Solid state spectroscopy : the transverse zeeman effect in CaF₂:Erᶾ⁺ crystals

(1)

THE TRANSVERSE ~EEMAN EFFECT

IN

A thesis

submitted for the Degree

of

Doctor of Philosophy in Physics

in the

University of Canterbury

by

University of Canterbury

(2)

(3)

1 312 1 912

the transverse Zeeman s1 e 1n Ca ' t . F 3

+

6 0 1 2:Er , at . tes a and 2 K. The dye laser beam is tuned to the

zi

transition at 18555.6 em

(4)

(5)

I thank

Professors A.G. McLellan

and B.G Wybourne

for

their interest throughout this project, and for making available

a Teaching Fellowship position.

I am particularly grateful to my supervisors Dr Glynn Jones

and Dr Rod Syme for their guidance and encouragement.

I would also like to thank,

- Dr John Campbell

for

his

interest,

and his late

night or early morning visits to the Laboratory during

the long experimental runs.

- Professor L.F. Phillips of the Chemistry Department

for

supplying

the

Rhodamine 6G

dye,

and

for

transferring

the Coumarin 6 dye

additive

(Cyclo-octatetraene) into a syringe.

- Dr W.T. Robinson of the Chemistry Department for

checking the orientation of a CaF 2 :Nd crystal using

X-rays.

My fellow

research students,

Robin Kennedy,

Hau

Kuok,

Stephen Payne, Mike Reid and Chris Tomblin for

many discussions.

I particularly thank Chris Tomblin

for giving his time freely to help with the changing

dyes in the dye laser.

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- Graham Freeth and Mrs. M. Naguleswaren of the Computer Science Department for maintaining the Word Processing Program FMT, by which the text of this thesis was produced.

- My wife Thelma, for preparing and editing much of the text for FMT.

- The University Computer Center staff for their co-operation.

- Mrs. Van Der Borch for assistance in the preparation of some of the diagrams.

- Janet Warburton for typing the formulae, Greek symbols, figure and table captions, references, and tables of contents.·

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A detailed investigation has been made of the transverse

Zeeman effect for erbium ions at tetragonal

c

₄v sites in CaF₂

crystals. Selective laser excitation of fluorescence from the

transverse Zeeman site using a dye laser beam enabled this site

to be distinguished from two other magnetically nonequivalent

sites in these crystals. Large intensity and energy variations

observed for some transverse Zeeman transitions as the crystal

was rotated in the magnetic field, were accounted for by a

switching of the symmetry labels and by magnetic field mixing

between levels. The

c

4v irrep designations of the crystal-field

levels were identified by studying the intensity variations, and

crystal and magnetic field energy calculations successfully

accounted for the energies of the transverse Zeeman levels. In

certain cases, the transverse Zeeman effect was analysed in the

more complex absorption spectra.

Previous undetected

c

₄v crystal-field energy levels in

3+

CaF₂:Er have been located using selective laser excitation

spectroscopy, and a few assignments of levels to the

c

_{4v site by}

earlier workers, were found to be incorrect.

Conventional optical absorption and fluorescence

measurements have been made on . Nd 3+ ions in CaF₂ _{and SrF2}

crystals, and infrared and infrared-Zeeman absorption spectra

examined for ce3+ and Nd3+ ions in both types of crystalline

hosts.

Crystal-field analyses have been carried out lor most

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CHAPTER 1 INTRODUCTION 1.1 Introduction

1.2 Rare Earths in Crystalline Hosts

1.3 Structure of the Alkaline~Earth Fluorides 1.4 Trivalent Rare-Earth Charge Compensation in

CHAPTER 2 THEORY

2.1 Crystal-Field Theory

2.2 Theory of the Transverse Zeeman Effect

CHAPTER 3 3.1 3.2

EXPERIMENTAL Crystals

3+

Optical Spectroscopy of CaF 2:Er

1

5

6

9

14

21 23

3.2.1 Instrumentation 23

3.2.2 Absorption Experiments 24

3.2.3 Laser Selected Fluorescence Experiments 26 3.2.4 Superconducting Magnet and Dewar

3.3 Optical Spectroscopy of MeF 2:Nd

3

+

3.3.1 Instrumentation 3.3.2 Optical Spectra

3.3.3 Low Temperature Dewar 3.4 Infrared Measurements

3.4.1 Instrumentation

3.4.2 Superconducting Magnet and Dewar

28

30

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CHAPTER 4 TRANSVERSE ZEEMAN EFFECT IN CALCIUM FLUORIDE CRYSTALS CONTAINING TRIVALENT ERBIUM

4.1 Introduction

PART I

4.3

PART II

4.4 4.5

POLARISATION AND SELECTION RULES 4.2.1 Tetragonal

c

4V Symmetry

4.2.2 Zeeman Effect for the Magnetic Field Along the Z Axis

4.2.3 Zeeman Effect for the Magnetic Field Perpendicular to the Z Axis

3+

Magnetically Nonequivalent Si·tes in CaF 2: RE

3+

ABSORPTION SPECTRA OF CaF₂:Er AND THE TRANSVERSE·ZEEMAN EFFECT

Introduction

4 4

The

z

₁(

r

1512) ~ L1( G1112) Absorption Spectra 4.5.1 Magnetic Field Parallel to the [100]

Crystal Axis

37

39

41

42

44

51 52

52 4.5.2 Magnetic Field Parallel to the [110] 54

Crystal Axis

4.5.3 Transverse Zeeman Effect for

4 4

Zl( Il5/2 ~ Ll( Gll/2) 58

4.6 The

z

₁( I

4

4 .

