Report No 1951/AP - Instytut Fizyki JÄ drowej PAN

DIPOLAR RELAXATION PROCESSES IN THE PRESENCE OF NEIGHBORING
QUADRUPOLE SPINS. LAF 3 CRYSTALS AS AN EXAMPLE
Danuta Kruk * , Oliver Lips, Alexei Privalov, and Franz Fujara
Institute of Solid State Physics, Technical University Darmstadt, Hochschulstr.6,
64289 Darmstadt, Germany
* also: Institute of Physics, Jagellonian University, Reymonta 4, 30059 Krakow, Poland
In multispin systems containing both quadrupolar ( S ≥ 1 ) and dipolar (I=½) nuclei
connected by mutual dipole-dipole interactions, transitions of the dipolar spins leading to their
longitudinal relaxation are accompanied by the quadrupole spin transitions between energy
levels determined by static quadrupole interactions together with Zeeman couplings. Only in
the high field limit, when the Zeeman coupling of the quadrupole spin is much stronger than
its quadrupole interaction the high spin is quantized in the laboratory frame. Thus, the
‘classical’ Solomon-Blombergen-Morgan (SBM) approach to dipolar relaxation, developed
under the assumption of a Zeeman energy structure for both interacting spins, cannot be
treated as a proper description of frequency dependent relaxation processes of the dipolar
spins. In addition, the high spin nucleus usually provides through its own relaxation
mechanism an additional source of relaxation for the dipolar nuclei. From the perspective of
the spin ½ the relaxation processes of the quadrupole spin contribute to time fluctuations of
the mutual dipole-dipole coupling in a manner similar to other stochastic processes like for
example jump diffusion. However, the quadrupole high-spin exhibit complex,
multiexponential relaxation. Under certain motional conditions, a well defined relaxation rate
can be assigned to each coherence associated with a quadrupole spin transition. Since the
dipolar spin senses the various quadrupole relaxation rates corresponding to particular
quadrupole spin modes and coherences, fluctuations of the mutual dipole-dipole coupling
cannot be described by one characteristic time constant. It should be emphasized that the field
dependent quadrupole relaxation rates are also affected by the static quadrupole coupling
through its contribution to the energy level structure of the quadrupole spin.
We present a general description of spin - lattice relaxation of a dipolar spin ½ induced
by its coupling to an ensemble of quadrupole spins, valid for an arbitrary magnetic field and
arbitrary quadrupole spin quantum number. Our approach includes the effects of the
quadrupole spins being quantized in a frame determined by a superposition of the quadrupole
and Zeeman interactions, as well as the multiexponential quadrupole relaxation. We provide
in this way a general tool appropriate for interpretation of field-dependent relaxation studies
for a wide class of solid state systems containing dipolar as well as quadrupole spins with
mutual dipole-dipole couplings. We prove also, that the general approach converges to the
SBM expression in the high field limit, if the lattice motion is significantly faster than the
quadrupole relaxation.
We apply the general approach to interprete frequency dependent fluorine relaxation
studies for LaF 3 crystals, and discuss its remarkable agreement with the experimental data.
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