High spins electronic Zeeman interaction

With the exception of transition metal ions at a site with cubic symmetry, the ZFS often exceeds the electron Zeeman interaction at magnetic fields <1 T, sometimes even at the highest accessible fields (high-spin Fe(III)). In this situation, only the lowest lying doublet of spin states may be populated and only transitions within this doublet can be observed. It is convenient to describe such a doublet by an effective spin S = The ZFS of the group spin 5 > j then contributes to the effective g-ten-sor of the spin S = For example, X-band ESR spectra of high-spin Fe(III) in a situation with maximum nonaxiality of the ZFS (E = D/3) exhibit a sharp feature at g = 4.3. Note that unlike the normal g-tensor, the effective g-tensor may depend on the applied magnetic field. 

For a perfect high-field case, where electron Zeeman interaction dominates ZFS and all other terms in the spin Hamiltonian, the only secular term in the dipolar interaction is given by... 

The unpaired electron with its spin S = 1/2 in a sample disposed into the resonator of the EPR spectrometer interacts magnetically a) with the external magnetic field H (Zeeman interaction) b) with the nuclear spin of the host atom or metal ion / (hyperfine interaction) c) with other electron spins S existing in the sample (dipole-dipole interaction). In the last case, electrons can be localized either at the same atom or ion (the so called fine interaction), for example in Ni2+, Co2+, Cr3+, high-spin Fe3+, Mn2+, etc., or others. These interac-tions are characterized energetically by the appropriate spin-Hamiltonian... 

These represent the nuclear spin Zeeman interaction, the rotational Zeeman interaction, the nuclear spin-rotation interaction, the nuclear spin-nuclear spin dipolar interaction, and the diamagnetic interactions. Using irreducible tensor methods we examine the matrix elements of each of these five terms in turn, working first in the decoupled basis set rj J, Mj /, Mi), where rj specifies all other electronic and vibrational quantum numbers this is the basis which is most appropriate for high magnetic field studies. In due course we will also calculate the matrix elements and energy levels in a ry, J, I, F, Mf) coupled basis which is appropriate for low field investigations. Most of the experimental studies involved ortho-H2 in its lowest rotational level, J = 1. If the proton nuclear spins are denoted I and /2, each with value 1 /2, ortho-H2 has total nuclear spin / equal to 1. Para-H2 has a total nuclear spin / equal to 0. 

The ESR signal is highly dependent on the nature of the local environment about the absorbing electron that is, the position of the ESR signal and the overall ESR spectral pattern depend on the environment conditions in the vicinity of the electron. The most important types of interactions in the spin system that affect the position and pattern of the ESR spectrum are the electron Zeeman, nuclear hyperfine, and ligand superhyperfine interactions (Wertz and Bolton, 1972). 

Spins are magnetic moments that are associated with angular momentum they interact with external magnetic fields (Zeeman interaction) and with each other (couplings). In most cases, the Zeeman interaction of the electron spin is the largest interaction in the spin system (high-field limit). The electron Zeeman (EZ) interaction can generally be described by the Hamiltonian below. 

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