Figure 4.3 Low-temperature site-selective excitation spectrum of the 5Ig —> 5F5 transition in the CaF2: Ho3+ C4v centre.
In the tetragonal (C4v) crystal field, the ground 5Ig multiplet splits into 4 doublets and 9 singlets,
~*Ig —^ 3Aj + 2A9 + 2Bj + 2B0 + 4E,
whereas the excited 5F5 multiplet splits into 3 doublets and 5 singlets,
5F5 —^ Aj + 2A2 + Bj + B0 + 3E.
For trivalent rare-earth ions in crystals, the crystal-field splittings are typically of the order of tens to hundreds of wavenumbers (Bleaney 1967, Macfarlane and Shelby 1987, Macfarlane 1992). As a result, one would expect that, at liquid helium temperatures, only the lowest crystal-field level in the ground multiplet is populated, and hence the energy levels of the excited-state crystal-field levels should be obtainable directly from the low-temperature excitation spectrum.
In the case of the C4v CaF2: Ho3+ centre, it can be seen that (Fig.4.3) the optical excitation lines appear in pairs with a separation within each pair of 1.7 cm '1 ; even though, for some pairs (two higher energy pairs), the intensity of one line is much weaker than that of its partner. As the doublet (pair) structure appears in all optical transitions, it can be concluded that the origin of such structure is in the ground multiplet. This conclusion implies that the two lowest ground- state crystal-field levels are separated by 1.7 cm '1 in agreement with the value derived from high field EPR (Kornienko and Rybaltobskii 1972), and hence the optical transitions 1 and 2
originate from the same excited-state crystal-field level. Likewise, optical transitions 3 and 4 originate from a single excited-state level as do optical transitions 5 and 6. The spectrum shown
in Fig.4.3 is therefore associated with transitions between two ground-state and three excited- state crystal-field levels.
The much weaker intensity lines will be shown to correspond to nominally group-theoretically
forbidden forced electric-dipole transitions. To become observable (partially-allowed), there
must be interactions that can result in the mixing of the wavefunctions, and it will be shown that
the mixing occurs between the two lowest ground-state levels. The details of the mixing will be given in Chapter 5 (Sec.5.4.1) where the analysis of higher resolution data is presented. By
examining the electric-dipole selection rules for the C4v symmetry (Table 4.1), it can be concluded that, as transitions involving doublet states are group-theoretically allowed, the weak lines should correspond to the group-theoretically partially-allowed forced electric-dipole
transitions between two singlets of different symmetry.
According to Mujaji (1992), six of the excited-state crystal-field levels can be established from the low-temperature excitation spectrum. As transitions involving doublet states (either doublet
<-» doublet or doublet <-> singlet transitions) are group-theoretically allowed, lines corresponding to transitions to all three 5F5 doublet states should always be presented in the excitation spectrum. Since, in the 5F5 multiplet, there are three A states (Aj + 2A2) and two B
states (B, + B->), the remaining three excited-state crystal-field levels, whose existence can be established from the excitation spectrum, should have A symmetry. The absence of transitions
to the two B singlet states implies that transitions from the two ground-state levels are not allowed. By examining the C4v selection rules (Table 4.1), it can be concluded that the two lowest ground-state crystal-field levels are both singlets with A symmetry (either Aj + Aj, or Aj + A2, or A0 + Aj, or A0 + A2).
For the highest energy pair in Fig.4.3, the intensity of the higher energy optical transition line (line 6) is much larger than that of its partner (line 5). Using the C4v selection rules, it can be concluded that (i) the two lowest ground-state crystal-field levels are singlets with different A symmetry (either Aj + A2 or A2 + Aj), and (ii) the excited-state crystal-field level is a singlet of
the same symmetry as that of the lowest ground-state singlet. The reversed situation for the middle energy pair (lines 3 and 4) implies that the associated excited-state crystal-field level is
also an A singlet but of the same symmetry as that of the second-lowest ground-state singlet.
