Hyperfine resonances in the tetragonal centre of Ho3+ in CaF2

JOURNAL OF

LUMINESCENCE

--

ELSEVIER

Journal of Luminescence 59 (1994) 36 1—368

Hyperfine resonances in the tetragonal centre of Ho3 + in CaF2 T. Boonyarith*, J.P.D. Martin, N.B. Manson Laser Physics Centre, Research School of Physical Sciences and Engineering, Australian National University, Canberra, ACT 0200, Australia (Received 7 September 1993; revised 3 January 1994; accepted 3 January 1994)

Abstract 3 + in CaF The ground state hyperfine resonances of the C4,, centre of Ho 2 have been detected by using a hole burning microwave-optical double-resonance technique. Resonances are detected, in zero magnetic field, at 2.250, 1.608 and 0.842 GHz corresponding to the transitions between the hyperfine levels of the ground electronic state. In addition, weaker signals are observed at 2.340, 1.669 and 0.872 GHz. These resonances correspond to the hyperfine transitions within the neighbouring electronic state 1.7 cm higher in energy, and result from thermally allowed electronic transitions between hyperfine levels with the same nuclear spin projection. The low field Zeeman behaviour of these resonances has also been studied and updated values for the hyperfine and crystal field splitting parameters are reported.

1. Introduction The ground 3 + in CaF state of the tetragonal (C4~)centre of Ho 2 has been shown to comprise of two electronic singlets strongly admixed by the hyperfine interaction [1,2]. The mixing effects give rise to anomalously large pseudoquadrupole splittings of the hyperfine components of the electronic singlets, and result in an unusual optical pattern for transitions from the ground had singlet levels.Martin An analysis of the optical spectrum enabled et al. [2] to obtain an estimate of the hyperfine splittings of 2.28(54), 1.63(49) and O.85(49)GHz in the two singlet states. The peak position in the optical spectrum however could only be determined to ±0.05 0Hz and hence these values have limited accuracy. In this paper, it is reported that opticalmicrowave double-resonance measurements have *

Corresponding author,

provided an order of magnitude improvement in resolution and differences are detected in the hyperfine splittings of the two singlets. Estimates of the quadrupole parameters for the ground and excited states are also obtained in the analysis.

2. Theory 3~is When a trivalent rare earth ion as Ho for incorporated into CaF 3 +such substitutes 2, the Hois usually achieved Ca2 and charge compensation by the inclusion of an additional F ion at one of the adjacent vacant body centre sites displaced along the <001> direction from the rare earth ion. This gives a centre of tetragonal symmetry, termed the A centre, which is the centre investigated in this paper. The spectroscopy of the centre is treated by Mujaji et al. [3], and the high resolution excitation of the ‘8 {A 5F 1, A2} =. 5{E, A2} transitions has been

0022-231 3/94/$07.00 © 1994 — Elsevier Science BY. All rights reserved SSDI 0022-231 3(94)00006-X

~,

362

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ci a!.

/ Journal of Luminescence 59 (1994) 361—368

given by [1,2]. The two lowest levels in the ground ‘8 multiplet are two singlets of A1 and A2 symmetry separated by 1.7 cm As their nearest neighbouring level (an E doublet) is at 83cm~ higher in energy, the two singlets will be treated in isolation. In zero applied magnetic field, the Hamiltonian describing these coupled singlets can be written as [2,4]

51

51 8(A1) and 8(A2) states, respectively. The associated eigenvalues are

~.

~

=

field

+

(1)

.)~‘hyperfjne

where h[ {A11 I~J~ + ~

.)~‘hyperfine

(I + .i

j÷ ~j.

+ j

+ P{I~ ~I(I + 1)}].

