# Phenomenological three-orbital spin-fermion model for cuprates

## Abstract

A spin-fermion model that captures the charge-transfer properties of Cu-based high critical temperature superconductors is proposed and investigated via Monte Carlo simulations. The strong Coulomb repulsion among *d* electrons in the Cu orbitals is phenomenologically replaced by an exchange coupling between the spins of the itinerant electrons and localized spins at the Cu sites, formally similar to double-exchange models for manganites. This interaction induces a charge-transfer insulator gap in the undoped case (five electrons per unit cell). Adding a small antiferromagnetic Heisenberg coupling between localized spins reinforces the global tendency towards antiferromagnetic order. To perform numerical calculations the localized spins are considered classical as in previous related efforts. Here, undoped and doped 8×8 clusters are analyzed in a wide range of temperatures. The numerical results reproduce experimental features in the one-particle spectral function and the density of states, such as: (i) the formation of a Zhang-Rice-like band with a dispersion on the order of ~0.5 eV and with rotational symmetry about the wave-vector (π/2,π/2) at the top of the band and (ii) the opening of a pseudogap at the chemical potential upon doping. We also observed incipient tendencies towards spin incommensurability. This simple model allows for an unbiased study ofmore »

- Authors:

- Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Universität Stuttgart (Germany)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1546552

- Alternate Identifier(s):
- OSTI ID: 1460749

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 3; Journal ID: ISSN 2469-9950

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; superconducting cuprates; charge-transfer insulator; multi-orbital models

### Citation Formats

```
Hussein, Mostafa Sherif Derbala Aly, Daghofer, Maria, Dagotto, Elbio, and Moreo, Adriana. Phenomenological three-orbital spin-fermion model for cuprates. United States: N. p., 2018.
Web. doi:10.1103/PhysRevB.98.035124.
```

```
Hussein, Mostafa Sherif Derbala Aly, Daghofer, Maria, Dagotto, Elbio, & Moreo, Adriana. Phenomenological three-orbital spin-fermion model for cuprates. United States. doi:10.1103/PhysRevB.98.035124.
```

```
Hussein, Mostafa Sherif Derbala Aly, Daghofer, Maria, Dagotto, Elbio, and Moreo, Adriana. Wed .
"Phenomenological three-orbital spin-fermion model for cuprates". United States. doi:10.1103/PhysRevB.98.035124. https://www.osti.gov/servlets/purl/1546552.
```

```
@article{osti_1546552,
```

title = {Phenomenological three-orbital spin-fermion model for cuprates},

author = {Hussein, Mostafa Sherif Derbala Aly and Daghofer, Maria and Dagotto, Elbio and Moreo, Adriana},

abstractNote = {A spin-fermion model that captures the charge-transfer properties of Cu-based high critical temperature superconductors is proposed and investigated via Monte Carlo simulations. The strong Coulomb repulsion among d electrons in the Cu orbitals is phenomenologically replaced by an exchange coupling between the spins of the itinerant electrons and localized spins at the Cu sites, formally similar to double-exchange models for manganites. This interaction induces a charge-transfer insulator gap in the undoped case (five electrons per unit cell). Adding a small antiferromagnetic Heisenberg coupling between localized spins reinforces the global tendency towards antiferromagnetic order. To perform numerical calculations the localized spins are considered classical as in previous related efforts. Here, undoped and doped 8×8 clusters are analyzed in a wide range of temperatures. The numerical results reproduce experimental features in the one-particle spectral function and the density of states, such as: (i) the formation of a Zhang-Rice-like band with a dispersion on the order of ~0.5 eV and with rotational symmetry about the wave-vector (π/2,π/2) at the top of the band and (ii) the opening of a pseudogap at the chemical potential upon doping. We also observed incipient tendencies towards spin incommensurability. This simple model allows for an unbiased study of charge-transfer insulators and offers a formalism intermediate between standard mean-field approximations that fail at finite temperatures in regimes with short-range order and sophisticated quantum Monte Carlo techniques that suffer sign problems.},

doi = {10.1103/PhysRevB.98.035124},

journal = {Physical Review B},

number = 3,

volume = 98,

place = {United States},

year = {2018},

month = {7}

}

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Works referenced in this record:

##
Band gaps and electronic structure of transition-metal compounds

journal, July 1985

- Zaanen, J.; Sawatzky, G. A.; Allen, J. W.
- Physical Review Letters, Vol. 55, Issue 4