1512> ~ D2( F912> Absorption Spectra 64

4.6.1 Magnetic Field Parallel to the [100]

Axis 64

4.6.2 Magnetic Field Parallel to the [110]

(10)

Rotational Zeeman Spectra

PART III FLUORESCENCE SPECTRA OF CaF

2:Er

3₊ _{AND THE}

TRANSVERSE ZEEMAN EFFECT

4.8 Introduction

4.9 Laser Selected Fluorescence Spectra for the

'Tetragonal Site in a Calcium Fluoride Crystal

4.10

Containing Trivalent Erbium Ions

4.9.1 Fluorescence from the Tetragonal

4

n

₁( F

912> Energy Level

4.9.2 Fluorescence from the Tetragonal

4 E₁(

s

312) Energy Level

3+ Crystal-Field Analysis of the CaF

2:Er

Tetragonal Site

4.10.1 Introduction

4.10.2 Intermediate Coupling for Er3

+

in

CaF 2

4.10.3 Crystal-field Calculations

4.10.4 4

r

Crystal-Field Parameters

4.10.5 Higher Energy Multiplets

4.11 Laser Selected Zeeman Fluorescence

4.12

Spectroscopy

3+ Sll Zeeman Site Fluorescence in CaF

2:Er 4.12.1 Energy Level Scheme

4.12.2 Sll Zeeman Site Fluorescence from the

4 _F

912

n

1 Level

72

83

85

89

100

102

106

108

111 113 113

(11)

4.13

4.12.3 Sll Zeeman Fluorescence from the

4 L

s

₃₁₂ E₁ Level 4.12.4 Summary of the

s

11 splitting Values

4

s

_{1 Zeeman fluorescence from the} F

9/ 2 D1 Level

4.14

s

3 Site Rotational Zeeman Spectra and the Transverse Zeeman .Effect

4.15 The

s

3 Site with the Magnetic Field along the [110] Axis

4.16 Transverse Zeeman Analysis

4.17 Intensity Variations in the Spectra of the

s

₁ and

s

3 Sites

4.17.1 Intensity Variations in the Transverse Zeeman Spectra Caused by Magnetic

Field Mixing of Levels

4.17.2 Intensity Dif rences Between Spectra

Recorded When Exciting the

o

1 and

o

2 Leve

4.17.3 Intensity Differences in the

s

₁ Spectra when Pumping the

o

₂ Level

4.17.4 Summary of Intensity Variations

4.18 Transverse Zeeman Fluorescence for the E

1 7 Z Transitions 4.19 Summary of the

s

₁ and

s

3[110] Magnetic Splitting Values

4.20 Rotational Zeeman Spectra for the

s

1 and

s

2 Zeeman Sites

4.21 Summary

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PART I

5.1 5.2 5.3 5.4

OPTICAL SPECTRA OF CALCIUM AND STRONTIUM FLUORIDE CRYSTALS CONTAINING NEODYMIUM Introduction

3+ Optical Spectra of CaF₂:Nd

Lifetime Measurements in CaF₂:Nd Optical Spectra of SrF₂:Nd3+

5.5 Luminescence and Absorption Results of Other

PART II

5.6 5.7 5.8 5.9

PART III 5.10 5.11

CHAPTER 6

Workers

INFRARED SPECTRA OF CALCIUM AND STRONTIUM FLUORIDE CRYSTALS CONTAINING NEODYMIUM Infrared Absorption Experiments

Infrared Zeeman Experiments

Infrared Zeeman Results for CaF₂:Nd Infrared Zeeman results for SrF₂:Nd 3+

PARMETERISATION OF THE CRYSTAL FIELD Crystal-Field Analysis of CaF 2 :Nd

3+ Crystal-Field Analysis of SrF

2:Nd

INFRARED SPECTRA AND CRYSTAL-FIELD ANALYSIS OF ce3

+

IONS IN CaF₂ AND SrF₂ CRYSTALS

6.1 Introduction

6.2 Infrared Absorption Results 6.3 Crystal-Field Analysis of CaF

(13)

