Zeeman splitting factor of the Er3+ ion in a crystal field

Abstract

Numerical computations are presented on the energy levels of the Er" ion in crystalline fields of cubic, trigonal, tetragonal and orthorhombic symmetry. Zeeman splitting factors were obtained from the level splitting in an additional magnetic field. For the quartet F8 states in cubic symmetry the Zeeman effect is described by an effective Hamiltonian gpBBJ + up5BJ' with the parameters g and u calculated for mixed fourth-and sixth-order potentials. For the eight doublets in the lower symmetry of an axial trigonal or tetragonal crystal field the principal g tensor components g i and gl were calculated. The results of such calculations for a ground-state doublet can exactly account for the experimental data obtained on around 70 erbium centers in various crystalline hosts. However, sometimes different sets of parameters give comparably good results. An empirical rule of constant trace g ip + 2g1 is supported by the calculations. In contrast to analytical treatments the effect of the crystalline field can be followed over a continuous range of the crystal field parameters. This allows one to establish relations on the relative signs of tensor components. It is found that the measured trace of tensors Ig n I + 2IgIis not always equal to their real trace g il + 2g1. In an exploratory calculation a nonaxial center was simulated in an orthorhombic field, with calculation of the three principal values g, g and g. A good agreement is obtained for the recently reported g values of an erbium center in silicon.

Crystal field and Zeeman parameters of substitutional Yb3+ ion in GaN

“…The lowest of these Kramers doublets give rise to the calculated g-values. Specific values g|| and g⊥ for a particular host depend on the strengths of the cubic and lower symmetry components of the crystalline electric field [36,37]. The Zeeman interaction ∧ HZ , can be written asĤZ = gJ B HĴ, where gJ is the Landé factor and ∧ J is the orbital angular momentum operator [39].…”

ESR study of rare-earth ions with the effective spin of 1/2 in LiNbO3 crystals

“…SH parameters of Er 3+ in CLN and MLN at 4 K. those which originated from Fe 3 §[1], an unintentional impurity remained in the sample and appeared as stronger signals after the vapor transport equilibrium treatment than before.The calculated gli + 2g• for Er 3+[12] in CLN is 18.66 for the center 1 and 15.58 for the center 2, as we determined. The value for the center 1 hardly differs from those reported by Milori et al (gla + 2g• = 19.41, see ref.…”

“…The calculated trace of g, g~l + 2g• of this center is 19.79. In addition, these g-values are much closer to the isotropic g-value of Er 3+ (g~so = 6 for the 1-'7 state and gi~o = 6.8 for the F 6 state [12]) than the g-values of the Er 3+ center at the Li site mentioned above. Therefore, we can expect the new Er 3 § in MLN should be located nearer to the isotropic site in LN.…”

Theoretical studies of the g factors for the tetragonal and orthorhombic Er3+ sites in ErBa2Cu3O7− superconductors

“…Obviously, the above theoretical methods can also be applied to other Er 3+ centers in orthorhombic environments, e.g., the recently reported orthorhombic Er 3+ centers in silicon [26][27][28].…”