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LASER SPECTROSCOPY OF RARE EARTH OXIDES
C. Linton
To cite this version:
C. Linton. LASER SPECTROSCOPY OF RARE EARTH OXIDES. Journal de Physique Colloques,
1987, 48 (C7), pp.C7-611-C7-615. �10.1051/jphyscol:19877148�. �jpa-00226969�
JOURNAL DE PHYSIQUE
Colloque C 7 , suppl6ment au n 0 1 2 , T o m e 48, decembre 1987
LASER SPECTROSCOPY OF RARE EARTH OXIDES
C. LINTON
University
of
N e w Brunswick, PhysicsDepartment,
P.O. B o x 4400.Fredericton, New Brunswick, Canada, E3B 5A3
ABSTRACT
Recent developments in the spectroscopy of the rare earth oxides using laser techniques are reviewed. A Ligand Field theoretical approach describing the electronic states is outlined along with the various experimental techniques that have been used as diagnostic tools to test various aspects of the theory.
Results for several molecules are outlined.
INTRODUCTION
The emission and absorption spectra of rare earth monoxides are extremely complex as a result of the large number of electronic states produced by electrons in unfilled f shells. Nevertheless, some extensive high resolution investigations have been carried out (1,2) and have shown that all the low lying states appear to have similar vibrational frequencies (-820-840 cm-l) and rotational constants (B-0.35 cm-'1. The states are classified according to Hund's case (c) in which Q is the only molecular quantum number defining the electronic states. Unfortunately, with one exception (1) there were no transirionr providing the energy linkages between low lying states that are necessary to determine basic electronic structure information such as electron configurations. In order to provide these linkages and simplify the high resolution spectra, we have used various laser techniques. This paper presents a brief, simplified review of the main experimental and theoretical developments resulting from application of these techniques.
Details of the techniques have been described elsewhere (3-5,lO-15).
Resolved fluorescence is used to provide energy linkages between electronic states, vibrational frequencies and relative electronic assignments (AQ=S)'-R").
The laser frequency is fixed to a given transition and the resulting
fluorescence dispersed by a monochromator. High resolution excitation spectra are obtained by scanning a single mode dye laser and detecting with the monochromator set at specific wavelengths which were selected to eliminate unwanted overlapping features. This gives detailed information on rotational structure, first line and hence Q assignments and, in some cases, hyperfine structure. Sub-Doppler Zeeman effect experiments have been performed using intermodulated fluorescence (11,12) in order to confirm S) and J assignments and test the calculated eigenfunctions using the observed g values.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19877148
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LIGAND FIELD THEORY The first laser experiments on CeO (3) and Pro (4) were very successful in providing assignments and energy linkages. It immediately became apparent that, in both molecules, the energy patterns closely resembled those of the Ce2'(fs) and PrZ+(fZs) atomic ions.
This is shown for CeO in figure 1. This led to the development of the Ligand Field Theory (LFT) approach (5,6) in which the metal oxide molecule, MO, is represented by the ionically bonded MZ+Oz-
.
The Oz- "ligandl' is represented as a point charge which electrostatically perturbs the states of M2+.J j...
416r(;,$f o...
I n = J. J.-1 J.-2 A-3 J.-4
Fig. 1. Low lying states of CeO and the 4f6s states of Ce2+ (right)
The OZ- field re-orders and splits the MZ+ states. The calculations (5) show that the ground state configuration is Mz+ (fns) for all the rare-earth oxides except EuO (f7) and YbO (fl') for which the half filled and filled f shell configuration is more stable. The molecular states from the fns configuration can be described in terms of three angular momentum quantum numbers, Jc, for the f electron core, Ja for the total free atomic-ion, and .Q, the projection of Ja on the internuclear axis. The f orbitals, centred on the metal ion, are small compared to the internuclear separation and the effect of the OZ- is small. The s orbitals are larger and are more affected by molecule formation. Thus, properties of the f electrons alone, such as spin orbit splitting, are similar
in the molecule and ion as seen by the separation of the XIXz and X,X, groups in CeO. Properties involving the s electron, such as the fs exchange interaction giving, for example, the XlX2 splitting in CeO, are more affected by molecule formation. This is clearly seen in figure 1. (The labelling of the states in figure 1 is explained in ref. 3).
The ground state can be predicted very easily using a simplistic LFT approach and some rules which derive from the theory. The usual rule for spin-orbit inversion in a more than half filled shell still applies. In
addition, the Ligand Field splitting (i.e. the separation of the Q=J and Q=J -1 stacks (see figure 1) is inverted when the half-shell is more than half full (i.e. for f4-f6 and fl1-f13). AS an example, we can examine DyO (7). In the ionic model this becomes ~y~'(f~s)O~-. The f9 core is more than half full and gives, as its lowest state, an inverted 6H state. The lowest component is
'H,.
