Abstract
After being a dormant field of research, Quantum Magnetism gained a renewed interest following the discovery of high-temperature superconductivity in the cuprate compounds family by Bednorz and Müller (1986) and the gigantic challenge it poses to the condensed matter physics community.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ament, Luuk J. P. et al. (2009). “Theoretical Demonstration of How the Dispersion of Magnetic Excitations in Cuprate Compounds can be Determined Using Resonant Inelastic X-Ray Scattering”. In: Physical Review Letters 103.11, p. 117003. DOI:10.1103/PhysRevLett.103.117003. URL:http://link.aps.org/doi/10.1103/PhysRevLett.103.117003 (visited on 09/09/2010).
Anderson, P.W. (1952). “An Approximate QuantumTheory of the Antiferromagnetic Ground State”. In: Physical Review 86.5, pp. 694–701. DOI:10.1103/PhysRev.86.694. URL:http://link.aps.org/doi/10.1103/PhysRev.86.694 (visited on 04/24/2012)
Anderson, P.W. (1987). “The Resonating Valence Bond State in La2CuO4 and Superconductivity”. In: Science 235.4793, pp. 1196–1198. DOI:10.1126/science.235.4793.1196. URL: http://www.sciencemag.org/content/235/4793/1196.abstract (visited on 01/10/2011).
Bednorz, J. G. and K. A. Müller (1986). “Possible highT c superconductivity in the Ba-La-Cu-O system”. en. In: Zeitschrift für Physik B Condensed Matter 64.2, pp. 189–193. ISSN: 0722–3277, pp. 1431–584X, DOI:10.1007/BF01303701. URL: http://link.springer.com/article/10.1007/BF01303701 (visited on 08/15/2013)
Bloch, F. (1930). “Zur Theorie des Ferromagnetismus”. de. In: Zeitschrift für Physik 61.3–4, pp. 206–219. ISSN, pp. 0044–3328, DOI:10.1007/BF01339661. URL: http://link.springer.com/article/10.1007/BF01339661 (visited on 11/12/2013)
Canali, C.M. and S. M. Girvin (1992). “Theory of Raman scattering in layered cuprate materials”. In: Physical Review B 45.13, pp. 7127–7160. DOI: 10.1103/PhysRevB.45.7127. URL: http://link.aps.org/doi/10.1103/PhysRevB.45.7127 (visited on 08/19/2013)
Chang, J. et al. (2008). “Anisotropic quasiparticle scattering rates in slightly underdoped to optimally doped high-temperature La\(_{2-x}\) superconductors”. In: Physical Review B 78.20, p. 205103. DOI:10.1103/PhysRevB.78.205103. URL: http://link.aps.org/doi/10.1103/PhysRevB.78.205103 (visited on 08/16/2013)
Christensen, N. B. et al. (2007). “Quantumdynamics and entanglement of spins on a square lattice”. In: Proceedings of the National Academy of Sciences 104.39, pp. 15264–15269. DOI: 10.1073/pnas.0703293104. URL: http://www.pnas.org/content/104/39/15264.abstract (visited on 09/28/2010)
Chuang, Y.-D. et al. (2004). “Bilayer splitting and coherence effects in optimal and underdoped \({\rm Bi}_{2}{\rm Sr}_{2}{\rm CaCu}_{2}{\rm O}_{8+\delta }\). In: Physical Review B 69.9, p. 094515. DOI:10.1103/PhysRevB.69.094515. URL: http://link.aps.org/doi/10.1103/PhysRevB.69.094515 (visited on 08/20/2013)
Coldea, R. et al. (2001). “Spin Waves and Electronic Interactions in La\(_{2}\)”. In: Physical Review Letters 86.23, p. 5377. DOI:10.1103/PhysRevLett.86.5377. URL: http://link.aps.org/doi/10.1103/PhysRevLett. 86.5377 (visited on 10/04/2010)
Dagotto, Elbio (1994). “Correlated electrons in high-temperature superconductors”. In: Reviews of Modern Physics 66.3, pp. 763–840. DOI:10.1103/RevModPhys.66.763. URL: http://link.aps.org/doi/10.1103/RevModPhys.66.763 (visited on 08/15/2013)
Dalla Piazza, B. et al. (2012). “Unified one-band Hubbard model for magnetic and electronic spectra of the parent compounds of cuprate superconductors”. In: Physical Review B 85.10, p. 100508. DOI: 10.1103/PhysRevB.85.100508. URL: http://link.aps.org/doi/10.1103/PhysRevB.85.100508 (visited on 07/11/2013)
Damascelli, Andrea, Zahid Hussain, and Zhi-Xun Shen (2003). “Angle-resolved photoemission studies of the cuprate superconductors”. In: Reviews of Modern Physics 75.2, pp. 473–541. DOI:10.1103/RevModPhys.75.473. URL: http://link.aps.org/doi/10.1103/RevModPhys.75.473 (visited on 08/15/2013)
Delannoy, J.-Y. P. et al. (2009). “Low-energy theory of the t -t\(^{\prime }\)”. In: Physical Review B 79.23, p. 235130. DOI:10.1103/PhysRevB.79.235130. URL: http://link.aps.org/doi/10.1103/PhysRevB.79.235130 (visited on 10/04/2010)
Devereaux, Thomas P. and Rudi Hackl (2007). “Inelastic light scattering from correlated electrons”. In: Reviews of Modern Physics 79.1, pp. 175-233. DOI:10.1103/RevModPhys.79.175. URL: http://link.aps.org/doi/10.1103/RevModPhys.79.175 (visited on 08/19/2013).
