FIELD DEPENDENCE OF SPIN-LATTICE RELAXATION TIMES OF Cr³⁺

Abstract

ABSTRACT.The changes in spin-lattice relaxation time with the magnitude and orientation of the de magnetic field, frequency, and temperatut'e have been calculated from simplified expressions for the spin-phonon transition probabilities of an S c 3/2 ion.The relaxation times for INTRODUCTION.II. THEORY OF SPIN-LATTICE RELAXATION.III.1. 2.The Interaction Hamiltonian.Spin-Phonon Transition Probabilities for the Direct Process.THE MEASUREMENT OF SPIN-LATTICE RELAXATION TIMES.1. 2.3.Relaxation Times in a S=~ Spin System.Pulse Saturation Measurements on a S)~ System. PROCEDURE. 1.Experimental. 2.Calculations.VIII. RESULTS AND DISCUSSION. 1.Cr 3 + in K 3 Co(CN) 6 .IX.x. .Cr 3 + in A 1 2 0 3 • 3.Cr 3 + in RbAl(S0 4 ) 2 .12H 2 0. 4.The Slopes in the Logarithmic Plots of T 1 versus 1/Z. 5.Calculations for Steady-State Saturation Conditions. CONCLUSIONS.BIBLIOGRAPHY. INTRODUCTIONWhen the thermal-equilibrium energy distribution of a group of paramagnetic ions, whose paramagnetism is due to a net magnetic dipole moment associated with their spins, is in sorne way disturbed, the subsequent return to equilibrium is said to take place through spin-lattice relaxation if it occurs as the result of the exchange of energy-conserving quanta between the spins and the thermal spectrum of the host lattice. by Mattuck and Strandberg (1960), the spin-lattice interaction of paramagnetic ions in crystals is understood to occur through the thermal modulation of the crystalline electric field. The theory predicts that at very low temperatures, T, the spin-lattice transition probability, wij' between spin states i and j will be determined by a direct, one-phonon process with wij varying as T, while at higher temperatures a two-phonon, Raman mechanism will dominate with wij varying as T 7 or T 9 .In the case of a two-level system the return to equilibrium of the population of levels 1 and 2 is characterized by a spin-lattice relaxation time T 1 where T 1 = l/2w 12 • No such simple relationship exists in the case of multi-level systems but an effective spin-lattice relaxation time TR is still used to describe the return to equilibrium of the population of a pair of levels, even though this generally involves all the *Woonton (1961) furnishes an excellent bibliography related to theoretical and experimental work on spin-lattice relaxation.-2-other spin levels as well.Much of the early theoretica1 and experimental work was centred on the ions of the 3d iron group.The measured values of TR often did not agree well with the theory, and exp1anationsfor some of the inconsistencies were proposed by Bloembergen et al (1959), who considered the role played by cross-relaxation, and by , Van Vleck (1961), and , who extended the concept of crossrelaxation to excited states.Several effects predicted by the theory of spin-lattice relaxation have been verified experimentally. Thus Pace et al (1960) and Feng and Bloembergen (1963) have verified 3+ the inverse temperature dependence for the 8=3/2 Cr ion in Al 2 o 3 at low temperatures, while , Rannestad and...