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

aA. 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 citationAltarelli, M. (2006). Resonant X-ray scattering: a theoretical introduction. Lecture Notes in Physics, Vol. 697, pp. 201–242. Heidelberg: Springer.Google Scholar
First citationArenholz, 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 citationArima, 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 citationAuthier, A. (2005). Dynamical Theory of X-ray Diffraction. Oxford University Press.Google Scholar
First citationAuthier, 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 citationBarois, 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 citationBeale, 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 citationBelyakov, V. A. (1975). Diffraction of Mössbauer gamma-radiation in crystals. Sov. Phys. Usp. 18, 267–299.Google Scholar
First citationBelyakov, V. A. & Aivazyan, Y. M. (1969). Quadrupole diffraction maxima in Mossbauer scattering. JETP Lett. 9, 393.Google Scholar
First citationBelyakov, V. A. & Dmitrienko, V. E. (1985). The blue phase of liquid crystals. Sov. Phys. Usp. 28, 535–562.Google Scholar
First citationBelyakov, V. A. & Dmitrienko, V. E. (1989). Polarisation phenomena in X-ray optics. Sov. Phys. Usp. 32, 697–719.Google Scholar
First citationBerestetskii, V. B., Lifshitz, E. M. & Pitaevskii, L. P. (1982). Quantum Electrodynamics. Oxford: Pergamon Press.Google Scholar
First citationBergevin, 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 citationBergevin, 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 citationBernhoeft, 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 citationBlume, M. (1985). Magnetic scattering of X-rays. J. Appl. Phys. 57, 3615–3618.Google Scholar
First citationBlume, 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 citationBrouder, C. (1990). Angular dependence of X-ray absorption spectra. J. Phys. Condens. Matter, 2, 701–738.Google Scholar
First citationBrunel, 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 citationCarra, P. & Thole, B. T. (1994). Anisotropic X-ray anomalous diffraction and forbidden reflections. Rev. Mod. Phys. 66, 1509–1515.Google Scholar
First citationCarra, 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 citationChampeney, D. C. (1979). The scattering of Mössbauer radiation by condensed matter. Rep. Prog. Phys. 42, 1017–1054.Google Scholar
First citationChen, 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 citationCollins, 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 citationCollins, 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 citationCollins, 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 citationCollins, 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 citationCracknell, A. P. (1975). Group Theory in Solid-State Physics. London: Taylor and Francis Ltd.Google Scholar
First citationCrooker, 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 citationDawson, 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 citationDetlefs, 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 citationDi Matteo, S., Joly, Y. & Natoli, C. R. (2005). Detection of electromagnetic multipoles by X-ray spectroscopies. Phys. Rev. B, 72, 144406.Google Scholar
First citationDmitrienko, V. E. (1983). Forbidden reflections due to anisotropic X-ray susceptibility of crystals. Acta Cryst. A39, 29–35.Google Scholar
First citationDmitrienko, V. E. (1984). Anisotropy of X-ray susceptibility and Bragg reflections in cubic crystals. Acta Cryst. A40, 89–95.Google Scholar
First citationDmitrienko, 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 citationEichhorn, 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 citationErskine, 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 citationFinkelstein, 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 citationGarcía, J. & Subías, G. (2004). The Verwey transition – a new perspective. J. Phys. Condens. Matter, 16, R145–R178.Google Scholar
First citationGarcía, 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 citationGibbs, 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 citationGleeson, 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 citationGoulon, 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 citationGoulon, 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 citationGoulon, 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 citationGukasov, 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 citationHagiwara, 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 citationHahn, Th. (2005). Editor. International Tables for Crystallography, Volume A, Space-Group Symmetry, 5th ed. Heidelberg: Springer.Google Scholar
First citationHannon, J. P., Trammell, G. T., Blume, M. & Gibbs, D. (1988). X-ray resonance exchange scattering. Phys. Rev. Lett. 61, 1245–1248.Google Scholar
First citationHart, 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 citationHill, J. P. & McMorrow, D. F. (1996). Resonant exchange scattering: polarization dependence and correlation function. Acta Cryst. A52, 236–244.Google Scholar
First citationHodeau, 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 citationInternational Tables for Crystallography (2004). Volume C, Mathematical, Physical and Chemical Tables, 3rd ed., edited by E. Prince. Dordrecht: Kluwer.Google Scholar
First citationInternational Tables for Crystallography (2008). Volume B, Reciprocal Space, 3rd ed., edited by U. Shmueli. Heidelberg: Springer.Google Scholar