(2)

—

The wavefunctions associated with these two orbital singlets are mixed by the axial term in the hyperfine interaction and are given by IA1, m)”

a(m)1A1, m>

b(m)1A2, m>

(3)

b(m)IA1, m> + a(m)1A2, m>

(4)

—

and IA2, m>’

=

where A~denotes the electronic component and m the z-component of the nuclear spin. The coefficients are given by a(m)

=

—

+

13)12)2 +

~2

2

—

—

{~((~13)12)2 + y

fl)/2)} ((~ 13)/2)}2 —

—

—

(5) and b(m)

=

{~((~ ~fl)/2)~ + ~2

—

((~

—

fl)/2)}2

(6) where 2 21/4), P1 (m 2 21/4), A + P2(m

(7)

—

(8)

mA
IA2>.

(9)

—

13

=

—

4

+

and =

=

—

significant interaction between these states in the experimental optical excitation spectra. For example, neither from the ground 51 of the transitions 51 5F state singlets 8(A1) and 8(A2) to the excited 5(B1) state are observed. In the absence of the hyperfine interaction and any external magnetic field, these transitions are group theoretically for5F there been any significant mixing 5F bidden; but had between the 5(B1) state and the adjacent 5(E) state, which can occur via the transverse component of the hyperfine interaction, ~A1{I+J_ + LJ+}, then these nominally forbidden transitions 5F would have gained intensity. An admixture of the 5F 5(E) 5F and either of the adjacent singlets, doublet 5(B1) or 5(A2), would be reflected in an irregularity in the hyperfine intensity pattern [5] but no such irregularity was observed. It can be 5F 5F concluded therefore that5Fthe 5(B1) singlet, the 5(E) doublet and the 5(A2) singlet can each be treated, in the first order, as isolated states. The 5F energies corresponding to the 5F 5{IE±,m>}and 5{1A2,m>} hyperfine states, in particular, are given by 2—21/4), E~(m)=E~ ±mA~+P~(m (11)

__________

+

=

_______________

((ci + Th/2) ~ 13)12)2 + ~2• (10) 5F In the excited 5 multiplet, the three lowest lying levels are a B1 singlet, an E doublet, and an A2 singlet located at 15605 cm 1, 15609.5 cm 1, and 15623 cm 1, respectively. There is no evidence of EA1(A2)(m)

Here, 24 represents 51 the 51 crystal-field splitting between the 8(A1) and 8(A2) states; P1 and P2 are the effective direct quadrupole parameters for the

and E~ 2 21/4), (12) 2(m)= E~+ P~(m where A~ 1is the axial dipole hyperfine coupling constant for the excited multiplet; E~and E~are the crystal field energies of the 5F 5F 5(E) and 5(A2) states; and P~and P~are the effective quadrupole parameters for the 5F 5F 5(E) and 5(A2) states, respectively. In the presence of an applied magnetic field (H), the Zeeman interactions, described by the Hamiltonian —

~

= =

~rdedtro~ Zeeman

t

~onuclear Zeeman

‘-~

gJ,JBJ.H— ~

(13)

T. Boonyarith ci al. / Journal of Luminescence 59 (1994) 361—368

have to be taken into account. Normally the effect of the nuclear Zeeman interaction is very small and therefore can be neglected in the first order. The axial component of the electronic Zeeman interaction, gJJJBHZJZ, can cause the mixing of the two electronic singlets in the same manner as that caused by the axial component of the magnetic hyperfine interaction. As a result, in an applied magnetic field, the energies of the ground state hyperfine levels, 518{IA1,m>’} and 5I8{1A2,m>’}, are

(a)

F

2.250

IiIt~c ~

I

2.150

B A

2.2~O

2.350

2.450

(b) H)

=

((~+ fl)/2)

1.608 1669

_________________

where

/~_fl)/2)2+(y+X)2,

X=gJ~JBHZ.

(14)

‘~

(15) 1.550

In the very low field limit, we have a linear Zeeman effect EAI(A2)(Fn,

J

2.340

~‘

given by EA1(A2)(m,

363

H)

~EAl(A2)(rn,O)

—

.

