EPR of Gd3+ in single crystal colquiriite and analysis of the spin Hamiltonian tensorsB 4 andB 6

Abstract

Abstraet. In single crystal colquiriite LiCaA1F 6 doped with Gd 3+ ions two EPR speetra of the Gd 3+ ions with the Laue site-symmetry groups C i and C3i were observed. The spectrum angular dependente for trigonal Gd 3+ centre was investigated in detail and corresponding spin Hamiltonian parameters were fitted. From analysis of the spin Hamiltonian tensors B 4 and B 6 it was established that Gd 3 § with the Laue group C3~ substitutes at Ca 2 § site with the excess charge compensation by an ion located along the threefold axis from this site. The transformation formulas for a sixth-rank irreducible Hermitian tensor under coordinate rotation are tabulated in an explicit form. By using the EPR data for Gd 3~ substituted in a variety of host crystals, the fourth-rank and sixth-rank tensors of Gd 3+ spin Hamiltonians were tabulated and correlated with structures of the coordination polyhedra al substitution sites. The results suppose a predominante of quadratic crystal field contributions into the spin Hamiltonian tensor B 4 of Gd 3+.

Low-Symmetry Spin Hamiltonian and Crystal Field Tensors Analysis: Fe3+ in Natrolite

“…Similarity in ionic radii dominates the preference for substitution comparing with valence equality. If in the case of LiCaAlF 6 (20) (11) can be explained only by the closeness in the ionic radii: R(Gd 3+ ) = 0.94Å, R(Ca 2+ ) = 1.04Å (3). The advantage of the topological approach involved is that each conjugate EPR spectrum may be related to a given coordination complex with a specified orientation.…”

“…The ZFS tensor B 4 for Fe 3+ at tetrahedral sites is mainly determined by its cubic component (15,17). The procedure (9) for extracting the maximum invariant component (MIC) of a given symmetry G s in the tensor B 4 was described in (6,11). The invariant sum for the cubic component, i.e., G s = O h , of the tensor B 4 is defined (11) as…”

“…Consequently the operatorsT LM are equivalent (to within the scaling factor for a given L) to the normalized Stevens (NS) operators of Gaite at al., e.g., (6,15); for details see (16) and the review (8). Explicit transformation formulas for the parameters B LM under coordinate rotations are given for L = 2, 4, 6 in (11,17). The rotational invariant for the ZFS tensor of rank L in Eq.…”

“…[1] is equivalent to the expanded form (8) of the ZFS Hamiltonians, whereas the operatorsT LM (11) belong to the category of the "normalized combinations of spherical tensor (NCST) operators" (8) introduced earlier in (13, 14); apart from the coefficient √ 2. Consequently the operatorsT LM are equivalent (to within the scaling factor for a given L) to the normalized Stevens (NS) operators of Gaite at al., e.g., (6,15); for details see (16) and the review (8).…”

“…where first term represents the Zeeman interaction, B LM are real ZFS parameters (11), andT LM are the corresponding hermitian combinations of irreducible tensor operators (12)…”