Raman electron spin-lattice relaxation with the Debye-type and with real phonon spectra in crystals

Electron spin-lattice relaxation temperature dependence was measured for Ti(2+) (S=1) and for Cu(2+) (S=1/2) ions in SrF(2) single crystal by electron spin echo method in temperature range 4-109K. The spin relaxation was governed by the two-phonon Raman processes. The relaxation theory is outlined and presented in a form suitable for applying with real phonon spectra. The experimental relaxation results were described using Debye-type phonon spectrum and the real phonon spectrum of SrF(2) crystal. The Debye approximation does not fit well the results for SrF(2) both at low and at high temperature. The relaxation rate is faster than that predicted by Debye-type phonon spectrum at low temperatures where excess of lattice vibrations over the Debye model exists but is slower at higher temperatures (above 50K) where density of phonon states continuously decreases when approaching to the maximal acoustic phonon frequency. The expected deviation from Debye approximation was analyzed also for Cu(2+) in NaCl and MgSiO(3) crystals for which phonon spectra are available. The fitting with the real phonon spectrum allowed us to calculate spin-phonon coupling parameter as 267 cm(-1) for Ti(2+) and 1285 cm(-1) for Cu(2+) in SrF(2).