/3)/2)~+

(c)

1.600 0 842

1.650

1.700

(16)

~

0.825

0.850

0.875

0.900

Microwave Frequency (0Hz) 3. Experiments and results 51 5F The 8(A1 A2)=. 5(E) optical transitions of Ho 3 + tons in tetragonal sites of CaF2:Ho ~ + (0.0005%) exhibit 100% spectral hole burning, The observation of strong superhyperfine resonances [1,2] implies that the dominant mechanism for hole burning is the nuclear 19Fspin nuclei flips surrounding within the frozen core of neighbouring the Ho3 + ion while the centre is in an optically excited state. This behaviour is consistent with other rare earth optical centre in lattices containing fluorine ions [6]. Satellite hole burning in the other hyperfine lines within the same optical transition has also been observed via two laser hole burning experiments. This satellite hole burning results from thermally induced ‘65Ho nuclear spin flips within the ground state singlet which attempt to restore the population in the hyperfine state resonant with the laser. In addition, as reported below, .

.

.

hole burning due to thermally allowed electron spin flips between the two ground state levels has

Fig. 51 1. The 5F experimental hyperfine ODMR spectra for the 8(A1)= 5(E) optical transition. Traces (a), (b), and (c) are obtained when the laser was tuned to saturate the optical hyperfine lines A, B, and C (shown on the top right corner), respectively.

also been observed with the simultaneous observation of two sets of hyperfine resonances. The CaF 3~ (0.0005%) single crystal was 2: Ho mounted within a microwave helix [7] and immersed in a pumped liquid helium bath. Microwave radiation was applied while the laser continuously saturated one of the optical hyperfine transitions. The change in the emission signal as the frequency of the microwaves coincided with a ground state resonance was recorded and averaged for repeated sweeps of the microwave radiation. The resultant hyperfine ODMR spectra for the 5I 5F 8(A1)=~~ 5(E) optical transition are shown in Fig. 1. When the laser is tuned to the hyperfine line A, corresponding

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/

Journal of Luminescence 59 (1994) 361—368

5Fs{IET,±~>}transitions to the 51 ±1), ~>‘}~. (see insert8{1A1, in Fig. a strong hyperfine resonance at 2.250(2) GHz is observed together with a weaker one at 2.340(3)0Hz (Fig. 1(a)). Exciting the 51

5F

5{IE~,±~>}optical transition also gives the same pair of microwave resonances but with the intensity of the two signals interchanged (not shown). The stronger resonance ob5I tained when pumping the 8(A1) state directly (Fig. 511(a)) is consequently taken to correspond to the 8{IA1, ±~>‘~IAi, ±~>‘} hyperfine transitions whereas the weaker one corresponds to the 51 8{1A2, ±~>‘~IA2, ±~>‘}hyperfine transitions. In assigning the above ODMR signals, it should be remembered that the two ground state singlets 8{1A2, ±~>‘}~

the hyperfine levels are populated at liquid helium temperatures are separated and by only there will 1.7cm’, be a thermal and hence cycling all between the levels. These thermally stimulated transitions between the hyperfine levels of the two electronic states will normally retain the same nuclear spin projection, in an analogous manner to that which occurs between the two electronic cornponents of an electronic doublet [5,8]. The electron spin flips present due to thermal excitation will result in the population in associated levels to be interconnected and depleting one level will deplete the other (Fig. 2). The application of microwave radiation at the resonant frequencies can then induce hyperfine transitions within both electronic singlets giving rise to the two sets of hyperfine ODMR resonances. The laser is, however, resonant with one ground state hyperfine level, and this is the only level which is directly depopulated. Microwave resonances associated with this level will give the larger signals. A similar result involving superhyperfine 3resonances has[9]. also been observed in this ~ centre CaF2: Ho the hyperfine line B gives two more Burning resonances at 1.608(3) and 1.669(3) GHz, Fig. 1(b), -~

and 51these are considered to be associated with 51 the 8{1A1, ±~>‘~IA1, ±~>‘}and 8{1A2, ±~>‘ ~IA2, ±~>‘} hyperfine transitions, respectively, Similarly, burning the C line gave a signal at 0.842(4)0Hz which we associate with the 51 8{IA1, ±~>‘.~.IA1,±~>‘} hyperfine transitions. The hyperfine splittings in both ground state singlets are therefore experimentally established and are