Einstein, A. (1905). “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt”. In: Annalen der Physik 322, pp. 132–148. ISSN, pp. 0003–3804, DOI: 10.1002/andp.19053220607. URL: http://adsabs.harvard.edu/abs/1905AnP...322.132E (visited on 11/11/2013)
Ellis, D. S. et al. (2010). “Magnetic nature of the 500 meV peak in \({\rm La}_{2-x}{\rm Sr}_{x}{\rm CuO}_{4}\) observed with resonant inelastic x-ray scattering at the Cu K-edge”. In: Physical Review B 81.8, p. 085124. DOI:10.1103/PhysRevB.81.085124. URL: http://link.aps.org/doi/10.1103/PhysRevB.81.085124 (visited on 09/06/2013)
Emery, V. J. (1987). “Theory of high-Tc superconductivity in oxides”. In: Physical Review Letters 58.26, pp. 2794–2797. DOI:10.1103/PhysRevLett.58.2794 .URL: http://link.aps.org/doi/10.1103/PhysRevLett.58.2794 (visited on 11/11/2013)
Eskes, H., G.A. Sawatzky, and L.F. Feiner (1989). “Effective transfer for singlets formed by hole doping in the high-Tc superconductors”. In: Physica C: Superconductivity 160.5–6, pp. 424–430. ISSN: 0921-4534. DOI:10.1016/0921-4534(89)90415-2. URL: http://www.sciencedirect.com/science/article/pii/0921453489904152 (visited on 09/03/2013).
Feynman, R. P. (1939). “Forces in Molecules”. In: Physical Review 56.4, pp. 340–343. DOI:10.1103/PhysRev.56.340. URL: http://link.aps.org/doi/10.1103/PhysRev.56.340 (visited on 11/12/2013)
Forte, Filomena, Luuk J. P. Ament, and Jeroen van den Brink (2008). “Magnetic excitations in La\(_{2}\) probed by indirect resonant inelastic x-ray scattering”. In: Physical Review B 77.13, p. 134428. DOI: 10.1103/PhysRevB.77.134428. URL: http://link.aps.org/doi/10.1103/PhysRevB.77.134428 (visited on 08/19/2013)
Graf, J. et al. (2007). “Universal High Energy Anomaly in the Angle-Resolved Photoemission Spectra of High Temperature Superconductors: Possible Evidence of Spinon and Holon Branches”. In: Physical Review Letters 98.6, p. 067004. DOI:10.1103/PhysRevLett.98.067004. URL: http://link.aps.org/doi/10.1103/PhysRevLett. 98.067004 (visited on 08/16/2013)
Guarise, M (2012). “Electronic and Magnetic Resonant Inelastic X-ray Study of Cuprates”. PhD thesis. École Polytechnique Fédérale de Lausanne. DOI: 10.5075/epfl-thesis-5519. URL: http://infoscience.epfl.ch/record/181539
Guarise, M. et al. (2010). “Measurement of Magnetic Excitations in the Two-Dimensional Antiferromagnetic Sr\(_{2}\) Insulator Using Resonant X-Ray Scattering: Evidence for Extended Interactions”. In: Physical Review Letters 105.15, p. 157006. DOI:10.1103/PhysRevLett.105.157006. URL: http://link.aps.org/doi/10.1103/PhysRevLett. 105.157006 (visited on 08/16/2013)
Haverkort, M.W. (2010). “Theory of Resonant Inelastic X-Ray Scattering by CollectiveMagnetic Excitations”. In: Physical Review Letters 105.16, p. 167404. DOI:10.1103/PhysRevLett.105.167404. URL: http://link.aps.org/doi/10.1103 /PhysRevLett.105.167404 (visited on 12/11/2012)
Headings, N. S. et al. (2010). “AnomalousHigh-Energy Spin Excitations in theHigh-Tc Superconductor-Parent Antiferromagnet La\(_{2}\)”. In: Physical Review Letters 105.24, p. 247001. DOI: 10.1103/PhysRevLett.105.247001. URL: http://link.aps.org/doi/10.1103/PhysRevLett.105.247001 (visited on 01/10/2011)
