Asymmetric lines in field-swept EPR: Cr3+ looping transitions in Ruby

Modeling EPR Powder Spectra Using Numerical Diagonalization of the Spin Hamiltonian

“…More generally, it can be inferred from the work of Kato (51) that there is no suitable method for sorting wavefunctions, such as the angular dependency H(, ) of every transition can be described as a differentiable function. Therefore, the simple ascending order sorting is generally preferred, although it fails in some special cases which can be classified as two types: (i) "Looping" transitions (18,46): There may exist {, } directions where two levels n and nЈ behave in such a way that 0 Ͻ ͉E n Ϫ E nЈ ͉ Ͻ h in a particular H interval and ͉E n Ϫ E nЈ ͉ Ն h outside of this interval. In that case, one transition appears at each extremity of the interval, and these two transitions are indexed as nnЈ p and nnЈ pϩ1 in our algorithm.…”

Simulation Methods for Looping Transitions

“…[3]) was near 30°or 89°, the two branches of looping transitions are seen in a magnetic field range that is a small multiple of the apparent linewidth. We discuss here the 30°case, which we have already visited in Fig.…”

“…Pilbrow et al (3) showed that when the angle between the magnetic field and the crystal c axis (z axis in Eq. [3]) was near 30°or 89°, the two branches of looping transitions are seen in a magnetic field range that is a small multiple of the apparent linewidth.…”

“…While a Lorentzian might be more fundamental, we opted for a Gaussian to mimic (slightly simplified) what Pilbrow et al (3) used to fit the ruby spectra. In any event, the nature of f is not paramount to our main point, to be explicated later [approx-…”

“…[3]. The magnetic field B is set at an angle of 29.4°with the z axis, and we have taken D ϭ Ϫ5.747 GHz ϭ Ϫ0.191699 cm Ϫ1 and g ϭ g Ќ ϭ g ϭ 1.9858.…”