Laser

(0Hz)

T2340

—~—±7f2

—

~

=

______

—

—

0.872

+ 1.669

—~~—±5f2

51.43

= —: ‘~‘

~I2

+ I

±~a .L

0.842 1.608 2.250

A Fig. 2. Diagrammatic explanation ofthe occurrence ofthe additional hyperfine ODMR resonances (see text). The wavy, dashed arrow, and solid arrow lines represent the thermally induced, microwave, and optical transitions, respectively.

summarised in Table 2. From the small differences between the resonant frequencies in the two electronic states and the form of the eigenvalues (Eqn. (10)), the sum of the electric quadrupole parameters can be precisely determined as 51 P1 + P2 = 0.015(2)0Hz and hence the 8{IA2, ±as~>‘beingIA2, ±~)‘}0Hz hyperfine splitting is estimated 0.872(5) which is plausible from Fig. 1(c). However, the determination of A 1 , zl,P1 and P2 simply from the microwave data is not straightforward, and an accurate remeasurement of the separation [61.173(100)0Hz] 51between the two hyperfine lines associated with the 8{1A1, 5F 51 5F ±~>‘} 5{IA2, ±~>}and 8{1A2, ±~>‘}~. 5{IA2, ±~>} optical transitions was required. Using the doubleresonance data and the optical measurement we obtained A = 25.542(77)GHz,Aii = ~—

T. Boonyarith ci al.

4.890 (22)0Hz, P1

=

0.035(5), and P2

=

/ Journal —

of Luminescence 59 (1994) 361—368

0.020

the earlier estimates A = 25.61(35)0Hz and Aii = 4.72(15)0Hz [2]. The current value of Note (5)0Hz. A11is that there areinonly excellent small changes agreement to with the value of 4.90(5)0Hz derived from the high-field Zeeman EPR experiments [10]. Following the analysis of the zero field values of the hyperfine splittings, low field Zeeman measurements (0—1500) on the ground-state hyperfine resonances were also conducted for the magnetic field applied along the <111> direction (Figs. 3 and 4). In this case, all the C4,, centres presented in the crystal

I

~ ~ ~c’3

~

I

~‘

I

I

I

365

I

(c)

,,~

:~i~

(d)

~ililil

(b)

~

Fig.

1.500

1.600

1.700

1.800

Microwave Frequency (GHz) 51

4. The experimental hyperfine51 ODMR spectra for the 8{1A1, ±~>“~IA1, ±~>‘} and 8{1A2, ± 51~>‘~IA2,±1>’} hyperfine 5F transitions associated with the 8{1A2, ±1>} 5{IET, ±~>}optical transitions in zero field (a), and in fields

(c)

I~

of44 the For G (b) field andof8888GG, (c the and optical d)applied hyperfine along the line<111> splitsdirection. into two components, and trace c (d) was obtained by exciting the higher (lower) energy component.

I

I

I

2.100

2.200

2.300

2.400

2.500

Microwave Frequency (0Hz) Fig. 3. The experimental hyperfine ODMR spectra for the 51 51 5I 8{1A1, ±~>“=Ai, ±4>’} and 8{1A2, ±~>“=~A2,± 1>’} hy5F perfine transitions associated with the 8{1A2, ±~>‘} 5{!E+, ±~>}optical transitions in zero field (a), and in fields of 44 G (b) and 88 G (c and d) applied along the 111 direction. For the field of 88 G, the optical hyperfine line splits into two components, and trace c (d) was obtained by exciting the higher (lower) energy component.

are equivalent, with their C4 axis making an angle of 0 = tan i(1/\/~)with the field direction, and hence each zero-field hyperfine line observed in the 51 5F 8(A1,A2) 5(E,A2) optical transitions splits into two components. The typical Zeeman hyper5I spectra associated 5F with hole burning fine ODMR in the 8{1A1, ±~>‘} 5{IE~,±~‘>} optical ~‘

transitions (denoted by A in Fig. 1) are shown in Fig. 3 for zero field (a), and fields of 44 0 (b) and 88 0 (c and d). As has been discussed before, the