,,
thus JC=7.5. This then combines with the s electron (j=$) to give J =J +$, i.e. J =8 or 7. The Ja=8 state lies lowest. The ligand field splitsa c
the J such that Q=Ja, Ja-1 ..-0. As the Ligand Field splitting for f9 is a
regular, the ground state will be .Q=Ja, i.e. n=8. This is confirmed by experiment (figure 2).
Recently, both Dulick (8) and Hocquet (9) have done some very sophisticated ab initio LFT calculations and predicted the energies of all the states from the fns configuration of all the rare earth oxides.
An example of the quality of the predictions is shown in figure 2, where the observed states of DyO (solid lines) are compared with Dulick's predictions (dashed lines). For each observed state, there is a corresponding calculated state of the right Q nearby and this has enabled us to assign the observed states to a particular Q-J stack.
The predictions for many states of the other molecules are equally good giving confidence in the ability of LFT to predict the low lying states.
Hyperfine Structure: The assignment of free ion quantum numbers (Jc,J ) on the basis of agreement with predicted energies is not definitive. We can, however, use hyperfine structure, where resolved, to make this assignment.
For the fns configuration, we can-write a simplified hyperfine Hamiltonian
Fig. 2. Low lying states of DyO Hhfs
-
aI.Jc+
b1.swhere the first term represents the contribution of the f electrons and the latter, the Fermi-Contact contribution of the s electron (s=f$). When the f and s angular momenta are aligned parallel (Ja=Jc+$), the contributions are added to give large hfs. However, if they are antiparallel (Ja=Jc-$), the two terms subtract, giving small hfs. Thus, by comparing hyperfine splittings, we can determine whether a state has J a c =J +$ or J
- 4
and also the relative contribution of the f and s electrons to the hfs. For example, the low lying states of HoO (11) have J2=8.5 ?qd-
7 5. Figure 3a shows the observed states and transitions.HoO ENERGY LEVElS PND TRbNSITICNS
n - J . n .J.-I
Fig. 3(a)
HOLMIUM OXIDE HYPERFME STRUCWE
I d , '
06 I I 0 4 "Fig. 3(b)
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The important parts of the diagram are transitions A and B from a common $2=7.5 state to Q=8.5 and 7.5 states, and transitions C and D from a common $2=6.5 state to low lying 7.5 and 6.5 states. The hfs of A and B and of C and D are compared in figure 3b which shows that the lower state of A has greater hfs than that of B. Similarly hfs (C)
>
hfs (D). Thus the 8.5 state (A) has Ja=8.5, the 6.5 state (D) has Ja=7.5. Of the two 7.5 states, B has Ja=7.5 and C has Ja=8.5.This determines the correct placement of the two 7.5 states in the $2-J stacks.
A more rigorous treatment of hyperfine effects in Pro has been presented by Dulick and Field (4).
Another way of assigning quantum numbers and testing the eigenfunctions is via the Zeeman effect as the electronic g values are dependent on the quantum numbers. The Zeeman patterns are also unique to $2 and J and can be used to check assignments. For CeO, Schall et al. (11) found excellent agreement between observed g values and those calculated from ab-initio eigenfunctions.
For SmO (12) the Zeeman patterns were used to confirm the assignments. This is discussed in more detail in a separate paper in these proceedings.
A useful diagnostic tool for distinguishing between configurations (e.g.
fn vs. fn-Is) is the vibrational frequency. The f orbitals are compact and therefore shield the 0'- from the added nuclear charge on the metal as we go across the rare earth group. Thus, the 0'- sees the same nuclear charge in each molecule, the force constant is therefore similar and all the vibrational frequencies are the same. However if, instead of fn-Is, the molecule has an fn ground state, the non-shielding s electron has beep replaced by a shielding f electron, reducing the megal nuclear charge seen by the 02' and reducing the vibrational frequency. Thus the fn-'s configuration states should have a higher vibrational frequency than the fn states. For all the rare earth oxides studied so far, the ground states have vibrational frequencies in the 820-840 cm-' range except for the ground states of EuO(f7) (13) and YbO(fl4) (14) which have vibrational frequencies of 690 cm-l. Thus vibrational frequencies obtained from low resolution data are a definitive guide to the electron configuration!
This paper has presented a simplified picture of the main ideas of LFT and some of the diagnostic spectroscopic tools used to test these ideas. Much of the detail has been left out and can be found in the references. Many molecules have been studied and the results have demonstrated the validity of applying LFT to a group of molecules for which molecular orbital calculations would be virtually impossible.
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