##
Correlation strength, gaps, and particle-hole asymmetry in high- ${T}_{c}$ cuprates: A dynamical mean field study of the three-band copper-oxide model

journal, August 2009

- de’ Medici, Luca; Wang, Xin; Capone, Massimo
- Physical Review B, Vol. 80, Issue 5

##
Pseudogap and superconductivity in two-dimensional doped charge-transfer insulators

journal, June 2016

- Fratino, L.; Sémon, P.; Sordi, G.
- Physical Review B, Vol. 93, Issue 24

##
Ground-state oxygen holes and the metal–insulator transition in the negative charge-transfer rare-earth nickelates

journal, October 2016

- Bisogni, Valentina; Catalano, Sara; Green, Robert J.
- Nature Communications, Vol. 7, Issue 1

##
Correlated electrons in high-temperature superconductors

journal, July 1994

- Dagotto, Elbio
- Reviews of Modern Physics, Vol. 66, Issue 3

##
Anderson Hamiltonian description of the experimental electronic structure and magnetic interactions of copper oxide superconductors

journal, December 1987

- Shen, Zhi-xun; Allen, J. W.; Yeh, J. J.
- Physical Review B, Vol. 36, Issue 16

##
Resonant photoemission study of ${\mathrm{Nd}}_{2\mathrm{-}\mathrm{x}}$ ${\mathrm{Ce}}_{\mathrm{x}}$ ${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$ : Nature of electronic states near the Fermi level

journal, January 1990

- Allen, J. W.; Olson, C. G.; Maple, M. B.
- Physical Review Letters, Vol. 64, Issue 5

##
$E$ versus k Relations and Many Body Effects in the Model Insulating Copper Oxide ${\mathrm{Sr}}_{2}$ Cu ${\mathrm{O}}_{2}$ ${\mathrm{Cl}}_{2}$

journal, February 1995

- Wells, B. O.; Shen, Z. -X.; Matsuura, A.
- Physical Review Letters, Vol. 74, Issue 6

##
Angle-resolved photoemission studies of the cuprate superconductors

journal, April 2003

- Damascelli, Andrea; Hussain, Zahid; Shen, Zhi-Xun
- Reviews of Modern Physics, Vol. 75, Issue 2

##
Effective Hamiltonian for the superconducting Cu oxides

journal, March 1988

- Zhang, F. C.; Rice, T. M.
- Physical Review B, Vol. 37, Issue 7

##
Phase diagram and single-particle spectrum of CuO _{2} high- *T* _{c} layers: variational cluster approach to the three-band Hubbard model

journal, May 2009

- Arrigoni, E.; Aichhorn, M.; Daghofer, M.
- New Journal of Physics, Vol. 11, Issue 5

##
Calculation of Coulomb-interaction parameters for ${\mathrm{La}}_{2}$ ${\mathrm{CuO}}_{4}$ using a constrained-density-functional approach

journal, May 1989

- Hybertsen, Mark S.; Schlüter, Michael; Christensen, Niels E.
- Physical Review B, Vol. 39, Issue 13

##
Derivation of a one-band Hubbard model for CuO planar materials

journal, October 1991

- Bacci, Silvia B.; Gagliano, Eduardo R.; Martin, Richard M.
- Physical Review B, Vol. 44, Issue 14

##
Theory of high- ${\mathrm{T}}_{\mathrm{c}}$ superconductivity in oxides

journal, June 1987

- Emery, V. J.
- Physical Review Letters, Vol. 58, Issue 26

##
High-Spin Polaron in Lightly Doped ${\mathrm{CuO}}_{2}$ Planes

journal, January 2011

- Lau, Bayo; Berciu, Mona; Sawatzky, George A.
- Physical Review Letters, Vol. 106, Issue 3

##
Iron-Based Layered Superconductor La[O _{1-} * *_{x} F * *_{x} ]FeAs ( *x* = 0.05−0.12) with *T* _{c} = 26 K

journal, March 2008

_{x}

_{x}

- Kamihara, Yoichi; Watanabe, Takumi; Hirano, Masahiro
- Journal of the American Chemical Society, Vol. 130, Issue 11

