ray Bragg diffraction by neptunium dioxide (NpO2). J. Phys. Condens. Matter, 24, 256009.Google Scholar
First citation Lovesey, S. W., Fernández-Rodríguez, J., Blanco, J. A., Sivia, D. S., Knight, K. S. & Paolasini, L. (2007). Vanadium magnetoelectric multipoles in V2O3. Phys. Rev. B, 75, 014409.Google Scholar
First citation Luo, J., Trammell, G. T. & Hannon, J. P. (1993). Scattering operator for elastic and inelastic resonant X-ray scattering. Phys. Rev. Lett. 71, 287–290.Google Scholar
First citation Mannix, D., Stunault, A., Bernhoeft, N., Paolasini, L., Lander, G. H., Vettier, C., de Bergevin, F., Kaczorowski, D. & Czopnik, A. (2001). Resonant enhancements at nonmagnetic ions: new possibilities for magneic X-ray scattering. Phys. Rev. Lett. 86, 4128–4131.Google Scholar
First citation Marri, I. & Carra, P. (2004). Scattering operators for E1–E2 X-ray resonant diffraction. Phys. Rev. B, 69, 113101.Google Scholar
First citation Materlik, G., Sparks, C. J. & Fischer, K. (1994). Editors. Resonant Anomalous X-ray Scattering. Theory and Applications. Amsterdam: North-Holland.Google Scholar
First citation Matsubara, M., Shimada, Y., Arima, T., Taguchi, Y. & Tokura, Y. (2005). Observation of nonreciprocal magnetoelectric X-ray scattering in magnetite. Phys. Rev. B, 72, 220404.Google Scholar
First citation Mazzoli, C., Fabrizi, F., Di Matteo, S., Paolasini, L., de Bergevin, F., Bombardi, A., Ghigna, P. & Caciuffo, R. (2007). Resonant magnetic X-ray scattering study of KCuF3. J. Magn. Magn. Mater. 310, 796–797.Google Scholar
First citation Morgenroth, W., Kirfel, A. & Fischer, K. (1994). Anisotropy of anomalous scattering in X-ray diffraction. 'Forbidden' axial reflections in tetragonal space groups. Z. Kristallogr. 209, 124–131.Google Scholar
First citation Murakami, Y., Kawada, H., Kawata, H., Tanaka, M., Arima, T., Moritomo, Y. & Tokura, Y. (1998). Direct observation of charge and orbital ordering in La0.5Sr1.5MnO4. Phys. Rev. Lett. 80, 1932–1935.Google Scholar
First citation Natoli, C. R., Brouder, C., Sainctavit, P., Goulon, J., Goulon-Ginet, C. & Rogalev, A. (1998). Calculation of X-ray natural circular dichroism. Eur. Phys. J. B, 4, 1–11.Google Scholar
First citation Nazarenko, E., Lorenzo, J. E., Joly, Y., Hodeau, J. L., Mannix, D. & Marin, C. (2006). Resonant X-ray diffraction studies on the charge ordering in magnetite. Phys. Rev. Lett. 97, 056403.Google Scholar
First citation Nye, J. F. (1985). Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford University Press.Google Scholar
First citation Ovchinnikova, E. N. & Dmitrienko, V. E. (1997). Combined effects of magnetic structure and local crystal fields in anisotropic X-ray anomalous scattering. Acta Cryst. A53, 388–395.Google Scholar
First citation Ovchinnikova, E. N. & Dmitrienko, V. E. (2000). Resonant X-ray scattering in the presence of several anisotropic factors. Acta Cryst. A56, 2–10.Google Scholar
First citation Paolasini, L. (2012). Magnetism in condensed matter: resonant and magnetic scattering by synchrotron radiation. In Italian School on Magnetism, Pavia 2012, pp. 1–83. Universita di Pavia.Google Scholar
First citation Paolasini, L., Caciuffo, R., Sollier, A., Ghigna, P. & Altarelli, M. (2002). Coupling between spin and orbital degrees of freedom in KCuF3. Phys. Rev. Lett. 88, 106403.Google Scholar
First citation Paolasini, L., Vettier, C., de Bergevin, F., Yakhou, F., Mannix, D., Stunault, A., Neubeck, W., Altarelli, M., Fabrizio, M., Metcalf, P. & Honig, J. (1999). Orbital occupancy order in V2O3: resonant X-ray scattering results. Phys. Rev. Lett. 82, 4718–4722.Google Scholar
First citation Partzsch, S., Wilkins, S. B., Schierle, E., Hamann-Borrero, J. E., Wadati, H., Soltwisch, V., Hill, J. P., Weschke, E., Souptel, D., Buchner, B. & Geck, J. (2012). Resonant soft X-ray scattering studies of multiferroic YMn2O5. Eur. Phys. J. Spec. Top. 208, 133–140.Google Scholar
First citation Platzman, P. M. & Tzoar, N. (1970). Magnetic scattering of X-rays from electrons in molecules and solids. Phys. Rev. B, 2, 3556–3559.Google Scholar
First citation Princep, A. J., Mulders, A. M., Staub, U., Scagnoli, V., Nakamura, T., Kikkawa, A., Lovesey, S. W. & Balcar, E. (2011). Triakontadipole and high-order dysprosium multipoles in the antiferromagnetic phase of DyB2C2. J. Phys. Condens. Matter, 23, 266002.Google Scholar
