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Bell System Technical Journal

Paramagnetic Spectra of Substituted Sapphires-Part I: Ruby*

E. O. Schulz-DuBois

Published Jan 1, 1959• 120 citations
Publisher

Abstract

The paramagnetic resonance properties of Cr+++ions in Al2O3(ruby) were investigated theoretically and experimentally in order to obtain information necessary for the application of this material as active material in a three-level solid-state maser (3LSSM). Numerically computed energy levels, together with their associated eigenvectors, are presented as a function of applied magnetic field for various orientations of the magnetic field with respect to the crystalline symmetry axis. A more detailed discussion is devoted to energy levels, eigenvectors and transition probabilities at angles O°, 54.74° and 90°, where certain simple relations and symmetries hold. Paramagnetic spectra for signal frequencies between 5 and 24 kmc are shown; agreement between computed and measured resonance fields is satisfactory.

DOI
10.1002/j.1538-7305.1959.tb01578.x

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Journal of the Physical Society of Japan•Aug 1, 1958•173 citations
The paramagnetic resonance properties of Cr+++ions in Al2O3(ruby) were investigated theoretically and experimentally in order to obtain information necessary for the application of this material as active material in a three-level solid-state maser (3LSSM). Numerically computed energy levels, together with their associated eigenvectors, are presented as a function of applied magnetic field for various orientations of the magnetic field with respect to the crystalline symmetry axis. A more detailed discussion is devoted to energy levels, eigenvectors and transition probabilities at angles O°, 54.74° and 90°, where certain simple relations and symmetries hold. Paramagnetic spectra for signal frequencies between 5 and 24 kmc are shown; agreement between computed and measured resonance fields is satisfactory.
The molecular structure of a 3d 5 configuration ion in a trigonal ligand field is theoretically established on the basis of the 252\times252 complete energy matrice. The optical absorption and the electron paramagnetic resonance spectra of the Fe3+ ion in the sapphire crystal (α-Al2 O3) have been studied by diagonalizing the complete energy matrice. The calculated results are in very good agreement with previous experimental observations. The strength of the transition probabilities between pairs of the energy levels have been calculated to determine the possibility to achieve a population inversion in the ground state by applying optical pumping to the crystal. Preliminary results based on the computed transition parameters and on the maser rate equations model show that a 31 GHz maser signal can be effectively generated depending on the cryogenic resonator design.
Paramagnetic ions in solid state crystals form the basis for many advanced technologies like lasers, masers, frequency standards, and quantum-enhanced sensors. One of the most-studied examples is the Cr3+ ion in sapphire (Al2O3), also known as ruby, which has been intensely studied in the 1950s and 1960s. However, despite decades of research on ruby, some of its fundamental optical and spin properties have not been characterized at ultra low-temperatures, yet. In this article, we present optical measurements on a ruby crystal in a dilution refrigerator at ultra-low temperatures down to 20 mK. Analysing the relative populations of its 4A2 ground state spin levels, we extract a lattice temperature of 143(7) mK under continuous laser excitation. We perform spin lattice relaxation T1 measurements in excellent agreement with the direct, one-phonon model. Furthermore, we perform optically detected magnetic resonance measurements showing magnetically driven transitions between the ground state spin levels for various magnetic fields. Our measurements characterize some of ruby's low temperature spin properties, and lay the foundations for more advanced spin control experiments.
In operating a three-level maser one wishes to know the external magnetic field and crystal orientation necessary to match a given pair of frequencies. In the case of Cr+++ a fourth-degree secular equation determines four energy levels for each value of external field H and crystal orientation θ. Determination of the latter two variables, given two desired frequencies of operation, ordinarily involves either the solution of a tremendous number of fourth-degree equations and extrapolation towards the required solution, or determination of the matching conditions by experimental methods. In the following a method is described, allowing direct calculation of H and θ for a three-level ruby maser.
Doubly resonant Raman electron paramagnetic transitions in ruby (Al2{}_{2}2​O3{}_{3}3​:Cr3+{}^{3+}3+) have been investigated using dye laser excitation tuned across the range of the Zeeman components of its well-known R1{R}_{1}R1​ emission line. With magnetic field B normal to c, the optic axis of ruby, it is seen that the Raman electron paramagnetic resonance (EPR) lines exhibit significant intensity enhancements due to the simultaneous occurrence of ``in resonance'' and ``out resonance,'' as visualized in the Kramers-Heisenberg formalism of inelastic light scattering. The specific Raman EPR features observed in the present study, together with their resonances, however, differ markedly from those observed in our previous investigation with $\mathbf{B}\ensuremath{\parallel}\mathbf{c}$. These differences can be traced to level mixing effects within the Zeeman multiplet of the 4A2{}^{4}{A}_{2}4A2​ (ground) state on the one hand, and the negligible value of ${g}_{\ensuremath{\perp}}$ for the $\mathrm{E\ifmmode \bar{}\else \={}\fi{}}$ (excited) state of the R1{R}_{1}R1​ emission line on the other. Furthermore, we note that with B\ensuremath{\perp}c and under resonant conditions, the experimentally observed \ensuremath{\Delta}mmm === \ifmmode\pm\else\textpm\fi{}1 pair of Stokes and anti-Stokes Raman lines are not connected by time-reversal symmetry.
The reversals of maser behaviour which occur in ruby at low fields on cooling from 80° to 4 oK are explained in terms of cross-relaxation transitions (resonant interchanges of energy between neighbouring paramagnetic ions). For an angle of 29° between the magnetic field and the crystal axis a cross-relaxation process has been demonstrated which involves groups of three ions and has a transition probability of 700± 100 per second in 0·013% ruby. The profile of the cross-relaxation resonance has a half-width of 190±30 Mcts at half-intensity, and has an approximately Gaussian shape. It should be possible to obtain useful low-field L-band maser action at 4 oK by pumping V41 with the magnetic field nearly perpendicular to the crystal axis, and also at 80 oK using a concentration ten times higher, i.e. 0·13%
The absorption intensities, widths and wave-numbers of R 1 , R 2 and B 1 B 2 lines of Cr 3+ in ruby for the polarized light E ⊥ C 3 and E // C 3 are experimentally studied at 20°K and 4.2°K. Zeeman effect is also studied, using a magnetic field H 0 =24,000 φ, for both R and B lines. The Zeeman effect has not been observed yet for the B lines, while Lehmann has already observed the Zeeman effect for R lines. In our results of R lines, the quantitative aspects of Lehmann's experiment are improved. The comparison is made with the theoretical results given in Part A and it is shown that nice agreements can be obtained when suitable assignments of the spectra are adopted and when fairly large g -shifts of the excited states are introduced.