Studies of the optical spectra and spin-Hamiltonian parameters for the trivalent ytterbium ions in lithium yttrium fluoride crystals

Neutron spectroscopic study of crystal-field excitations and the effect of the crystal field on dipolar magnetism inLiRF4(R=Gd, Ho, Er, Tm, and Yb)

“…Our results are broadly in good agreement with previous studies. A discrepancy is found for the less well-known LiYbF 4 [22,24]. Although the energy-level scheme is found to be in agreement with those measured, we cannot capture very well the Q dependence of the intensities in our neutron scattering measurements.…”

“…Additionally, some isotopes of R carry a nuclear magnetic moment and a further hyperfine interaction H HF between the electronic and nuclear spin degrees of freedom may need to be taken into account. Many studies have attempted to address the CEF environment of LiRF 4 using Raman scattering, infrared spectroscopy, and susceptibility measurements [1,[16][17][18][19][20][21][22][23][24]. However, there are a large range of values reported and only few studies have used inelastic neutron scattering as an experimental probe.…”

Theoretical investigation of the optical and EPR spectra for ytterbium(III) in strontium tungstate crystal

“…For a Yb 3+ (4f 13 ) ion under a tetragonal symmetry, the ground state 2 F 7/2 may be split into four Kramers doublets and the excited state 2 F 5/2 may be split into three due to the effect of spin–orbit coupling and tetragonal crystal field 9, 10. The energy Hamiltonian for a Yb 3+ ion in the crystal under an external magnetic field can be written as 11–14 where H f is the term of free ion. The spin–orbit coupling term H so = ζ ( LS ) with the spin–orbit coupling coefficient ζ , here we take ζ ≈ 2900 cm −1 12, L and S are the orbital and spin momentum operators, respectively.…”

“…The crystal‐field interaction term H cf is where $B_k^q$ and $C_k^q$ are the crystal field parameters and tensor operators, respectively. For a 2 S +1 L J manifold, the Zeeman and hyperfine interaction terms H z and H hy can be expressed as 9–14 where g J , µ B , $\hat {J}$ , and $\hat {B}$ are the Landé factor, the Bohr magneton, the angular momentum operator, and the external magnetic field, respectively. P is the dipolar hyperfine structure coefficient that possesses different values for the different ions or isotopes [ i.e ., the free Yb 3+ ion values, P ( 171 Yb) ≈ 392 × 10 −4 cm −1 and P ( 173 Yb) ≈ −108 × 10 −4 cm −1 9].…”

“…By diagonalizing the full energy matrix, the energy eigenvalues ( i.e ., the optical absorption spectra band positions) can be obtained. The spin‐Hamiltonian g factors and hyperfine structure constants A i are calculated by the following formulas 11–14 where E z ( i ) ( i = z , x ) are, respectively, the Zeeman splitting obtained by diagonalizing the energy m atrix for 4f 13 ions in crystals under an external magnetic field B along the z‐ and x‐axes . Δ E hf ( i ) denote the hyperfine splitting in the cases of the equivalent operator $\hat {N}$ of magnetic hyperfine structure along the z ‐ and x ‐axes.…”