366

T. Boon~arithci a!.

/

Journal of Luminescence 59 (1994) 361—368

two resonances observed in zero field correspond respectively to the 518{1A1, ±~>‘~IA1, ±~>‘}and 5I 8{IA2, ±~>‘~IA2, ±~>‘} hyperfine transitions. degeneracy Applicationofofthe anhyperfine external levels. magnetic For field the magnetic lifts the 5I field of 440, however, both the 8{IA1, + 5F 51 5F ~>‘}~~ 5{IE, + ~)} and 8{IA1, ~>‘}~. 5{IE+,

2.50

(a) 2.40

__

2.30

N

—

~>} optical transitions can still be simultaneously excited by the laser as the associated hyperfine lines still overlap. This led to the observation of 51 four resonances in Fig. 3(b), associated respectively (from lower to higher 51 energy) with the 8{1A1, 51 ~>‘.~A1, ~>‘}~ 8{1A2, ~>‘~IA2, 51 ~>‘}~ 8{1A1, + ~>‘~‘A1,+ ~>‘}~ and 8{1A2, + ~ —

—

—

—

~o

2.20

~

2.10

.~

0

—

IA2, + ~>‘} hyperfine transitions. In a magnetic field of 88 0, the hyperfine line A resolves into 51 two components, one corresponding to the 8{IA1

5F 51 3F Exciting one5{IE, optical therefore genenergy) + ~>‘}~and the other + component ~>} to optical the can transition 8{IA1, (higher 5{IE+, ~)} optical transition (lower energy). erate only two hyperfine 5I resonances; either those associated with the 8{1A1, + ~)‘.~.IA1, + ~>‘} 51 and 8{1A1, + ~>‘~IA2, + ~>‘}hyperfine transitions (Fig. 3(c)) or those associated with the 51 5I 8{IA1, ~>‘~IA1, ~>‘} and 8{1A2, IA2, ~>‘} hyperfine transitions (Fig. 3(d)). The corresponding Zeeman hyperfine ODMR 51 spectra associated 5F with hole burning in the 8{1A1, ±~>‘}-~~~ 5{IE4, ±~>}optical transitions (line B) are shown in Fig. 4. As can be seen from Fig. 5, excellent agreement between the observed Zeeman splitting and the predicted behaviour was obtained. In the lowfield (0—ISOG) region, we have a linear Zeeman effect.~From the measured slopes, the zero field frequencies, and the form of equation (16); the value of gjis estimated to be 7.59(26) in reasonable agreement with the earlier reported value of 7.40(5) [10]. Using the1.2346 intermediate 5I~) = [3], the coupled free-ion g value g~( matrix element is estimated to be 6.15(21) in reasonable agreement with the value of 5.922 calculated from crystal-field wavefunctions [3]. With established, we futher estimate A1 I = 0.795(27)0Hz which is comparable to the51 values of the magnetic hyperfine constant 3~ A( 8) = 0.812(1)GHz reported for the free Ho —

20

40

60

80

20

40

60

80

1.85

(b) 1 75 5.)

L55 1

—

—

—

—

1.45 0

magnetic field H~(0)

—

Fig. 5. Comparison of the observed (symbols) and predicted (solid lines) Zeeman splitting 51behaviour for (a) the 51 8{1A1, ±~>“IA1, ± and 8{1A2, ±~>‘6~’IA2, ±~>‘}~ 51 5l

1>’}

1>.~.

and (b) the 8{1A1, ±1>’.=IAi, ±4>’} and 8{1A2, ± IA2, ±~>‘}hyperfine transitions in the ground state.

