Higher-order Zeeman and spin terms in the electron paramagnetic resonance spin Hamiltonian; their description in irreducible form using Cartesian, tesseral spherical tensor and Stevens’ operator expressions

Abstract

In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS(3) and BS(5). Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, [Formula: see text] Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.

First principles calculation of spin-related quantities for point defect qubit research

“…Such terms are also possible, however, most often they can be safely neglected. 116 Theoretical formulas for the higher order interaction terms can be found in the literature, 116,117 however, less attention has been paid to the implementation and calculation of corresponding higher order g-tensor parameters so far. On the other hand, in recent experiment on the spin-3/2 silicon vacancy qubits in 4H-SiC forbidden electron spin transitions were observed in the ODMR spectrum.…”

Particle Swarm Fitting of Spin Hamiltonians: Magnetic Circular Dichroism of Reduced and NO-Bound Flavodiiron Protein

“…• The splitting of magnetic sublevels is significantly smaller than the line width of the transition. • The influences 20 where we use boldface (H) to represent an operator, an arrow (H ⃗ ) to represent a vector, and a tilde (g) to represent a matrix or tensor. Here, μ B is the Bohr magneton, H ⃗ is the applied magnetic field, α(β) indexes the paramagnetic spin centers of the system, g̃α is the g matrix for center α, D ̃α is the zero-field splitting (ZFS) tensor for center α, and J ̃αβ is the exchange matrix coupling centers α and β.…”

“…The J̃ αβ matrix coupling centers α and β are often discussed in terms of its isotropic (trace, −2 J αβ ), antisymmetric ( G⃗ αβ ), and anisotropic (symmetric, D̃ αβ ) components: boldS⃗ α J̃ α β boldS⃗ β = ( − 2 ) J α β boldS⃗ α · boldS⃗ β + G⃗ α β · boldS⃗ α × boldS⃗ β + boldS⃗ α D̃ α β boldS⃗ β where the (−2) prefactor varies by definition. For S > 3/2 systems, terms of higher order in S can be added . Any contributions from weaker interactions (hyperfine, nuclear Zeeman, etc.)…”