6.4 Infrared Zeeman Results

CHAPTER 7 CONCLUSIONS

APPENDIX I INTERMEDIATE COUPLING FOR Nd3+ and Er3+

IONS IN LaF 3

APPENDIX II INTENSITY CALCULATIONS

REFERENCES

249

257

260

264

(14)

TABLE PAGE 2.1 Electric dipole selection rules for the

c

2 and Cs point groups

3.1 Resolution of the Jarrell-Ash double monochromator measured at various slitwidths using the 3131

A

Hg doublet

4.1 Selection rules for the

c

4v group 4.2 Polarisation selection rules for the

c

4 group 4.3 Polarisation selection rules for the C group

s

· 4.4 A summary of the zero-field polarisation selection rules for the tetragonal

c

4V site, when the magnetic field is in the tranverse plane along a Cs axis of symmetry

4.5 Peak absorption energies, linewidths and absorption coefficients of the

zi

+ L

1 Zeeman

transitions measured in the B 1 k spectrum (at 2 K) in CaF

2:Er

3₊ _{crystals at a magnetic field strength}

20

23

40

42

43

49

of 6.0 tesla along the [100] axis. 54

4.6 Peak absorption energies, linewidths and

absorption coefficients of the

zi

+ L₁ Zeeman transitions measured in the B 1 k spectrum at 2 K in CaF

2:Er

3_{+ crystals at a magnetic field}

(15)

4.7 Energies of the CaF 2:Er

3+ L

zl + Ll spectral lines

measured in the B

II

_-

k spectra at a magnetic field strength of 6.0 tesla in the (001) plane

at a temperature of 2 K

4.8 Peak absorption energies, linewidths and

absorption coefficients in the ~ 1 ~ spectrum

(at 2 K) for the z

1 + D2 Zeeman transitions recorded at a magnetic field strength of 6.0

tesla

4.9 Energies (at 2 K) and Zeeman site assignments

3+ L

of the CaF

2:Er

z

1 +

o

2 tetragonal absorption lines measured at a magnetic field strength of

6.0 tesla in the {001) plane

4.10 Fluorescence energies and linewidths of the

4

tetragonal

o

1 +

r

1512 transitions measured

at 2 K for CaF 2:Er

3+

3+ 4 4

4.11 CaF

2:Er

z

1(

r

1512) + F912 tetragonal transition energies obtained by laser excitation spectroscopy

at 2 K

4.12 Energies, 1inewidths and relative intensities of

4 3+

the

c

4V E1 + IlS/2 transitions in CaF 2 :Er at 2 K

4.13 Energies, linewidths and relative intensities

4 3+

of the

c

4V E1 +

r

1312 transitions in CaF2:Er at 2 K

61

70

76

88

89

94

(16)

4.15

field energy levels obtained for the CaF 2:Er

3₊

crystal at 2 K

4 3+

F

912 crystal-field energy levels for CaF2:Er ,

99

calculated with and without intermediate coupling 101

4.16 4.17 4.18 4 .19 4.20 3+ Barycentre energies of CaF

2:Er compared with

those for LaF 2:Er

3+

Calculated and experimental 11

free ion11

energies 3+

for the CaF₂:Er multiplets

Energies and eigenvectors for the intermediate 3+

coupled states of Er in CaF₂

Energy levels and

{c₄V) 41 manifold

3+ g-values for the CaF₂:Er

3+

Energy levels for the CaF₂:Er

c

₄V multiplets

4.21 Energies, linewidths and relative intensities of

h E 3+ t l ' t L(4 ) 4

t e CaF

2: r te ragona s~ e

o

1 F912 +

r

1512 81! Zeeman fluorescence transitions recorded at

6.0 tesla and 2 K

4.22 Energies, linewidths and relative intensities of

3+ l . L ( 4 ) ₄₁

the CaF

2:Er tetragona s~te E1

s

312 + 15; 2

103 104 105 107 109 116

8ll

Zeeman transitions recorded at 6.0 tesla and 2 K 126

4.23 Measured and calculated 8

11 Zeeman site energy

(17)

4.24 Energies, linewidths, and relative intensities for the

n

1 ~

z

1

,z

2

,z

3 transitions of the

s

1 site in

3+

CaF

2:Er , measured at various magnetic field strengths

4.25 Energies, linewidths, and relative intensities for the

n

1 ~

z

1

,z

2

,z

3 transitions of the

s

3[Il0] site in CaF

2:Er 3_+,

measured at various magnetic field strengths and high resolution

4.26 Energies, linewidths and relative intensitiGs for the E

1 ~

z

1

,z

2

,z

3 transverse Zeeman transitions, measured at 6.0 tesla and 2 K from the high resolution (0.5 cm-1) B II k spectra

4.27 Summary of the

s

₁ and

s

3[110] splitting values at 6.0 tesla and 2 K

4.28 Transition energies of the

s

_{1 and}

s

2 sites at 2 K and 6.0 tesla

5.1 Peak absorption energies (cm-1) measured at 80 K

1 3+

in the 4000 em- _{infrared region in CaF 2 :Nd} (0.1%)

5.2 Splitting values of the

c

₄

v r

4 ₁₁₁₂ levels in CaF

2:Nd at 3.0 tesla.