51 ion 3~in [11] LiYF and A( 8) = 0.839 GHz reported for Ho 4 [12]. In addition to determining the hyperfine parameters for the two ground state singlets, the accurate establishment of the ground state hyperfine splittings makes it possible to deduce from the optical data the quadrupole splittings that are5F associated5Fwith each of the excited 5F state levels, 5(E) and 5(A2). In the case of the 5(A2) 5F singlet, the quadrupole splittings between the 5{IA2, ±5F ~>} 5F and 5{1A2, ±~)} and between the 5 5F {1A2, ±~>}and 5{IA2, ±~>}hyperfine levels had been found to be 0.148 (35) and 0.092 (35) 0Hz, respectively. Under the assumption of isolated 5F 3(A2) singlet, an obtained. estimate of P~ of 0.024 (5)0Hz is therefore —

T. Boonyarith ci a!.

/ Journal of Luminescence 59

For the 5I8(A1,A2)=~’.5F5(E)transitions, only the optical hyperfine5Flines corresponding to the 51 5I 8{1A1, ±~>‘}~. 5{IE4, ±~>}, 8{IAi, ±~>‘} 5F 51 5F ~ 3{IE~, ± ~>}~ 8{1A2, ±~>‘}~ 5{IE4, ±~>}~ 51 5F and 8{1A2, ±~>‘}~. 5{IE~, ±~>} transitions are completely resolved. As a result, using the ground state hyperfine ODMR and the optical data, splittings between the 5F only the hyperfine 5F 5{IE±,± ~)} and 5{IE±,± ~>}and between 5F 5F the 5{IE±,±~>}and 5{IET, ±~)} ~Ofl2~DO 5F nents of the excited 5(E) doublet state can be determined, and are found to be 0.711(50) and 0.904 5F (50)0Hz, respectively. If this 5(E) doublet is treated in isolation, then ArIII = 0.808(35)0Hz, and P~= 0.016(6)0Hz is obtamed. Again, there is only a small change to the earlier estimate ATiII = 0.826(11)0Hz obtained from the somewhat less accurate measurement of the separation between the optical hyperfine lines [2]. Using the crystal-field wavefunctions of [3], we obtain 5F the value of A~1= + 0.543(24)0Hz for the 5 multiplet which is significantly lower than the free-ion estimate of 5F A( 5) = + 0.659 MHz calculated from the formulas of Wybourne [13] (using the free-ion intermediate-coupling wave functions of Mujaji [3]) and the free-ion ground-state value [11]. As have been pointed out by Sharma and Erickson [14], such a discrepancy may arise from neglecting interactions such as the configuration interaction and J-mixing.

Ground multiplet

18.

Excited 5F,: multiplet

367

Table 2 Experimental and theoretical hyperfine splittings of the ‘18{A1 (Ocm_i),A2 (l.7cm~’)}and ‘F5{E (15609.5cm_i), A2 (15623.0cm i)} levels Crystal-field Hyperfine

Experimental

Calculated

level (cm~) transitions

hyperfine splittings (GHz)

hyperfine splittings (GHz) 0.048d

5F 5(A2) (15623.0) 5F 5(E) (15609.5)

—

51 Table 1 Hyperfine parameters 3of+ at the2K 8(A A2).ez.’F5(E, A2) optical transitions of CaF2: Ho Crystal field state Effective hyperfine parameters

(1994) 361—368

±l/2~±3/2 ±3/2~±5/2 ±5/2~±7/2 ~ 7/2.~.T5/2 T5/2~T3/2 ±3/2’~±l/2 ~1/2~±1/2 ±l/2~±3/2 ±3/2~±5/2 ±5/~=±7/2

*

0.904(50)’

0.712’ 0744’ 0.776’ 0.808’ 0.840’ 0.872’ 0.904’

±7/2~±5/2 ±s/2~±3/2 ±3/2-~± 1/2 ±3/2~±1/2 ±5/2~±3/2 ±7/2~±5/2

2.340(3)” 1.699(3)” 0.872(5)’

2.340’ 1.669’ 0.8731

0.092(35)a 0.148(35)a 0.711(50)’ * * * *

0096d 0144d

51 8(A2) (1.7) ‘18(A1) (0)

