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Australian Journal of Physics

Cross-Relaxation Effects in a Ruby L?Band (1440 Mc/s) Maser at Low Magnetic Fields

G S Bogle, F. F. Gardner

Published Sep 1, 1961• 4 citations

Abstract

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%

DOI: 10.1071/ph610381

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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%

Cross relaxation effects in ruby maser crystals are treated by introduction of a cross relaxation probability in the rate equations. Detailed solutions have been obtained for several specific processes and compared to recent experiments. It is shown that cross relaxation can improve maser performance even in the absence of impurity doping. Pulse experiments at 0.06 and 0.14% chromium ion concentrations in a ruby traveling wave maser are interpreted in terms of a five-spin process in addition to a four-spin process.

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 magnetization of ruby in a magnetic field at 300\ifmmode^\circ\else\textdegree\fi{}K is changed when the ruby is optically pumped with linearly polarized radiation from a

Q

-switched ruby laser. With a magnetic field parallel to the trigonal axis, laser light polarized parallel to this axis induces transitions from the spin \ifmmode\pm\else\textpm\fi{}\textonehalf{} levels of the

^{4}A_{2}

ground state to the levels of the

\overline{E}(^{2}E)

excited state. The change in

{M}_{z}

is linearly proportional to

H

except near the anticrossing points of the

^{4}A_{2}

spin levels at 2.07 and 4.14 kG. At these field strengths, there is an enhancement of the magnetization caused by state mixing of the

^{4}A_{2}

wave functions. When

H

has a small component perpendicular to the

z

axis, a magnetization is detected parallel to this component in the vicinity of 4.14 kG. The effect requires a long ground-state relaxation time. In a separate experiment, the relaxation of

{M}_{z}

was found to vary from 0.13 \ensuremath{\mu}sec in zero magnetic field to a constant value of 0.57 \ensuremath{\mu}sec for fields above 60 G.

Transition probabilities of spin-lattice relaxation (RTP) based on the Kronig-Van Vleck mechanism are calculated for ruby for the orientations θ = 90 and 54° and for magnetic fields up to 15 kG. Inversion ratios are evaluated on the basis of the RTP's for various pumping modes. Experimental measurements of the inversion ratio and pumping power at a signal frequency of fs = 22.2 GHz are carried out. The Kronig-Van Vleck mechanism is shown to be the principal mechanism of spin-lattice relaxation for high magnetic fields and low concentrations of paramagnetic ions.