Electron Spin Resonance of Paramagnetic Crystals

Theoretical Studies of the EPR Parameters of Nd3+ in LiYF4

“…For an Nd 3+ (4f 3 ) ion under tetragonal symmetry, its ground 4 I 9/2 configuration may be split into five Kramers doublets because of the spin-orbit coupling and tetragonal crystal-field interactions. According to theḡ[= (g + 2g ⊥ )/3 ≈ 2.34] of the experimental g factors of Nd 3+ in LiYF 4 [6], it can be attributed to the lowest doublet Γ 6 , whose average valueḡ would be about 2.67 for a 4f 3 ion [7,8]. In [7,8] only the contributions to the EPR parameters from the first-order perturbation terms were included.…”

“…According to theḡ[= (g + 2g ⊥ )/3 ≈ 2.34] of the experimental g factors of Nd 3+ in LiYF 4 [6], it can be attributed to the lowest doublet Γ 6 , whose average valueḡ would be about 2.67 for a 4f 3 ion [7,8]. In [7,8] only the contributions to the EPR parameters from the first-order perturbation terms were included. However, besides the lowest Γ 6 , the other 10 irreducible representations Γ x (i.e., five Γ 6 and five Γ 7 ) due to the tetragonal splitting of the ground 4 I 9/2 and the first excited 4 I 11/2 levels would mix with the lowest Γ 6 via crystal-fieldĤ CF and orbital angular momentumĴ (or hyperfine structure equivalent operatorN) interactions and lead to the second-order perturbation contributions to g factors (or hyperfine structure constants), as pointed out in [9,10].…”

“…where the diagonal elements g J (or N J ) of the operator J (orN) for various states can be obtained from [7,8].…”

“…Thus the D 2d symmetry turns out to be a good approach, and we still take D 2d approximation here for simplicity. For the Nd 3+ (4f 3 ) ion in D 2d symmetry, the crystal-field interactionĤ CF in the above formulas can be written in terms of the Stevens operator equivalents as [8,10] H CF = B …”

Investigations of the EPR g Factors for Er3+ in CaMoO4

“…For an Er 3+ (4f 11 ) ion in a tetragonal (S 4 ) site without inversion symmetry, the 4 I 15/2 ground state may be split into eight Kramers doublets. The lowest doublet can be (Γ 5 + Γ 6 ) or (Γ 7 + Γ 8 ), corresponding to the cubic (T d ) representation Γ 6 or Γ 7 , with an average valueḡ [= (g + 2g ⊥ )/3] of about 6.8 or 6 [15], respectively (note: the above notation for T d [15] is an exchange of that for octahedral cubic O h symmetry in [16,17]). According to the observedḡ(≈ 6) for Er 3+ in CaMoO 4 [10,11], the lowest doublet should be (Γ 7 + Γ 8 ).…”