Spin lattice Orbach process

Fig. 3.3. Lattice and spin transitions are coupled by (A) direct processes, (B) Raman processes, (C) Orbach processes. The proximity of the excited electronic state favors both Orbach and Raman processes. The electronic states are labeled with n, the lattice vibrational states are labeled with V. A and 8 indicate energy separations with excited states coupled to the ground state by spin-orbit coupling.

At low temperature, the processes of spin-lattice relaxation between the triplet substates are slow. With temperature increase, the sir rates increase strongly. For Pt(2-thpy)2, three different processes govern the sir. At a temperature below T = 3 K, the sir rate is exclusively determined by the direct process. Above T = 3 K, the Orbach process and above T = 6 K, the Raman process, become additionally important. For Pd(2-thpy)2, the processes that govern the sir have not been determined yet, but it is suggested that the Raman process is of main importance, since no real electronic state lies in the energy vicinity of the Tj state. (Figs. 19, 21, and Refs. [24,60,62,64,65].)... 

Indeed, both the exponential temperature dependence that characterize the Orbach process and the T behavior associated with the Raman type process have been observed in spin lattice relaxation ... 

Fig. 4. Experimental results for the spin-lattice relaxation rate of Nd ions in lanthanum magnesium nitrate (LaMN), magnetic field normal to c-axis. The data are fitted to a combination of an Orbach process, 6.3 x lO expf—47.6/T) and a direct process, 0.3cotanh(h( /2fcr). (After Ruby et al. 1962.)...

The ESR of Ce ", Nd ", Dy ", Er ", and Yb in the hydrated trichloride, YCI3 6H2O, has been investigated by Schulz and Jeffries (1967). In these materials the lanthanide site symmetry is only C2, however the ESR results indicate an effective CEF of nearly Ce or C h symmetry. Spin-lattice relaxation time measurements were also made on these systems (except for Yb " ) as indicated by the data tabulation in table 18.28. Usually a Raman process term was found, of order (Ti) " lO" T sec . An exponential Orbach process was... 

Orbach Process of Spin-Lattice Relaxation. When a real state III) lies above the states 11) and II) with an energy separation A above state II), one phonon may be absorbed, while a second phonon can be emitted from this state III) (Fig. 14c). This process of sir, called Orbach process, can be described by resonant upward and downward direct processes. The corresponding rate is roughly approximated to [97,223,224,226,227] ... 

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