5.3 Splitting values (at 3.0 tesla) for the 4

r

₁

i;

₂ Y

2 and Y3 levels in CaF2:Nd; with and without intermediate coupling

144

160

191

195

200

225

230

(18)

5.5

5.6

912

energies (at 15 K) in SrF₂:Nd(0.05%) for

B II <111> crystal direction

3+ Energy levels and g-values for the CaF

2:Nd

4

(c

4

v>

r

1112 and

r

912 multip1ets

3+ Energy levels and g-va1ues for the SrF₂:Nd (c

4

v>

4

_r

4

1112 and

r

912 multip1ets

6.1 Energies, linewidths and relative intensities (at 15 K) of the 2F

512 + 2

F

712 c4V absorption transitions in CaF

2 and SrF2 crystals containing C e 3+ . 1ons

6.2 Energies (cm-1) of infrared absorption transitions 3+

(at 80 K) in CaF₂:ce which are not related to the . c 4V site

6.3 Summary of the crystal-field parameters for rare-earth ions in CaF₂

6.4 Energies (em -1 ) of the two lower 2 F 2 512 + F712 c

4V absorption transitions (at 15 K) in SrF2:ce 3+ (0.05%) crystals, at various magnetic field strengths

(J;! II <111> crystal direction)

232

234

237

243

248

(19)

FIGURE PAGE 1.1 Structure of the alkaline-earth fluorides 6

1.2 Model of the

_c4v

symmetry site 8

2.1 A summary of the transverse Zeeman effect for

ions in sites of

_c4v

symmetry 19

3.1 Block diagram of the experimental apparatus for

the laser selected Zeeman fluorescence experiments 27

3.2 Dewar and crystal holder used for optical Zeeman

spectroscopy 29

3.3 Sketch of the rotating drum discriminator 32

3.4 Infrared Zeeman superconducting magnet dewar 35

<'

4.1 Energy level diagram for the tetragonal

z

1 + L1 3+

Zeeman transitions in CaF₂:Er 53

4.2 B 1

~

absorption spectra (at 2 K} of the

zi

+ L

1

3+

transitions in CaF₂:Er at 6.0 tesla 55

4.3 B

II

~polarisation absorption spectra (at 2 K} of

L 3+

the

z

1 + L1 transitions in CaF2:Er at a

magnetic field strength of 5.0 tesla along the

[110 1 axis 57

4.4 CaF 3+ L

2:Er tetragonal

z

1 + L1 B

II

k rotational

(20)

1 2

3+

Zeeman transitions in CaF 2:Er

4.6 ~ 1 ~ and ~

II

~ spectra (at 2 K) for the

z

L ₁ +

o

2

3+

Zeeman absorption transitions in CaF₂:Er recorded at a magnetic field strength of 6.0 tesla parallel to the [100] and [110] axes

4. 7 Unpolarised and circularly polarised ~

II

~ spectra L

(at 2 K) for the

z

1 + D2 Zeeman absorption tran-sitions recorded with a magnetic field (of

6.0 tesla) parallel to the [lOO]axis

4.8 Crystal alignment (in the (001) plane) using the

Z~

+

o

2 Zeeman transitions in the B 1 k spectrum at 2 K and 6.0 tesla

4.9 CaF 3+ L

2:Er tetragonal

z

1 + D2 rotational Zeeman

65

66

67

71

(B

II

~) spectra, recorded at 6. 0 tesla and 2 K 7 3

3+ L

4.10 CaF

2 :Er tetragonal

z

1 +

o

2 ~ 1 k rotational

Zeeman spectra recorded at 6.0 tesla and 2 K 75

4.11 Energy level diagram for the tetragonal

z

₁ + El

3+

Zeeman transitions in CaF₂:Er 78

4.12 Absorption spectra (at 2 K) of the

z

L ₁ + E1

c

4V transitions in CaF

2:Er

3_{+ at a magnetic field} strength of 6.0 tesla along the [lOO]axis

L 4.13 Tetragonal

z

₁ + E

1 ~ 1 ~ absorption spectra (at 2 K) recorded at various magnetic field strengths along the [100] axis

79

(21)