First citationIshii, 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 citationJi, 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 citationJoly, 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 citationKim, 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 citationKirfel, 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 citationKirfel, A. & Petcov, A. (1991). Anisotropy of anomalous dispersion. An application to partial structure determination. Z. Kristallogr. 195, 1–15.Google Scholar
First citationKirfel, 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 citationKirfel, A., Petcov, A. & Eichhorn, K. (1991). Anisotropy of anomalous dispersion in X-ray diffraction. Acta Cryst. A47, 180–195.Google Scholar
First citationKokubun, 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 citationKolpakov, 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 citationLaan, 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 citationLaan, 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 citationLander, G. H. (2012). Resonant elastic X-ray scattering from 5f systems. Eur. Phys. J. Spec. Top. 208, 129–132.Google Scholar
First citationLovesey, 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 citationLovesey, S. W. & Collins, S. P. (1996). X-ray Scattering and Absorption by Magnetic Materials. Oxford: Clarendon Press.Google Scholar
First citationLovesey, 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 citationLovesey, 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 citationLuo, 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 citationMannix, 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 citationMarri, I. & Carra, P. (2004). Scattering operators for E1–E2 X-ray resonant diffraction. Phys. Rev. B, 69, 113101.Google Scholar
First citationMaterlik, G., Sparks, C. J. & Fischer, K. (1994). Editors. Resonant Anomalous X-ray Scattering. Theory and Applications. Amsterdam: North-Holland.Google Scholar
First citationMatsubara, 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 citationMazzoli, 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 citationMorgenroth, 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 citationMurakami, 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 citationNatoli, 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 citationNazarenko, 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 citationNye, J. F. (1985). Physical Properties of Crystals: Their Representation by Tensors and Matrices. Oxford University Press.Google Scholar
First citationOvchinnikova, 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 citationOvchinnikova, 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 citationPaolasini, 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 citationPaolasini, 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 citationPaolasini, 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 citationPartzsch, 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 citationPlatzman, 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 citationPrincep, 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 citationRenevier, 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 citationRogalev, 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 citationSchütz, 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 citationSeideman, T. (1990). The liquid-crystalline blue phases. Rep. Prog. Phys. 53, 659–705.Google Scholar
First citationSirotin, Y. & Shaskolskaya, M. P. (1982). Fundamentals of Crystal Physics. Moscow: Mir.Google Scholar
First citationStrange, P. (1994). Magnetic absorption dichroism and sum rules in itinerant magnets. J. Phys. Condens. Matter, 6, L491–L495.Google Scholar
First citationSubías, 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 citationTanaka, 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 citationTanaka, 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 citationTanaka, 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 citationTempleton, D. H. & Templeton, L. K. (1980). Polarized X-ray absorption and double refraction in vanadyl bisacetylacetonate. Acta Cryst. A36, 237–241.Google Scholar
First citationTempleton, 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 citationTempleton, D. H. & Templeton, L. K. (1985). Tensor X-ray optical properties of the bromate ion. Acta Cryst. A41, 133–142.Google Scholar
First citationTempleton, D. H. & Templeton, L. K. (1986). X-ray birefringence and forbidden reflections in sodium bromate. Acta Cryst. A42, 478–481.Google Scholar
First citationThole, 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 citationThole, 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 citationTonnere, 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 citationVeenendaal, M. van (2003). Resonant X-ray magnetic scattering at nonmagnetic ions. Phys. Rev. B, 67, 134112.Google Scholar
First citationVettier, C. (2001). Resonant X-ray scattering in transition metal and rare-earth materials. J. Electron Spectrosc. Relat. Phenom. 117, 113–128.Google Scholar
First citationVettier, C. (2012). Resonant elastic X-ray scattering: Where from? Where to? Eur. Phys. J. Spec. Top. 208, 3–14.Google Scholar
First citationWalker, 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 citationWright, D. C. & Mermin, N. D. (1989). Crystalline liquids: the blue phases. Rev. Mod. Phys. 61, 385–432.Google Scholar