Relaxation and phonon bottleneck of 169Tm nuclear spins in TmPO 4 : evidence for the direct process ?

Magnetic properties of the lanthanide phosphates

“…In the former, effects of the phonon bottleneck were studied by Roinel et al [35]. For this compound relaxation times for the direct process were deduced by acoustic measurements [36].…”

Quadratic Zeeman effect and spin-lattice relaxation of Tm3+ :YAG at high magnetic fields

“…We also measure the spin-lattice relaxation of the thulium sites with the longest hyperfine lifetime as a function of the magnetic field strength and temperature. We identify the contribution from the direct phonon process, finding that it only becomes larger than the two-phonon Orbach relaxation process for fields greater than 4 T -this holds even at temperatures below 2 K. These results reveal that the phonon coupling strength in Tm:YAG is much smaller than what has been previously estimated for thulium in other hard oxide crystals, suggesting that past measurements [16][17][18] [14,15]. Each parallelepiped represents the orientation of the local D2 point symmetry for a subset of sites.…”

“…If we approximate v by the acoustic velocity averaged over the single longitudinal mode and the two transverse modes, then, for our field orientation where γ = 400 MHz/T, Bleaney's approach predicts a direct phonon coefficient on the order of 10 −26 (Hz K T 2 ) −1 , somewhat smaller than our observed value but within the range expected considering the approximations involved in the theoretical estimate. The only cases that we are aware of in which direct phonon relaxation has been suggested for 169 Tm 3+ have been related to studies of TmPO 4 and TmVO 4 materials for nuclear cooling applications [16][17][18]. In these works, the observed relaxation rates require exceedingly large phonon coupling coefficients of 6 × 10 −11 (Hz K T 2 ) −1 in TmPO 4 [17] and 4×10 −8 (Hz K T 2 ) −1 in TmVO 4 [17].…”

“…In these works, the observed relaxation rates require exceedingly large phonon coupling coefficients of 6 × 10 −11 (Hz K T 2 ) −1 in TmPO 4 [17] and 4×10 −8 (Hz K T 2 ) −1 in TmVO 4 [17]. It was subsequently proposed that the observed relaxation was due to paramagnetic impurities rather than phonon interactions [31,32], although explanations in terms of phonon bottleneck effects were also proposed [18]. Considering the small value of α D observed in our work and the reasonable agreement of this value with theoretical predictions, our results support this conclusion.…”

Enhanced nuclear acoustic resonance: some theoretical considerations

“…The latter has been confirmed for 1 313 ] thulium ethylsulphate and praseodymium sulphate by the calculation of Vaisfel'd (1972); a more general demonstration, based on simple order-of-magnitude arguments, is given by Abragam & Bleaney (1983). A comprehensive study (Roinel et al 1985) of 169Tm in Tm P04 between 50 mK and 2.2 K, and in field to 5.5 T, has revealed the presence of a phonon bottleneck, with relaxation times for the direct process ranging up to 200 h.…”