4.14

4.15

4.16

L

Absorption spectra (at 2 K) of the z

1 + E1

t t e ragona 1 t rans1 1ons 1n ' t ' ' C F a ₂: r E 3+ at a magnet1c · field strength of 6.0 tesla along the [110]

crystal axis

4

o

₁ +

r

1512 fluorescence (at 2 K) for the

c

4V site in CaF

2:Er 3+

(a) _El ₊ 4 1_{15/2 fluorescence spectrum (at 2} K)

for the

c

4V site in CaF2:Er 3+

recorded when

'

pumping zl + El at 18628.6 em -1 with the dye

laser beam

(b) Fluorescence spectrum (at 2 K) for the C site in CaF

2:Er 3_+,

recorded when pumping the transition at 18626.0 cm-l

82

87

91

4.17 Absorption spectra recorded at 2 K, showing the

4.18

4.19

overlapping of the

c

₄V (z₁ + E_{1 )} and C site

ab-3+

sorption lines in CaF ₂: Er 9 2

El + 4 115/2 tetragonal fluorescence spectrum

(at 2 K) for CaF 2:Er

3+ ₉₅

4

El + 113/2 tetragonal fluorescence spectrum

(at 2 K) for CaF₂:Er 3+ 97

4.20 Energy level diagram (at 2 K and 6.0 tesla) for the

(22)

4.22

1512

and 6. 0 tesla) for the

s

11 site in CaF 2 :Er

3+

L 4 D

1 -+

r

1512 ~ 1 ~ fluorescence spectrum (at 3+

2 K and 6.0 tesla) for the

s

11 site in CaF2:Er

4.23 Polarised

oi-+

4

r

1512 (Z1

,z

2

,z

3) fluores?ence

spectra recorded at 6.0 tesla and 2 K for the

3+

Sll _{site in CaF 2 :Er}

116

117

120

4.24 B 1 ~fluorescence spectrum (at 2 K and 6.0 tesla)

3+

for the unidentified site in CaF

2:Er 122

4.25 (a) EL 4 B 1 k fluorescence spectrum (at

1

-+

115/2

2 K and 6.0 tesla) for the

s

11 site

. 3+

1n CaF

2:Er

(b) EL 4 B II k fluoresence spectrum

1

-+

115/2

(at 2 K and 6. 0 tesla) for the

s

11 site in

3+

CaF₂:Er

4.26 Parallel splitting values of the CaF₂:Er3+

4

_r

1512

(z

1

,z

2

,z

3) levels as a function of the

4.27

magnetic field strength

Dl

_-+

4 1_15/2B 1 k fluorescence

-at 2 K and 6.0 tesla)

CaF 2:Er

3+

_.

_{Dye laser}

-1

15 4 2 7 . 7 + 1. 0 em

for the

pumping

spectrum (recorded

s1 site in

ZL

-+

1 DL 2 at

4.28

o

1 -+

4

_r

1512 B II ~fluorescence spectra (at 2 K)

for the

s

1 site recorded at 4.0 and 6.0 tesla

124

125

128

131

(23)

4.29

4.30

4 D

1 +

r

1512 fluorescence spectra (at 2 K and 6.0 tesla) for the

s

1 site in CaF2:Er

3_+. _Dye

laser pumping

z~

+

o

1 at 15406.2 cm-l

4 -1

D₁ + 1

1512 high resolution (0.4 em ) B l k

3+ spectrum f. or the S ₁ site in CaF

2 : Er , measured at 2 K and 6.0 tesla. Dye laser pumping ·

134

z~

+

D~

at 15428 cm-l 136

4.31 4.32 4.33 4.34 4 D

1 +

r

1512 polarisation spectra recorded for the

3+

s

₁ and

s

3[110] sites in CaF2:Er at 2 K and

5.0 tesla

4

Magnetic energy variations of the

r

1512

<z

1

,z

2

,z

3)

s

₁ site levels in ~aF

₂

:Er 3+

3+ Perpendicular splitting values of the CaF

2:Er

4

_r

1512

<z

1

,z

2

,z

3) levels as a function of the magnetic field strength

+ 41 _{high resolution} -1 B l k

Dl _15/2 (0.5 em }

_-

-spectra (at 2 K) for the sl (C~ symmetry) and

83[110]

( c"

_s symmetry) sites 1n CaF. 3+

2:Er at

various magnetic field strengths

4.35 D

1 +

4

_r

1512 high resolution (0.5 cm-1

) _!!II

~

spectra (at 2 K) at various magnetic field 3+

strengths, for CaF₂:Er

137

138

139

140

(24)

4.37

4.38

4.39

4.40

and 8

3[110] sites in CaF2:Er

3_{+, recorded at various} magnetic field strengths and low resolution

("' 2 em -l)

4

D₁ +

r

1512 (Z1

,z

2

,z

3) ~II ~rotational Zeeman

3+ .

spectra for CaF₂:Er recorded at 2 K and 6.0 tesla when exciting the

zi

+

D~

8

3 site transition with a a-polarised dye laser

4

D

1 +

r

1512

(z

1

,z

2

,z

3) B 1 k rotational Zeeman 3+

spectra for CaF

2:Er , recorded at 2 K and 6.0 tesla (in the (001) plane) when exciting the

L L

z

₁ + D

2 83 transition 4

D

1 ->-

r

1512 (Z1

,z

2

,z

3) ~II ~rotational Zeeman 3+

speGtra for CaF₂:Er recorded at 2 K and 4.0 tesla

. . L DL

(in the (001) plane), when exc1t1ng the

z

₁ +

2 transition with a a-polarised dye laser beam

4 D

1 +

r

1512

(z

1

,z

2

,z

3) ~II ~rotational Zeeman spectra (at 2 K) recorded for the 8

3 site in 3+

CaF

2:Er , at 4.5 tesla (in the (001) plane). Dye laser is a-pol. and pumping the

zi

+

D~

8

3 transition 4.41 D

1 + 4

_r

1512

(z

1

,z

2

,z

3)