##
Superconducting Properties of the Fe-Based Layered Superconductor ${\mathrm{LaFeAsO}}_{0.9}{\mathrm{F}}_{0.1-\delta}$

journal, July 2008

- Chen, G. F.; Li, Z.; Li, G.
- Physical Review Letters, Vol. 101, Issue 5

##
Superconductivity at 41 K and Its Competition with Spin-Density-Wave Instability in Layered ${\mathrm{CeO}}_{1-x}{\mathrm{F}}_{x}\mathrm{FeAs}$

journal, June 2008

- Chen, G. F.; Li, Z.; Wu, D.
- Physical Review Letters, Vol. 100, Issue 24

##
Superconductivity at 25 K in hole-doped (La _{1-x} Sr _{x} )OFeAs

journal, March 2008

- Wen, Hai-Hu; Mu, Gang; Fang, Lei
- EPL (Europhysics Letters), Vol. 82, Issue 1

##
Nematic State of Pnictides Stabilized by Interplay between Spin, Orbital, and Lattice Degrees of Freedom

journal, July 2013

- Liang, Shuhua; Moreo, Adriana; Dagotto, Elbio
- Physical Review Letters, Vol. 111, Issue 4

##
Anisotropy of Electrical Transport in Pnictide Superconductors Studied Using Monte Carlo Simulations of the Spin-Fermion Model

journal, July 2012

- Liang, Shuhua; Alvarez, Gonzalo; Şen, Cengiz
- Physical Review Letters, Vol. 109, Issue 4

##
Magnetic Domains and Stripes in a Spin-Fermion Model for Cuprates

journal, March 2000

- Buhler, Charles; Yunoki, Seiji; Moreo, Adriana
- Physical Review Letters, Vol. 84, Issue 12

##
Robust *D* -Wave Pairing Correlations in a Hole-Doped Spin-Fermion Model

journal, April 2002

- Moraghebi, Mohammad; Yunoki, Seiji; Moreo, Adriana
- Physical Review Letters, Vol. 88, Issue 18

##
Quasiparticles in the copper-oxygen planes of high- ${T}_{c}$ superconductors: An exact solution for a ferromagnetic background

journal, December 1988

- Emery, V. J.; Reiter, G.
- Physical Review B, Vol. 38, Issue 16

##
The dynamics of a doped hole in a cuprate is not controlled by spin fluctuations

journal, October 2014

- Ebrahimnejad, Hadi; Sawatzky, George A.; Berciu, Mona
- Nature Physics, Vol. 10, Issue 12

##
Antiferromagnetism, localization, and pairing in a two-dimensional model for ${\mathrm{CuO}}_{2}$

journal, July 1987

- Hirsch, J. E.
- Physical Review Letters, Vol. 59, Issue 2

##
Canonical perturbation theory and the two-band model for high- ${T}_{c}$ superconductors

journal, June 1988

- Zaanen, Jan; Oleś, Andrzej M.
- Physical Review B, Vol. 37, Issue 16

##
Three-band Hubbard model: A Monte Carlo study

journal, May 1990

- Dopf, G.; Muramatsu, A.; Hanke, W.
- Physical Review B, Vol. 41, Issue 13

##
Variational Cluster Approach to Correlated Electron Systems in Low Dimensions

journal, November 2003

- Potthoff, M.; Aichhorn, M.; Dahnken, C.
- Physical Review Letters, Vol. 91, Issue 20

##
Variational cluster approach to spontaneous symmetry breaking: The itinerant antiferromagnet in two dimensions

journal, December 2004

- Dahnken, C.; Aichhorn, M.; Hanke, W.
- Physical Review B, Vol. 70, Issue 24

##
Competition between Antiferromagnetism and Superconductivity in High- ${T}_{c}$ Cuprates

journal, April 2005

- Sénéchal, David; Lavertu, P. -L.; Marois, M. -A.
- Physical Review Letters, Vol. 94, Issue 15

##
Physics of cuprates with the two-band Hubbard model: The validity of the one-band Hubbard model

journal, April 2005

- Macridin, A.; Jarrell, M.; Maier, Th.
- Physical Review B, Vol. 71, Issue 13

##
Single-particle spectral weight of a two-dimensional Hubbard model

journal, August 1992

- Dagotto, E.; Ortolani, F.; Scalapino, D.
- Physical Review B, Vol. 46, Issue 5

##
Ferromagnetic Kondo model for manganites: Phase diagram, charge segregation, and influence of quantum localized spins

journal, September 1998

- Dagotto, E.; Yunoki, S.; Malvezzi, A. L.
- Physical Review B, Vol. 58, Issue 10

##
Optical spectra of ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4}$ : Effect of carrier doping on the electronic structure of the ${\mathrm{CuO}}_{2}$ plane

journal, April 1991

- Uchida, S.; Ido, T.; Takagi, H.
- Physical Review B, Vol. 43, Issue 10

##
Pairing, charge, and spin correlations in the three-band Hubbard model

journal, March 2001

- Huang, Z. B.; Lin, H. Q.; Gubernatis, J. E.
- Physical Review B, Vol. 63, Issue 11

