Field-dependent nuclear relaxation of spins 1/2 induced by dipole–dipole couplings to quadrupole spins: LaF3 crystals as an example

Field Dependent Electron and Quadrupole Spin Relaxation: A Unified Treatment

“…The idea of this approach is to let the S spin to be a part of a composite lattice for the I spin [8,9,[11][12][13][14][15][20][21][22][23]. The composite lattice includes quantum mechanical degrees of freedom related to the S spin subsystem as well as classical degrees of freedom.…”

“…(12) as the perturbing interaction one can derive formulae for relaxation rates describing evolution of individual magnetization modes and coherences of the I spin. In particular, for I = 1/2, the I spin spin-lattice relaxation rate, R 1(I→S) caused by the dipole-dipole interaction to an arbitrary spin S can be obtained from the expression R 1(I→S) = 2Re K DD IS (−ω I ) [8,9,[11][12][13][14][15][20][21][22][23]. The spectral density, K DD IS (−ω I ), is defined as the Fourier transform of the corresponding correlation function G DD IS (τ ) [8,9,11]:…”

“…(12), the spectral density K DD 11 (−ω I ) may be written as [8,9,[11][12][13][14][15][20][21][22][23][24]:…”

“…The independence of the dynamics of the S spin of the motion modulating "directly" the dipole-dipole interaction leads to the separation of the correlation function G DD IS (t) into one function involving only the S spin part and another one including the remaining degrees of freedom: [11][12][13][14][15][20][21][22][23][24]:…”

“…while for the exchange motion between crystal sites, as a first attempt, one can use the formula [3,23,26]:…”