Hirsch, J. E. (1985). “Two-dimensional Hubbard model: Numerical simulation study”. In:Physical Review B 31.7, pp. 4403–4419. DOI:10.1103/PhysRevB.31.4403. URL: http://link.aps.org/doi/10.1103/PhysRevB.31.4403 (visited on 11/11/2013).
Ho, Chang-Ming et al. (2001). “Nature of Spin Excitations in Two-DimensionalMott Insulators: Undoped Cuprates andOtherMaterials”. In: Physical Review Letters 86.8, pp. 1626–1629. DOI:10.1103/PhysRevLett.86.1626. URL: http://link.aps.org/doi/10.1103/PhysRevLett.86.1626 (visited on 07/17/2013).
Holstein, T. and H. Primakoff (1940). “FieldDependence of the IntrinsicDomainMagnetization of a Ferromagnet”. In: Physical Review 58.12, pp. 1098–1113. DOI:10.1103/PhysRev.58.1098. URL: http://link.aps.org/doi/10.1103/PhysRev.58.1098 (visited on 11/12/2013)
Hybertsen, Mark S. et al. (1990). “Renormalization from density-functional theory to strongcoupling models for electronic states in Cu-O materials”. In: Physical Review B 41.16, pp. 11068–11072. DOI: 10.1103/PhysRevB.41.11068. URL: http://link.aps.org/doi/10.1103/PhysRevB.41.11068 (visited on 09/03/2013)
Inosov, D. S. et al. (2007). “Momentum and Energy Dependence of the Anomalous High-Energy Dispersion in the Electronic Structure of High Temperature Superconductors”. In: Physical Review Letters 99.23, p. 237002. DOI:10.1103/PhysRevLett.99.237002. URL: http://link.aps.org/doi/10.1103/PhysRevLett.99.237002 (visited on 08/16/2013)
Katanin, A. A. and A. P. Kampf (2003). “Theoretical analysis ofmagnetic Raman scattering in La\(_{2}\): Two-magnon intensity with the inclusion of ring exchange”. In: Physical Review B 67.10, p. 100404. DOI:10.1103/PhysRevB.67.100404. URL: http://link.aps.org/doi/10.1103/PhysRevB.67.100404 (visited on 08/19/2013)
Kubo, Ryogo (1952). “The Spin-Wave Theory of Antiferromagnetics”. In: Physical Review 87.4, pp. 568–580. DOI:10.1103/PhysRev.87.568. URL: http://link.aps.org/doi/10.1103/PhysRev.87.568 (visited on 07/11/2013)
LaRosa, S. et al. (1997). “Electronic structure of CuO\(_{2}\) planes: From insulator to superconductor”. In: Physical Review B 56.2, pp. R525–R528, DOI:10.1103/PhysRevB.56.R525. URL: http://link.aps.org/doi/10.1103/PhysRevB.56.R525 (visited on 08/16/2013)
Lee, Patrick A., Naoto Nagaosa, and Xiao-GangWen (2006). “Doping aMott insulator: Physics of high-temperature superconductivity”. In: Reviews of Modern Physics 78.1, p. 17. DOI:10.1103/RevModPhys.78.17. URL: http://link.aps.org/doi/10.1103/RevModPhys.78.17 (visited on 09/16/2010)
Lorenzana, J., G. Seibold, and R. Coldea (2005). “Sum rules and missing spectral weight in magnetic neutron scattering in the cuprates”. In: Physical Review B 72.22, p. 224511. DOI:10.1103/PhysRevB.72.224511. URL: http://link.aps.org/doi/10.1103/PhysRevB.72.224511 (visited on 08/20/2013)
Lu, Donghui et al. (2012). “Angle-Resolved Photoemission Studies of Quantum Materials”. In: Annual Review of Condensed Matter Physics 3.1, pp. 129–167. DOI: 10.1146/annurevconmatphys-020911-125027. URL: http://www.annualreviews.org/doi/abs/10.1146/annurev-conmatphys-020911-125027 (visited on 11/27/2013)
MacDonald, A. H., S. M. Girvin, and D. Yoshioka (1988). “t/U expansion for the Hubbard model”. In: Physical Review B 37.16, p. 9753. DOI: 10.1103/PhysRevB.37.9753. URL: http://link.aps.org/doi/10.1103/PhysRevB.37.9753 (visited on 10/04/2010)
