The coupled representation matrix of the pair hamiltonian

Abstract

A complete treatment of the spin hamiltonian for a pair of exchange coupled metal ions is given. The results obtained through the use of the Wigner-Eckart theorem are unrestricted with respect to the relative orientation of the single-ion tensors, and appropriate for both the S1 = $2 and 314 32 cases. The necessary constants are derived so that matrix elements within a given spin multiplet can be treated by ordinary operator algebra with the coupled representation state vectors, I SM), as a basis set. Explicit algebraic formulae for matrix elements between spin multiplets are presented for the first time. Symmetry restrictions are discussed in general and illustrated for the simple case of two ions related by an inversion centre, pair symmetry Ci.

The effect of antisymmetric exchange on the E.P.R. spectra of coupled pairs of transition metal ions

“…It should also be A. Bencini and D. Gatteschi mentioned that d could be a first order effect when orbital degeneracy is present and might be included in the spin hamiltonian describing the exchange interaction between ions with orbitally degenerate ground states [9][10][11]. A convenient formalism for expressing the matrix elements of the exchange hamiltonian is that given by Scaringe et al [12]. However they did not include AET in their hamiltonian and to our knowledge no general expression for the matrix elements of the complete spin hamiltonian has been reported.…”

“…With these assumptions it is possible to reproduce the experimental data with D a numerically equal to Dai p but with the x and y axes interchanged. The sign of D a to be used is given by (12). The relevant parameters are D a = -0.03 cm -1, E/D = 0, which correspond to l az/70l : 0.48 cm -1.…”

“…The other symbols have been defined in [12] and equation (10). Diagonalization of the hamiltonian matrix at various field values yields the eigenvalues and the eigenvectors.…”

Anisotropic double exchange in a valence-delocalized [Fe2.5+Fe2.5+] cluster. Spin–orbit coupling in the Anderson–Hasegawa double exchange model

“…The origin of the ZFS parameters for the exchange clusters was considered in Refs. [41][42][43][44][45]10]. Single-ion ZFS [42,44,45], the Dzyaloshinsky-Moriya antisymmetric exchange [46,47], anisotropic (pseudodipolar) exchange [41,42] and the dipole-dipole interaction [42] contribute to the cluster ZFS parameters D S , E S of the localized exchange systems of monovalent ions.…”

“…[41][42][43][44][45]10]. Single-ion ZFS [42,44,45], the Dzyaloshinsky-Moriya antisymmetric exchange [46,47], anisotropic (pseudodipolar) exchange [41,42] and the dipole-dipole interaction [42] contribute to the cluster ZFS parameters D S , E S of the localized exchange systems of monovalent ions. For the MV systems, the account of the spin-orbit coupling for the transfer of hole between the neighboring sites in doped La 2 CuO 4 results in the spin-orbit hopping term and symmetric anisotropic exchange [48].…”