~II ~rotational

Zeeman spectra (at 2 K) recorded for the

s

₃ site in

3+ CaF

2:Er at 5.0 tesla. Dye laser is a-pol. and

142

148

149

152

153

[image:24.597.73.542.74.775.2]

(25)

4.42

o

4

1 + I1512

<z

1

,z

2 ,z 3) .!=!II k rotational Zeeman spectra (at 2 K) for the

s

3 site in CaF2:Er

3

₊

recorded at 6.0 tesla when pumping

zi

+

o

1 with

a a-pol. dye laser beam 155

4.43

o

1 +

4

_r

1512 (Z1

,z

2,z3) high resolution (0.5 cm-1₎

.!=! II k rotational Zeeman spectra (at 2 K) for the

3+ 8

3 site in CaF2:Er , recorded at 5.0 tesla 157 4.44 Magnetic energy variations of the 4

r

1512 (Z1

,z

2,z3) 8

3[110] site levels in CaF2:Er

3+

4.45 Splitting values of of the 8₃[110] site

of the magfietic field strength

4.46 Energy level scheme for the

s

₁ s (i.e. B

II

c~

4.47 Energy level scheme for the

s

3[ 0] site (i.e. B

II

C" axis)

s

4.48 Dl + Zl,z2,z3

II

~spectra (at 2 K) for the sl and

s

3[110] sites in CaF2:Er 3

+, recorded at 5.0 tesla and a resolution of 0.5 em 1

(a-pol.) pumping

zi

+

D~

Dye laser

4.49 Energy level schemes and sketches of intensity patterns for the

c

₄V D₁ +

z

3 transverse Zeeman 3+

transitions in CaF

2:Er crystals

158

159

164

165

166

(26)

4 I

1512 (Z1

,z

2

,z

3) transverse Zeeman levels in 3+

CaF

2:Er , as a function of the magnetic field direction (in the (001) plane)

4.51 Pur of the

c

₄

v

z~

and

z~

transverse Zeeman

3+ levels in CaF

2:Er as a function of the magnetic

field strength

4.52 Calculated Zeeman energies of the

zu

₁ and ZL 2 transverse Zeeman levels in CaF

2 :Er 3+

for B

parallel to the C' and C" axes

s s

4.53 _{Calculated Zeeman energy positions of the z3}

transverse Zeeman levels in CaF₂:Er 3+ for B

parallel to the I _and II _axes

4.54 Purity of the

c

4V irrep labels for the

z

2 and

4.55

4.56

. 3+

z

₃

?

₃ transverse Zeeman levels ln CaF

2:Er , as a function of the magentic field strength

4

E

1 -+

r

1512 (Z1,

z

2, z3) ~

II

k rotational Zeeman 3+ spectra (at 2 K) for the

s

₃ site in CaF

2:Er , recorded at 6.0 tesla (in the (001) plane) when

exciting

zt

-+ E₁ with a n-po1. dye laser beam

Comparison of the E1 -+ _Zl,Z2,Z3 _~

II

k spectra

-(at 2 K and 6.0 tes1a) for the _sl and 83 [110]

sites ' ln C F a E J+

2: r , obtained with the dye laser

a

and n-polarised and pumping ZL ₁ -+ E1

173

176

178

179

181

188

(27)

4.57 E 4

1 +

r

1512 (Z1

,z

2

,z

3) ~ 1 k rotational Zeeman spectra {at 2 K) for the 8

3 site in CaF2:Er 3_+,

recorded at 6.0 tesla and a resolution of 0.5 cm-l 192

4.58 Comparison of the E₁ -+

z

1

,z

2

,z

3 B 1 ~ spectra {at

2 K and 6.0 tesla) for the 8₁ site, obtained with

the dye laser a and 'IT-polarised and pumping ZL ₁ -+ El 193

4.59 D₁ -+

z

1

,z

2

,z

3 B II ~rotational Zeeman spectra

( at 2 K ) f or t e h 8₁ s1te 1n CaF. . 3+ d d 2:Er , recor e

at 6.0 tesla and a resolution

of~

2 cm-l 197

4. 60

o

1 -+

z

1,

z

2,

z

3 ~

II

~ rotational Zeeman spectra

( at 2 K ) f or t e h 8 ₂ s1 e 1n CaF. t . 3

+

d d 2:Er , recor e

at 6.0 tesla and a resolution

of~

2 cm-l 198

4.61

5.1

5.2

5.3

Dl + Zl,Z2,Z3 ~

II

k spectra (at 2 K) for the 8 2

-site in CaF 2:Er

3+

recorded

,

with the dye laser

a

and rr-polarised {and pumping the ZL+DL ₁ ₂ ₈₂ transition), at a magnetic f ld strength of 6.0 tesla; 70 0

form the [100) axis in the {001) plane of the crystal

Absorption spectrum _{( 1 9/2}4 _-+ 4 _{F 3/2) of CaF} 2:Nd (0.05%), recorded at 82 K

