Spin–spin relaxation of nuclear quadrupole resonance coherences and the important role of degenerate energy levels

Abstract

We present an extension of a Redfield approach for calculating spin-spin relaxation rates of zero-field nuclear quadrupole resonance (NQR) coherences, which was published in [Kruk et al., PCCP, 2018, 20, 23414-23426]. The oversimplification of the secular approximation made in the recent paper makes the calculation invalid for zero-field NQR and has led to partially large deviations between predicted and experimental data from 209 Bi-containing molecular crystals. Furthermore, these deviations led to speculations about an additional dipole-dipole relaxation mechanism besides the main electric field gradient (EFG) fluctuations. Here, we demonstrate how a complete application of the Redfield relaxation expression eliminates the deviation from experimental data without the need for additional assumptions. In particular, we point out the important role of off-diagonal elements in the Redfield relaxation matrix within the 3/2-1/2 block appearing due to degenerate energy levels. The resulting coupling between single and double coherence spin density elements leads to a faster coherence decay than for all other transitions. The pseudo rotational model for EFG fluctuations, as proposed in the earlier publication and usually applied for isotropic liquids, is extended in a second analysis by introducing a vibrational mode to account for the case of crystalline solids.

Local Structure of Multinary Hybrid Lead Halide Perovskites Investigated by Nuclear Quadrupole Resonance Spectroscopy

“…T 2 relaxation times for pure and cesium-substituted FAPbI 3 were measured and all T 2 relaxation times were in the range of 100 μs, being significantly longer than the chosen echo delay. T 2 relaxation in NQR is dominated by fluctuations of the EFG . In the studied materials, these fluctuations in the NQR timescale are expected to be caused by anion diffusion and vibrations of the inorganic lead halide cage .…”

“…T 2 relaxation in NQR is dominated by fluctuations of the EFG. 55 In the studied materials, these fluctuations in the NQR timescale are expected to be caused by anion diffusion and vibrations of the inorganic lead halide cage. 44 An enhanced T 2 relaxation is expected for species experiencing higher structural dynamics.…”

Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory

“…However, when dealing with Kramers systems in zero external magnetic field, additional terms of R2italicab,italiccd2−ph also survive the secular approximation in virtue of the spectrum degeneracy that makes additional terms (ω ac + ω db ) vanish. For instance, the population-coherence transfer process R2italicaa,italicbcn−ph, with E b = E c , and coherence transfer terms R2italicad,italicbcn−ph, with E b = E c and E a = E d , would not be washed out by the secular approximation and could, in principle, contribute to the spin-phonon dynamics ( 40 , 41 ).…”

“…, with E b = E c and E a = E d , would not be washed out by the secular approximation and could, in principle, contribute to the spin-phonon dynamics (40,41).…”

Towards exact predictions of spin-phonon relaxation times: an ab initio implementation of open quantum systems theory

“…However, when dealing with Kramers systems in zero external magnetic field, additional terms of R2 n−ph ab,cd also survive the secular approximation in virtue of the spectrum degeneracy that makes additional terms (ω ac + ω db ) vanish. For instance, the population-coherence transfer process R2 n−ph aa,bc , with E b = E c , and coherence transfer terms R2 n−ph ad,bc , with E b = E c and E a = E d , would not be washed out by the secular approximation and could in principles contribute to the spin-phonon dynamics [40,41].…”