PHYSICAL REVIEW B VOLUME 21, NUMBER 11 1 JUNE 1980 Optical measurement of spin-lattice relaxation of dilute nuclei: LaF3'. Pr + R. M. Shelby, R. M. Macfarlane, and C. S. Yannoni /BM R~'.wnnh Lahoiati~i~, Saii Joe', Cnfifi~iitia M5IM3 (Received 14 January 1980) We describe a method of measuring spin-lattice relaxation rates of' dilute nuclei using optical hole burning. This was applied to ' '. Pr nuclei doped into LaF3 at low concentrations (0.01 to 2.0 at. "/~i). The observed relaxation rates varied by about two orders of magnitude between 2 and 4. 5 K. At the lowest concentrations the data are interpreted in terms of two mechanism»: resonant two-phonon (Orbach) relaxation with a 57-cm ' activation, and praseodymium- lanthanum cross relaxation. At higher concentrations an additional hole-filling process wa» ob- served and attributed to homonuclear Pr — Pr dipolar coupling. Theoretical estimates of the phonon-induced relaxation rates are given and agree approximately with experiniental values. I. INTRODUCTION A number of optical methods have been used to measure the spin-lattice relaxation of electron spins, principally the detection of population changes by magnetic circular dichroism' or Faraday rotation. ' It is not expected that these methods would be useful in the case of nuclear spin systems since the small nuclear moments would not lead to easily observable magneto-optic effects. This is particularly true for di- lute nuclear spins. Conventional magnetic resonance relaxation measurements' of dilute nuclei are also difficult. However, the recent discovery in LaF3. Pr + of an optical pumping cycle which leads to laser- induced optical hole burning has provided the means 5 to monitor Pr(l = —, ) nuclear spin populations opti- cally. Excitation by monochromatic laser light leads to (optical) frequency-selective redistribution of nu- clear population which results in a reduction in ab- sorption. The laser absorption thus provides a sensi- tive probe of these populations, and this has previ- ously been used to detect nuclear spin transitions in- duced by rf irradiation. ' The recovery time of these holes provides a direct measurement of the nuclear spin-lattice relaxation times. ' As previously noted, this recovery time varies by almost three orders of magnitude between 1. 8 and 4. 2 K. An understanding of this effect in terms of mechanisms for nuclear spin-lattice relaxation motivated the present study. The optical pumping cycle used to produce the ground-state nuclear polarization involves the transi- tion from the lowest crystal-field component of H4 (the ground state of the Pr'+ ion) to the lowest crystal-field component of 'D2 at 5925.2 A. The crystal field of C2 symmetry removes the 2J +1-fold degeneracy, leaving singly degenerate electronic lev- els. The ground-state nuclear spin levels consist of three doubly degenerate levels split by the second- order hyperfine interaction as well as the relatively small nuclear electric quadrupole interaction (see Fig. 1). The second-order interaction requires the pres- ence of nearby electronic levels, ' located in this case 57 cm ' above the ground state and 23 cm ' above the excited state. ' The presence of a three-level nuclear spin system complicates the relaxation dynamics somewhat, since the three relaxation times corresponding to the three possible transitions among these levels need not be equal. This leads to nonexponential relaxation behavior. " By applying saturating rf radiation at the frequency of one of the three transitions, it can be shown that the recovery reduces to a single exponen- tial. Repetition of this experiment for the other two transitions gives enough information to derive the three individual nuclear relaxation times. This idea was first applied to relaxation studies in pure nuclear quadrupole resonance" and has been used with limit- ed success for electron spin-lattice relaxation in excit- ed triplet states of organic molecules. "' In the present study, it provides the simplification needed to properly identify the nature of the relaxation mechanisms which are operative. We have measured the relaxation times in the ground state of LaF3. 'Pr'+ between 1. 5 and 4.6 K and find contributions to T~ from two different mechan- isms: (i) Resonant two-phonon (Orbach) relaxation" involving the first excited crystal-field level at an en- ergy of 57 cm '. This mechanism is dominant above — 3.5 K. (ii) A concentration and temperature- independent process which is important below 3 K and which we attribute to Pr-La cross relaxation. In addition, we find a temperature-independent but concentration-dependent hole recovery process which appears below 3 K and which is due to Pr — Pr nuclear flip flops. This T2-like process provides a mechanism for hole recovery when ions having different optical freq uencies are in vo 1ved. We also present a derivation of phonon-induced re- laxation rates' for the case of nuclear levels which are split by the second-order hyperfine interaction. 21 5004 ~@1980 The American Physical Society