Defects in inorganic photorefractive materials and their investigations

6 B. Briat et al.
breaking their equivalence. Also such bound polarons lead to strong optical
absorptions [7, 11], due to the long transition dipole between the initial and
a neighboring oxygen ion in the tetrahedron. For more details, see Section 6.
Some of the photorefractive crystals, such as congruently melting LiNbO 3
(LN), Sr 1−x Ba x Nb 2 O 6 (SBN)orBa 1−x Ca x TiO 3 (BCT), are strongly disordered.
This leads to considerable spatial fluctuations of the defect levels,
causing wide lines in all spectroscopic studies [12]. Furthermore, the mobility
of quasifree charge carriers tends to be reduced in such materials.
3 Methods of defect investigation
We start by giving a qualitative overview of the electron paramagnetic resonance
(EPR) method. The electronic ground state of a paramagnetic defect
is characterized by its spatial distribution and by its spin number. Within
the spatial range of their wavefunction, the unpaired electrons collect all interactions
by which they can couple with their surroundings, among these:
spin-spin- and spin-orbit-coupling, also in combination with crystal fields, and
hyperfine interaction of the electrons with the ’visited’ nuclei, representing local
probes in the crystal. If a static external magnetic field is applied, Zeeman
interaction is also active. EPR methods probe the energy splittings between
the lowest states caused by these couplings. The external magnetic field provides
a reference direction and thus allows the symmetry of the interactions
to be identified. They are of tensorial character if the defect as a whole or
the positions of the interacting nuclei are non-cubic. This analysis leads to
the most essential information supplied by the method: the symmetry of the
coupling tensors and the orientation of their principal axes with respect to the
crystal lattice, strongly narrowing down possible defect models. For a recent
overview on the application of EPR and related techniques, especially optical
ones, to the elucidation of defect properties see, e.g., Ref. [13].
It is an advantage of the EPR method that it allows to determine the concentration
of paramagnetic defects [14], opening the way to the quantitative
analysis of the performance of a photorefractive material on the basis of EPR
studies alone. For further details see Section 5. EPR can ’count’ defect densities
down to a few ppm. Only neutron activation analysis, see for example [15]
is more sensitive. But there it is not possible to detect intrinsic defects or to
differentiate between the various charge states which the same defect element
can assume, such as e.g. Fe 3+ and Fe 5+ , a task which can be solved by EPR.
All interactions probed by the electron(s) are usually summarized by a
spin-Hamiltonian, for example:
H = µ B BgS + SDS + ∑ SA i I i + ..... (1)
where only three representative terms are given for illustration. The first one
describes the Zeeman interaction, the second a crystal field interaction and