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Jahn-Teller, pseudo-Jahn-Teller, and spin-orbit coupling Hamiltonian of a d electron in an octahedral environment
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10.1063/1.4751439
/content/aip/journal/jcp/137/11/10.1063/1.4751439
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/11/10.1063/1.4751439
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Enumeration of the corners of the octahedron (A, B, C, A′, B′, C′) and the corners of the enclosing cube (1…8).

Image of FIG. 2.
FIG. 2.

Representation of the first-order electrostatic JT Hamiltonian, , in the spin-orbital basis (9). a, b, c, d are real parameters representing linear T 2g × t 2g coupling (a), T 2g × e g coupling (c), E g × e g coupling (b) and T 2g E g PJT coupling by the t 2g mode (d).

Image of FIG. 3.
FIG. 3.

Representation of the second-order electrostatic JT Hamiltonian, , of the t 2g mode in the spin-orbital basis (9). A, B, C, D are real parameters representing quadratic T 2g × t 2g coupling (A, B), quadratic T 2g × e g coupling (C) and quadratic T 2g E g PJT coupling by the t 2g mode (D).

Image of FIG. 4.
FIG. 4.

Representation of the second-order electrostatic JT Hamiltonian, , of the e g mode in the spin-orbital basis (9). A′ and C′ are real parameters representing quadratic T 2g × t 2g coupling (A′) and quadratic E g × e g coupling (C′).

Image of FIG. 5.
FIG. 5.

Representation of the electrostatic JT Hamiltonian bilinear in the t 2g and e g modes, , in the spin-orbital basis (9). E, F, G are real parameters representing bilinear T 2g × (t 2g + e g ) JT coupling (E) and bilinear T 2g E g PJT coupling (F, G). See Appendix B for the definition of , , , .

Image of FIG. 6.
FIG. 6.

Representation of the zeroth-order SO coupling Hamiltonian, , in the spin-orbital basis (9). Δ and ρ are real parameters.

Image of FIG. 7.
FIG. 7.

Representation of the first-order SO coupling Hamiltonian of the t 2g mode, , in the spin-orbital basis (9). α, β, δ, ɛ are real parameters representing relativistic linear T 2g × t 2g coupling (α), E 2g × t 2g coupling (ɛ) and T 2g E g PJT coupling (δ, ɛ).

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/content/aip/journal/jcp/137/11/10.1063/1.4751439
2012-09-17
2014-04-21
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Jahn-Teller, pseudo-Jahn-Teller, and spin-orbit coupling Hamiltonian of a d electron in an octahedral environment
http://aip.metastore.ingenta.com/content/aip/journal/jcp/137/11/10.1063/1.4751439
10.1063/1.4751439
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