Quadratic crystal field tensors and spin Hamiltonian tensors of Fe3+ in Li2Ge7O15 above and below the phase transition temperature

Abstract

Dopant Fe 3 t ions in tetrahedral and octahedral positions of Ge 4 I in the crystal Li,GePI5 were studied using EPR. Fe H substitutes for Gc 4 + with a local charge compensation. The octahedral site and the tetrahedral sites significantly differ by the value of the invariant sum S(B 4 ) of the B 4 tensor of the spin Hamiltonian of Fe H . The irreducible tensor products {V 4®V4 } 4 and {V 4®V4 } , of the V 4 tensor of the crystal field calculated using the point-charge model for octahedral and tetrahedral complexes provide the predominant contribution of the crystal field to the B 4 and B, tensors of the spin Hamiltonian of Fe H , respectively. A comparison of the fourth-rank tensors B 4 of the spin Hamiltonian and {V 4 ® V 4 } 4 of the crystal field determined at 300 K with those determined at 77 K supports the conclusion that the phase transition is accompanied by combined rotations of the [Ge0 41 tetrahedra with the [Ge(l)061 octahedron almost unaltered. The spectrum lines are narrow and the variety of point defects in the vicinity of the paramagnetic impurity ions Fe H , Cr 3 + and Cu" is not detected. These facts are inconsistent with the statistically distributed model for the Li(2) atom. In specific cases at 300 K, when the wings of the two spectrum lines of the M -M+ I and the M+ 2 -M+ 3 transitions of Fe H ions belonging to one system of translationally equivalent positions overlap an extra line appears in the center between these lines. It is suggested that this effect is due to the soft phonon mode above the phase transition temperature.

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

“…Within this model, the SH parameters BLM are represented asa sum of the individual contributions from each ion of the nearest coordination. For the regular octahedron and tetrahedron the resulting tensors of the rank L = 4 are of opposite sign [9], whereas those of the rank L = 6 are of the same sign. This can be established by the use of the transformation properties (Table 1) of the tensors B4, B 6 under coordinate rotation through the Eulerian angles a, 13, y.…”

“…This can be established by the use of the transformation properties (Table 1) of the tensors B4, B 6 under coordinate rotation through the Eulerian angles a, 13, y. For L = 4, such analysis has been carried out in [9]. In this paper we will present the results of drawing up of tensors BŸ ~t for L = 6.…”

“…For the fourth-rank SH tensor, these contributions can be represented in the form of expansion in terms of the irreducible tensor products: The inverse splitting pattern for ions in cubic and octahedral crystal fields is determined by the CF tensor V 4 and is in line with the superposition model of CF. The fact that a sign of the parameter of cubicity of the SH tensor B 4 for Gd 3 § is unaffected by the geometry of surrounding, permits one to consider, as in the case of ions Mn 2+ and Fe 3+ [9,31], that the tensor B 4 is determined predominantly by the quadratic CF contributions represented by the irreducible tensor product [V 4 | V414;…”

“…The developed Eqs. (8) for L = 2; 4 are given in [9]. In this paper such formulas for L = 6 are obtained and listed in Table 2 The matrix elements of operators Tz~t(S) are calculated by the formula [8]:…”

The analysis of spin Hamiltonian and crystal field tensors for Fe3+ in crystals of LiCaAlF6 and LiSrAlF6

“…The dominant crystal field (CF) contributions into the spin Hamiltonian (SH) tensors B2 of rank 2 and B4 of rank 4 determined respectively by the BlumeOrbach [1] and Watanabe [2] mechanisms were established for Mnz+ in ZnSeO g x 6H20 [3] and for Fei in Li2Ge,O 15 [4]. These contributions are represented by the irreducible tensor products [V4 ®V4] 2 and [V4 ®V4] 4 of the CF tensor V4 of rank L = 4.…”