Energy level scheme of the

c

_4Vsite in CaF₂:Nd 3+

3+

3+ Optical fluorescence spectra recorded for CaF

2:Nd (0.05%)

199

205

206

[image:27.595.84.544.71.764.2]

(28)

5.5

5.6

5.7

5.8

912 312 2

{0.05%)

Optical fluorescence spectrum recorded for SrF

2:Nd

3

+(0.05%)

3+ Energy level scheme of the

c

₄V site in SrF

2:Nd

4

_r

4

912 +

r

1112 absorption spectrum (at 15 K) for CaF

2:Nd

3_+(0.05%)

4

Tetragonal 1

1112 energy level diagram for CaF2: Nd3+(0.05%) obtained from infrared absorption experiments (at 15 K)

4 + 4₁

5.9 1

912 1112 absorption spectrum of SrF2:Nd(0.05%) recorded at 80 K

5.10 Tetragonal energy level diagram for SrF

2:Nd(0.05%); obtained from infrared absorption experiments

5.11 4 1 4

912 (Z) +

r

1312 (X) absorption spectrum SrF

2:Nd

3_{+(0.05%) recorded at 80 K}

212 214 216 221 221 222 223 224

5.12

c

4V

4 1

912 (Z1) + 4

1

1112 infrared Zeeman transitions 3+

in CaF

2:Nd forB

II

k 227

5.13 Calculated 4 1 4

912 (Z1) and 11112

c

4V energy levels 3+

for CaF

2:Nd as a function of the parallel and

(29)

6.1

6.2

6.3

3+

Infrared absorption spectra of CaF₂:ce recorded at 80 K.

3+ Infrared absorption spectra of SrF

2:ce recorded at 80 K.

3+ Energy level diagram for CaF₂:ce

6.4 Infrared Zeeman absorption spectrum (~II ~) 3+

(at 15 K) for CaF₂:ce (0.1%), recorded at a magnetic f ld of 4.0 tesla parallel to a <111> crystal direction

6.5 Comparison of the theoretical and experimental

6.6

infrared Zeeman absorption en,ergies for CaF

2:ce

3_+; _{with B}

II <111> crystal direction

Zeeman energy splittings of the 2191 cm-l 2F

712

3+ level in CaF

2:ce (:§,

II

<111> crystal direction) 6.7 Infrared Zeeman absorption spectra (~II ~) (at 15 K)

3+ for SrF

2:ce (0.05%), recorded at a magnetic field of 4.0 tesla parallel to a <111> crystal direction.

241

244

247

250

252

253

(30)

(31)

CHAPTER 1 INTRODUCTION

1.1

INTRODUCTION

The

main

purpose

of this

thesis

is to report on

experimental investigations of the transverse Zeeman effect for

ions in sites of C

symmetry.

The transverse Zeeman effect has

4v

reqently been analysed for ions in uniaxial crystals by Judd and

( 1)

Runciman

They ptedict large variations in the intensity of

the purely a-polarised transitions of ions in sites of D

,

c

4

4v

or

D

symmetry as the crystal is rotated about the c axis in a

2d

transverse magnetic field.

The aim

of this

research was

to

veri

these predictions for ions in C

symmetry, and to obtain

4v

information

on

the

crysta

field

energy

levels

and

wave functions.

Variations in transverse Zeeman patterns were

reported

as

(2)

early as 1934 by Lehmann

for ruby.

More recent investigations

(3,4,5)

(6)

have

been made on CoCs Cl

, erbium ethylsulphate

, and

(7)

holmium ethylsulphate

3 5

In a series of papers

(8,9,10,11,12,13)

by the Ames Laboratory group,

theoretical analyses have

been

made

for ions in C

, D and D

crystal-field symmetries.

The

(32)

mathematical formulation in these papers was elegantly simplified and extended to other point groups by Judd and

(1) (14) 3+

Runciman Since then, Noor has studied Er ions in

lanthanum ethylsulphate and

u

ions in Zircon using the formalism of Judd and Runciman.

In this work, calcium fluoride crystals containing trivalent erbium ions were chosen. for investigation because there are tetragonal (C ) symmetry sites in these crystals.