Manousakis, Efstratios (1991). “The spin-12 Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides”. In: Reviews of Modern Physics 63.1, pp. 1–62. DOI: 10.1103/RevModPhys.63.1. URL: http://link.aps.org/doi/10.1103/RevModPhys.63.1 (visited on 09/19/2013)
Matsukawa, Hiroshi and Hidetoshi Fukuyama (1989a). “Effective Hamiltonian for High-Tc Cu Oxides”. In: Journal of the Physical Society of Japan 58.8, pp. 2845–2866. DOI:10.1143/JPSJ.58.2845. URL: http://jpsj.ipap.jp/link?JPSJ/58/2845/ (visited on 09/03/2013).
Matsukawa, Hiroshi and Hidetoshi Fukuyama (1989b). “Local Singlet State in Effective Hamiltonian for a CuO\(_{2}\) Layer: Case of a Single Cu Spin and a Hole”. In: Journal of the Physical Society of Japan 58.10, pp. 3687–3697. DOI: 10.1143/JPSJ.58.3687. URL: http://jpsj.ipap.jp/link?JPSJ/58/3687/ (visited on 09/03/2013)
Mourigal, Martin et al. (2013). “Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain”. en. In: Nature Physics 9.7, pp. 435–441. ISSN, pp. 1745–2473, DOI: 10.1038/nphys2652. URL: http://www.nature.com/nphys/journal/v9/n7/full/nphys2652.html (visited on 08/20/2013)
Muller, J. (1980). “A15-type superconductors”. en. In: Reports on Progress in Physics 43.5, p. 641. ISSN, pp. 0034–4885, DOI:10.1088/0034-4885/43/5/003. URL: http://iopscience.iop.org/0034-4885/43/5/003 (visited on 08/15/2013)
Nomura, Takuji and Jun-ichi Igarashi (2005). “Analysis of resonant inelastic x-ray scattering in La\(_{2}\)”. In: Physical Review B 71.3, p. 035110. DOI: 10.1103/PhysRevB.71.035110. URL: http://link.aps.org/doi/10.1103/PhysRevB.71.035110 (visited on 08/19/2013).
Norman, M. R. et al. (1999). “Extraction of the electron self-energy from angle-resolved photoemission data: Application to Bi\(_{2}\)Sr\(_{2}\)CaCu\(_{2}\)O\(_{8+x}\)”. In: Physical Review B 60.10, pp. 7585–7590. DOI: 10.1103/PhysRevB.60.7585. URL: http://link.aps.org/doi/10.1103/PhysRevB.60.7585 (visited on 11/28/2013)
Ronning, F. et al. (2005). “Anomalous high-energy dispersion in angle-resolved photoemission spectra from the insulating cuprate Ca\(_{2}\)”. In: Physical Review B 71.9, p. 094518. DOI:10.1103/PhysRevB.71.094518. URL: http://link.aps.org/doi/10.1103/PhysRevB.71.094518 (visited on 08/16/2013)
Scalapino, D. J. (2012). “A common thread: The pairing interaction for unconventional superconductors”. In: Reviews of Modern Physics 84.4, pp. 1383–1417. DOI: 10.1103/RevModPhys.84.1383. URL: http://link.aps.org/doi/10.1103/RevModPhys.84.1383 (visited on 11/25/2012)
Schilling, A. et al. (1993). “Superconductivity above 130 K in the Hg-Ba-Ca-Cu-O system”. en. In: Nature 363.6424, pp. 56–58. DOI: 10.1038/363056a0. URL: http://www.nature.com/nature/journal/v363/n6424/abs/363056a0.html (visited on 08/15/2013)
Tanamoto, Tetsufumi, Hiroshi Kohno, and Hidetoshi Fukuyama (1993). “Magnetic Properties of Extended t-J Model. I. Static Properties”. In: Journal of the Physical Society of Japan 62.2, pp. 717–730. DOI:10.1143/JPSJ.62.717. URL: http://jpsj.ipap.jp/link?JPSJ/62/717/ (visited on 11/06/2013)
Tohyama, Takami and Sadamichi Maekawa (1990). “Physical Parameters in Copper Oxide Superconductors”. In: Journal of the Physical Society of Japan 59.5, pp. 1760–1770. DOI:10.1143/JPSJ.59.1760. URL: http://jpsj.ipap.jp/link?JPSJ/59/1760/ (visited on 09/03/2013).