For the lowest energy pair, both optical transitions 1 and 2 are of reasonable intensity and hence
are both associated with the group-theoretically allowed forced electric-dipole transitions. Since
the two lowest ground-state singlets are of different A symmetry, the excited-state crystal-field level is an E doublet. This conclusion was strengthened by the observation of the splitting, in an
applied magnetic field, of this excited-state crystal-field level into two components (Sec.4.2.2.1).
The results of the above analysis, which support the earlier assignments made by Mujaji et al
(1992), are schematically summarized in Fig.4.4. As it is not possible to experimentally distinguish between Aj and A2 (Bj and B2) singlets, the specific symmetry assignment of the
crystal-field levels can only be made by employing the crystal-field calculation. The results of such a calculation (Mujaji 1992, Mujaji et al 1992) suggest that the lowest 5Ig ground-state
crystal-field level is an Aj singlet, and that the lowest 5F5 excited-state crystal-field level is a singlet of Bj symmetry located at 4.5 cm '1 below the E doublet. The existence of this Bj level had been experimentally established from fluorescence spectra by Mujaji (1992). This Bj
singlet is also included in Fig.4.4.
5 5 I 8 singlet singlet doublet singlet doublet singlet singlet 6 5 > / 4 3 / > ' 2 1 ' y /< 2s 25 2S 25 2S 2 --- ^ --- Specific Symmetry Assignment 'S Energy (cm 1) 15682.0 15623.0 15609.5 15605.0 83.0 1.7
0
l 1 6 5 4 3 2 ◄---energyFigure 4.4 Crystal-field energy level diagram for the low-lying levels in the ground 5Ig and the excited 5F5 multiplets of the A centre.
4.2.2 Confirmation of the existence of the
level in the
excited 5F5 multiplet
In the previous section, it had been established that the two lowest crystal-field states in the ground multiplet are singlets of Aj and A9 symmetry. According to the C4v selection rules, in the absence of an applied field, electric-dipole transitions between states of A and B symmetry are not allowed. As a result, the existence of the two excited-state crystal-field levels having Bj
and B9 symmetry could not be established from the low-temperature zero-field excitation spectrum. However, it has been established by analysing fluorescence spectra that the lowest crystal-field level in the excited 5F5 multiplet is a Bt singlet (Mujaji 1992). In this section, the results of two alternative experiments which confirm the existence of this Bj singlet will be presented.
4.2.2.1 Mixing between crystal-field levels by an applied
magnetic field
One way to observe zero-field forbidden A — > B transitions is to mix into the excited B state a
state in which transitions from the ground states are allowed. This can be achieved by applying an external magnetic field 3 in an appropriate direction. The oriented CaF2: Ho3+ crystal was mounted in an Oxford Instruments 5T helium exchange gas cryostat within the bore of a superconducting magnet (Sec.3.6). A typical Zeeman spectrum is shown in Fig.4.5 for a magnetic field of 3.057 Teslas applied along the (100) direction. In this configuration, there will be two inequivalent orientations of the C4v centres with respect to the field which are (a) those
having the C4 axis parallel to the field (to be called axial centres), and (b) those with the C4 axes
perpendicular to the field (transverse centres). As shown in Fig.4.5 for the field of 3.057
Teslas, thirteen excitation peaks are observed, and ten of these (denoted by a to j) are attributed to the transverse centres. The remaining three peaks (denoted by a, ß, and y) belong to the axial
centres. The two lowest energy peaks, a and b, correspond respectively to the 5I8 (A2) -A
5F5(Bj) and the 5I8(Aj) —> 5F5(Bj) transitions which are now partially-allowed due to the mixing between the 5F5 (Bj) and 5F5 (E) levels by the transverse component (perpendicular to
the C4v axis) of the applied magnetic field. The experimental Zeeman energy level diagram for
the low-lying 5F5 levels of the transverse centres, obtained under the assumption that the Aj singlet at 15682.0 cm '1 does not move in the field, is shown in Fig.4.6. The existence of the Bj
level at 15605.0 cm '1 can be established by extrapolating to zero field.
6390
wavelength (Ä)
Figure 4.5 Low-temperature high-field Zeeman excitation spectra for the A centre: (a) zero field, and (b) in a field of 3.057 T applied along the (100) direction. Peaks