First citation Renevier, H., Joly, Y., García, J., Subías, G., Proietti, M. G., Hodeau, J. L. & Blasco, J. (2001). Diffraction anomalous fine structure of forbidden Bragg reflections: charge localization and structure of the octahedral site in magnetite. J. Synchrotron Rad. 8, 390–392.Google Scholar
First citation Rogalev, A., Wilhelm, F., Jaouen, N., Goulon, J. & Kappler, J.-P. (2006). X-ray magnetic circular dichroism: historical perspective and recent highlights. Lecture Notes in Physics, Vol. 697, pp. 71–89. Heidelberg: Springer.Google Scholar
First citation Schütz, G., Wagner, W., Wilhelm, W., Kenle, P., Zeller, R., Frahm, R. & Materlik, G. (1987). Absorption of circularly polarized X-rays in iron. Phys. Rev. Lett. 58, 737–740.Google Scholar
First citation Seideman, T. (1990). The liquid-crystalline blue phases. Rep. Prog. Phys. 53, 659–705.Google Scholar
First citation Sirotin, Y. & Shaskolskaya, M. P. (1982). Fundamentals of Crystal Physics. Moscow: Mir.Google Scholar
First citation Strange, P. (1994). Magnetic absorption dichroism and sum rules in itinerant magnets. J. Phys. Condens. Matter, 6, L491–L495.Google Scholar
First citation Subías, G., García, J., Blasco, J., Herrero-Martín, J., Sánchez, M. C., Orna, J. & Morellón, L. (2012). Structural distortion, charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X-ray scattering. J. Synchrotron Rad. 19, 159–173.Google Scholar
First citation Tanaka, Y., Collins, S. P., Lovesey, S. W., Matsumami, M., Moriwaki, T. & Shin, S. (2010). Determination of the absolute chirality of tellurium using resonant diffraction with circularly polarized X-rays. J. Phys. Condens. Matter, 22, 122201.Google Scholar
First citation Tanaka, Y., Kojima, T., Takata, Y., Chainani, A., Lovesey, S. W., Knight, K. S., Takeuchi, T., Oura, M., Senba, Y., Ohashi, H. & Shin, S. (2010). Determination of structural chirality of berlinite and quartz using resonant X-ray diffraction with circularly polarized X-rays. Phys. Rev. B, 81, 144104.Google Scholar
First citation Tanaka, Y., Takeuchi, T., Lovesey, S. W., Knight, K. S., Chainani, A., Takata, Y., Oura, M., Senba, Y., Ohashi, H. & Shin, S. (2008). Right handed or left handed? Forbidden X-ray diffraction reveals chirality. Phys. Rev. Lett. 100, 145502.Google Scholar
First citation Templeton, D. H. & Templeton, L. K. (1980). Polarized X-ray absorption and double refraction in vanadyl bisacetylacetonate. Acta Cryst. A36, 237–241.Google Scholar
First citation Templeton, D. H. & Templeton, L. K. (1982). X-ray dichroism and polarized anomalous scattering of the uranyl ion. Acta Cryst. A38, 62–67.Google Scholar
First citation Templeton, D. H. & Templeton, L. K. (1985). Tensor X-ray optical properties of the bromate ion. Acta Cryst. A41, 133–142.Google Scholar
First citation Templeton, D. H. & Templeton, L. K. (1986). X-ray birefringence and forbidden reflections in sodium bromate. Acta Cryst. A42, 478–481.Google Scholar
First citation Thole, B. T., Carra, P., Sette, F. & van der Laan, G. (1992). X-ray circular dichroism as a probe of orbital magnetization. Phys. Rev. Lett. 68, 1943–1946.Google Scholar
First citation Thole, B. T., van der Laan, G. & Sawatzky, G. (1986). Strong magnetic dichroism predicted in the M4,5 X-ray absorption spectra of magnetic rare-earth materials. Phys. Rev. Lett. 55, 2086–2088.Google Scholar
First citation Tonnere, J.-M. (1996). X-ray magnetic scattering. In Magnetism and Synchrotron Radiation. Lectures Notes, edited by E. Beaurepaire, B. Carriere & J.-P. Kappler, pp. 245–273. Mittelwihr: Les Editions de Physique.Google Scholar
First citation Veenendaal, M. van (2003). Resonant X-ray magnetic scattering at nonmagnetic ions. Phys. Rev. B, 67, 134112.Google Scholar
First citation Vettier, C. (2001). Resonant X-ray scattering in transition metal and rare-earth materials. J. Electron Spectrosc. Relat. Phenom. 117, 113–128.Google Scholar
First citation Vettier, C. (2012). Resonant elastic X-ray scattering: Where from? Where to? Eur. Phys. J. Spec. Top. 208, 3–14.Google Scholar
First citation Walker, H. C., McEwen, K. A., McMorrow, D. F., Bleckmann, M., Lee, J. G. P. S., Iga, F. & Mannix, D. (2009). X-ray resonant scattering study of the structural and magnetic transitions in PrB6. Phys. Rev. B, 79, 054402.Google Scholar
First citation Wright, D. C. & Mermin, N. D. (1989). Crystalline liquids: the blue phases. Rev. Mod. Phys. 61, 385–432.Google Scholar