Tohyama, Takami and Sadamichi Maekawa (2000). “Angle-resolved photoemission in high Tc cuprates fromtheoretical viewpoints”. en. In: Superconductor Science and Technology 13.4, R17. ISSN: 0953-2048. DOI: 10.1088/0953-2048/13/4/201. URL: http://iopscience.iop.org/0953-2048/13/4/201 (visited on 08/16/2013).
Tranquada, J.M. et al. (1987). “X-ray absorption studies of \({\rm La}_{2-x}{\rm (Ba, Sr)}_{x}{\rm CuO}_{4}\) superconductors”. In: Physical Review B 35.13, pp. 7187–7190. DOI: 10.1103/PhysRevB.35.7187. URL: http://link.aps.org/doi/10.1103/PhysRevB.35.7187 (visited on 11/11/2013)
Vaknin, D. et al. (1990). “Antiferromagnetism in Sr\(_{2}\)”. In: Physical Review B 41.4, p. 1926. DOI: 10.1103/PhysRevB.41.1926. URL: http://link.aps.org/doi/10.1103/PhysRevB.41.1926 (visited on 02/14/2011).
Walters, Andrew C. et al. (2009). “Effect of covalent bonding on magnetism and the missing neutron intensity in copper oxide compounds”. en. In: Nature Physics 5.12, pp. 867–872. ISSN, pp. 1745–2473, DOI: 10.1038/nphys1405. URL: http://www.nature.com/nphys/journal/v5/n12/full/nphys1405.html (visited on 08/20/2013)
Wells, B. O. et al. (1995). “E versus k Relations andMany Body Effects in theModel Insulating Copper Oxide Sr2CuO2Cl2”. In: Physical Review Letters 74.6, pp. 964–967. DOI: 10.1103/PhysRevLett.74.964. URL: http://link.aps.org/doi/10.1103/PhysRevLett.74.964 (visited on 08/16/2013)
Yokoyama, Hisatoshi andMasao Ogata (1996). “Phase Diagram and Pairing Symmetry of the Two-Dimensional t-J Model by a Variation Theory”. In: Journal of the Physical Society of Japan 65.11, pp. 3615–3629. DOI:10.1143/JPSJ.65.3615. URL: http://jpsj.ipap.jp/link?JPSJ/65/3615/ (visited on 10/11/2013).
Zaanen, J., G. A. Sawatzky, and J. W. Allen (1985). “Band gaps and electronic structure of transition-metal compounds”. In: Physical Review Letters 55.4, pp. 418–421. DOI: 10.1103/PhysRevLett.55.418. URL: http://link.aps.org/doi/10.1103/PhysRevLett.55.418 (visited on 11/11/2013)
Zhang, F. C. and T. M. Rice (1988). “Effective Hamiltonian for the superconducting Cu oxides”. In: Physical Review B 37.7, pp. 3759–3761. DOI: 10.1103/PhysRevB.37.3759. URL: http://link.aps.org/doi/10.1103/PhysRevB.37.3759 (visited on 11/06/2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Dalla Piazza, B. (2016). Modeling the Spin-Wave Dispersion of Insulating Cuprate Materials. In: Excitation Spectra of Square Lattice Antiferromagnets. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-26419-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-26419-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26418-9
Online ISBN: 978-3-319-26419-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)