hal-03095209
https://univ-pau.hal.science/hal-03095209
doi:10.1103/PhysRevB.102.235118
[CNRS] CNRS - Centre national de la recherche scientifique
[UNIV-PAU] Université de Pau et des Pays de l'Adour - E2S UPPA
[IPREM] Institut des sciences analytiques et de physico-chimie pour l'environnement et les matériaux
[INC-CNRS] Institut de Chimie du CNRS
[UNIV-LILLE] Université de Lille
[TEST-HALCNRS] Collection test HAL CNRS
[PHLAM] Laboratoire de Physique des Lasers, Atomes et Molécules
[UPPA-OA] uppa-oa
[TEST2-HALCNRS] TEST2-HALCNRS
Adiabatic connection in spin-current density functional theory
Desmarais, Jacques
Flament, Jean-Pierre
Erba, Alessandro
[CHIM.MATE] Chemical Sciences/Material chemistry
[CHIM.POLY] Chemical Sciences/Polymers
[CHIM.THEO] Chemical Sciences/Theoretical and/or physical chemistry
[CHIM.ANAL] Chemical Sciences/Analytical chemistry
ART
Current density
Density functional theory
Magnetic field effects
Magnetization
Matrix algebra
Quantum theory
Spin orbit coupling
The spin-current density functional theory (SCDFT), when formulated in a basis of Pauli spinors, provides a proper theoretical framework for the study of materials in an arbitrarily oriented external magnetic field and/or upon inclusion of spin-dependent relativistic effects, such as spin-orbit coupling. The SCDFT is formulated in terms of the particle-number density n, the Cartesian components of the magnetization mx, my, and mz, the orbital-current density j, and the three spin-current densities Jx, Jy, and Jz, where each of these density variables depends on specific blocks of the density matrix. Exchange-correlation (xc) functionals within the SCDFT should therefore depend on all of these eight fundamental density variables: Fxc[n,mx,my,mz,j,Jx,Jy,Jz], which makes their parametrization a formidable task. Here, we formulate the adiabatic connection of the SCDFT for a treatment of exact Fock exchange in the theory. We show how the inclusion of a fraction of Fock exchange in standard functionals of the (spin) DFT (either in their collinear or noncollinear versions: Fxc[n], Fxc[n,mz] and Fxc[n,mx,my,mz]) allows for the two-electron potential to depend on all those blocks of the density matrix that correspond to the eight density variables of the SCDFT, in a sensible and yet practical way. In particular, in the local-density and generalized-gradient approximations of the SCDFT, the treatment of the current densities solely from the Fock exchange term is formally justified by the short-range behavior of the exchange hole. We discuss that the adiabatic coupling strength parameter modulates the two-electron coupling of the orbital- and spin-current densities with the particle-number density and magnetization. Formal considerations are complemented by numerical tests on a periodic model system in the presence of spin-orbit coupling and in the absence of an external magnetic field.
2020-12
en
Physical Review B
American Physical Society