0842(4)b

1.608(3)” 2.250(2)”

l.609~ 2.2501

cannot be determined experimentally as the associated hyperfine lines are not resolved. a calculated from the difference between optical and ODMR data. bobtained directly from ODMR spectra. c calculated from ODMR data. 5F dobtained by treating the 5(A2) level as an isolated state with 5F P’4 = — 0.024(5)GHz. ‘obtained by treating the 5(E) level as an isolated state with *

P’3 = — 0.016(6)GHz and Ar1 51 = — 0.808(35)GHz. ‘obtained by treating the ‘18(A1) and 8(A2) levels as an isolated system with A = 25.542(77)GH2, A11 = 4.890(22) GHz, P~= 0.035(5) GHz, and P2 = — 0.020(5) GHz.

All the fitted parameters are summarised in Table 1 and a comparison between the experimental and calculated hyperfine splittings is given

A 1 (0cm_i) A2 (1.7cm~’)

P, = 0.035 (5)GHz P2 = — 0.020 (5)GHz A1 = 4.890(22)GHz

in Table 2.

E (15609.5cm_i)

P’

4. Conclusions 3

=

—

0.0l6(6)GHz

Ar1KE+IJ,IE+N A2 (15623.0cm_i)

=

0.808

(35)GHz P’4 = — 0.024(5) GHz

___________________________________________

In summary, the hole burning microwave-optical double-resonance technique has been employed

to make accurate measurements of the hyperfine

368

T. Boonyariih ci a!.

/ Journal of Luminescence

splittings in the two lowest ground state singlets of the CaF2: Ho3~tetragonal system. Using this data with measurements of the observed 5I 8(A1, A2)=~. 5F 5(E,A2) optical transitions, the effective magnetic hyperfine coupling constants and the quadrupole parameters of all involved levels are established.

Acknowledgements We would like to thank M.3 Mujaji and G.D. Jones + crystal and for access for crystal supplying CaF2: Ho to fieldthedata. References [1] J.D.P. Martin, T. Boonyarith, NB. Manson and Z. Hasan, J. Phys.: Condens. Matter 4(1992) L411. [2] J.D.P. Martin, T. Boonyarith, NB. Manson, M. Mujaji and GD. Jones, J. Phys.: Condens. Matter 5 (1993) 1333.

59 (1994) 361—368

[3] M. Mu,jaji, GD. Jones and R.W.G. Syme, Phys. Rev. B46 (1992) 14398; M. Mujaji, Ph. D. Thesis (1992), University of Canterbury, New Zealand, unpublished. [4] C. Carboni, L. Cone, Z.-P.12-C8, Han and land, J. Phys.R.CoIl. 49 (1988) 843.M.A.H. McCaus[5] T. Boonyarith, J.D.P. Martin and NB. Manson, Phys. Rev. B 47 (1993) 14696. [6] D.P. Burum, R.M. Shelby and R.M. Macfarlane, Phys. Rev. B 25(1982) 3009. [7] MR. Pearlman and RH. Webb, Rev. Sci. Instrum. 38 (1967) 1264. [8] J.P.D. Martin, N.E. Rigby and NB. Manson, J. Lumin. 55 (1993) 31. [9] J.P.D. Martin, T. Boonyarith and NB. Manson, J. Lumin., [10] L.S.beKornienko to published. and A.O. Rybaltovskii, Soy. Phys.-Solid State 13 (1972) 1785. [11] B. Bleaney, Quantum Electronics III, eds. P. Grivet and N. Bloembergen (Columbia University Press, New York, 1964) p. 595. [12] J. Magarino, J. Tuchendler, P. Beauvillain and 1. Laursen, Phys. Rev. B 21(1980)18. [13] B.G. Wybourne, Spectroscopic Properties of Rare Earths (Interscience, New York, 1965) p. 115. [14] K.K. Sharma and L.E. Erickson, Phys. Rev. Letts. 45 (1980) 294.