On the Exactness of the Spin-Hamiltonian Description of Fe³⁺in Sapphire

Hybrid electron spin resonance and whispering gallery mode resonance spectroscopy of Fe3+in sapphire

“…The values are far from those already estimated in the past. However, the mean value of g is close to that obtained by Symmons and Bogle 12 and Kornienko and Prokhorov. 13 In addition, it appears that the g factor is dependent on the ion concentration.…”

“…12,13,18,19 Three levels exist at zero applied magnetic field, with the dependence of these levels on a dc magnetic field described by the following Hamiltonian:…”

“…For the Fe 3+ ion in sapphire, the g-factor determination is a poorly represented measurement in the literature. 39 Kornienko and Prokhorov 13 and Symmons and Bogle 12 have estimated this parameter and claimed that g is independent of temperature, while they found the other Hamiltonian parameters to be temperature dependent. This is in contradiction to other materials and ions where the g factor is ordinarily temperature dependent; 30,33 thus we expect that the earlier measurements were not achieved with enough accuracy to reveal temperature-induced variations.…”

“…Several experiments have attempted to measure the spin-spin relaxation time, or the number of ions involved in the maser process, but have given results which contradict the values given by the manufacturer of the crystals, or those found in the literature. [10][11][12][13] This difference is essentially due to the method used to interact with the ions in sapphire, namely, the excitation of high-Q whispering gallery modes at frequencies coincident with the electron spin resonance (ESR) frequency of the ion. The spatial distribution of these modes acts as a filter, selecting only the population of ions which fall inside its field pattern.…”

Linear and nonlinear effects of electron paramagnetic resonance in high-Q cryogenic sapphire microwave resonators

“…As a result of the manufacturing process, paramagnetic Fe 3+ ions are included in the sapphire lattice at a concentration of 150 ppb (∼ 10 16 spins in the lattice). 27 The crystal field splitting results in an inhomogeneously broadened electron spin resonance (ESR) with 27 MHz linewidth 28 at zero applied DC magnetic field, corresponding to the spin-|1/2 , |3/2 , and |5/2 states of the ion. Within the system a complex interaction occurs between the microwave input field, a dilute paramagnetic Fe 3+ spin system, and 27 Al lattice ions, which ultimately results in the production of signal and idler photons equally spaced in frequency, characteristic of degenerate FWM.…”