##
Characterizing the three-orbital Hubbard model with determinant quantum Monte Carlo

journal, April 2016

- Kung, Y. F.; Chen, C. -C.; Wang, Yao
- Physical Review B, Vol. 93, Issue 15

##
Density matrix formulation for quantum renormalization groups

journal, November 1992

- White, Steven R.
- Physical Review Letters, Vol. 69, Issue 19

##
Density-matrix algorithms for quantum renormalization groups

journal, October 1993

- White, Steven R.
- Physical Review B, Vol. 48, Issue 14

##
Photoemission spectra of ${\mathrm{Sr}}_{2}$ ${\mathrm{CuO}}_{2}$ ${\mathrm{Cl}}_{2}$ : A theoretical analysis

journal, April 1995

- Nazarenko, A.; Vos, K. J. E.; Haas, S.
- Physical Review B, Vol. 51, Issue 13

##
Comparison of 32-site exact-diagonalization results and ARPES spectral functions for the antiferromagnetic insulator ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{2}{\mathrm{Cl}}_{2}$

journal, September 1997

- Leung, P. W.; Wells, B. O.; Gooding, R. J.
- Physical Review B, Vol. 56, Issue 10

##
*t* - *J* model and nuclear magnetic relaxation in high- ${\mathrm{T}}_{\mathrm{c}}$ materials

journal, September 1989

- Shastry, B. Sriram
- Physical Review Letters, Vol. 63, Issue 12

##
Derivation of a single-band model for ${\mathrm{CuO}}_{2}$ planes by a cell-perturbation method

journal, April 1992

- Jefferson, J. H.; Eskes, H.; Feiner, L. F.
- Physical Review B, Vol. 45, Issue 14

##
Optical weights and waterfalls in doped charge-transfer insulators: A local density approximation and dynamical mean-field theory study of ${\text{La}}_{2-x}{\text{Sr}}_{x}{\text{CuO}}_{4}$

journal, October 2008

- Weber, Cédric; Haule, Kristjan; Kotliar, Gabriel
- Physical Review B, Vol. 78, Issue 13

##
Calculated Momentum Dependence of Zhang-Rice States in Transition Metal Oxides

journal, February 2008

- Yin, Quan; Gordienko, Alexey; Wan, Xiangang
- Physical Review Letters, Vol. 100, Issue 6

##
Universal waterfall-like feature in the spectral function of high temperature superconductors

journal, September 2007

- Graf, J.; Gweon, G. -H.; Lanzara, A.
- Physica C: Superconductivity and its Applications, Vol. 460-462

##
Momentum and Energy Dependence of the Anomalous High-Energy Dispersion in the Electronic Structure of High Temperature Superconductors

journal, December 2007

- Inosov, D. S.; Fink, J.; Kordyuk, A. A.
- Physical Review Letters, Vol. 99, Issue 23

##
Numerical study of the two-dimensional Hubbard model for various band fillings

journal, February 1990

- Moreo, A.; Scalapino, D. J.; Sugar, R. L.
- Physical Review B, Vol. 41, Issue 4

##
Incommensurate magnetic fluctuations in ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_{4}$

journal, September 1991

- Cheong, S-W.; Aeppli, G.; Mason, T. E.
- Physical Review Letters, Vol. 67, Issue 13

##
Incommensurate Magnetic Fluctuations in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{O}_{6.6}$

journal, February 1998

- Dai, Pengcheng; Mook, H. A.; Doǧan, F.
- Physical Review Letters, Vol. 80, Issue 8

##
Spin fluctuations in YBa2Cu3O6.6

journal, October 1998

- Mook, H. A.; Dai, Pengcheng; Hayden, S. M.
- Nature, Vol. 395, Issue 6702

##
Coexistence of, and Competition between, Superconductivity and Charge-Stripe Order in ${\mathrm{La}}_{1.6-\mathit{x}}{\mathrm{Nd}}_{0.4}{\mathrm{Sr}}_{\mathit{x}}{\mathrm{CuO}}_{4}$

journal, January 1997

- Tranquada, J. M.; Axe, J. D.; Ichikawa, N.
- Physical Review Letters, Vol. 78, Issue 2

##
Striped superconductors: how spin, charge and superconducting orders intertwine in the cuprates

journal, November 2009

- Berg, Erez; Fradkin, Eduardo; Kivelson, Steven A.
- New Journal of Physics, Vol. 11, Issue 11