4v

Trivalent erbium ions were chosen as the rare-earth because: 1) Many of the optical C crystal-field levels have

4v

been identified by earlier workers using either spin-lattice relaxation measurements to relate E.P.R. and

(15) (16)

optical spectra or optical Zeeman measurements

(16)

2) From the optical Zeeman studies, Rector et al. report the parallel and perpendicular magnetic splitting values for some of the tetragonal levels. 3) For the laser selected Zeeman fluorescence experiments (Chapter 4), there are absorption transitions accessible for dye laser excitation and the resulting fluoresce,nce is in the visible reg ion of the electromagnetic spectrum.

(33)

different charge compensated erbium ions and their corresponding

5

nonequivalent Zeeman sites in the cubic (0 ) symmetry calcium

h

fluoride crystals, the technique of laser selected Zeeman

fluorescence spectroscopy was developed. A dye laser is tuned

to excite selectively a Zeeman absorption transition. Provided

that for a given polarisation the absorption lines for the

different sites do not overlap, fluorescence is restricted to

that from the particular Zeeman site excited. This technique

was used to determine unambiguously the optical Zeeman spectral

lines of the erbium

c

sites. Similarly, it was also used to

4v

locate and identify previously unobserved erbium

c

site

4v

crysta field levels.

As will be ~hown, a detailed investigation of the

transverse Zeeman spectra for tetragonal C trivalent erbium

4v

ions in calcium fluoride crystals can be satisfactorily

(1) accounted for using the analysis of Judd and Runciman

Another research topic was to measure the C crystal field

4v

energy levels of neodymium and cerium ions in calcium and

strontium fluoride crystals. This topic was motivated by the

4 4

need to redetermine the energy levels of the I and I

9/2 11/2

multiplets of neodymium in calcium fluoride following

(17)

(34)

(18)

McMahon and by some anomalous crystal-field

(19) 3+

results reported by Manthey for CaF :Ce 2

analysis

Both fluorescence and infrared absorption techniques were

3+

used for Nd ions and successful crystal-field analyses were achieved for the C site when both intermediate coupling and

4v

crystal-field mixing were included. Fluorescence lifetime measurements were also obtained for several of the neodymium

4 4 4

transitions ( F ->I , I ).

3/2 9/2 11/2

Infrared absorption measurements correct the fluorescence

(19) 3+

results of Manthey for CaF :Ce and the resulting crystal-2

field analysis gives parameters for cerium which are consistent with those obtained for other rare-earth ions in calcium fluoride.

(35)

1.2 RARE-EARTHS IN CRYSTALLINE HOSTS

All the investigations have been carried out on trivalent ·rare-earth ions in alkaline-earth fluoride host crystals. The rare-earths belong to the lanthanide series which is characterised by the progressive filling of the 4f-shell. · As a

(20)

result of the lanthanide contraction and the subsequent

2 6

shielding of the f-electrons by the closed (5s) (5p) shells, the 4f-shell behaves as an inner shell. Thus the shell is relatively insensitive to the atomic environment and does not interact strongly with the neighbouring atoms or ions of the crystalline lattice. This accounts for the sharp optical transitions observed in the spectra of crystals containing rare-earth ions. Rare-Earth ions usually enter into chemical combination in the trivalent valence state.

1.3 STRUCTURE OF THE ALKALINE-EARTH FLUORIDES

The alkaline-earth fluorides (CaF ,SrF ,BaF ) form cubic

2 2 2

5

crystals having the space group symmetry 0 • The alkaline-earth h

ions

2+ 2+

(Ca ,Sr

2+

,Ba ) are located at the centre of a cube of fluorine ions and every alternate cube of fluorines is empty

2+

(Figure 1.1) • Both the alkaline-earth ions (Me ) and interstitial (empty cation) sites have cubic 0 point symmetry

(36)

Figure 1o1

/ /

/

Me

2

+

Structure of

()

-,0-/

, I'

I .

/

I

-o

_I

I /

0 Alkaline Earth Fluorides .

whi the fluorines have tetrahedral (T ) point symmetry.

d

1.4 TRIVALENT RARE-EARTH CHARGE COMPENSATION IN MeF

2

3+

When trivalent rare-earth ions (RE } are introduced into the alkaline-earth fluorides, they substitute for the divalent

2+

[image:36.595.137.478.75.515.2]

(37)

required for the crystal to maintain charge neutrality. Charge

compensation sites have been investigated for most of the

rare-earth ions in alkaline-rare-earth fluoride (MeF ) crystals by means

2

of optical spectroscopy using the concentration series

(21,22,31)

method optical Zeeman

. (16,23,24,25) measurements

{26,27)

E. P.R.

(27)

and Endor Infrared spectroscopy using

hydride ion local mode vibrations has also been used to

investigate charge compensation sites in hydrogenated

3+

MeF :RE 2

{28,29,30) crystals

For low concentrations of trivalent rare-earth ions, charge

compensation arrangements involving single rare-earth ions are

expected to predominate. One common arrangement in CaF

2

3+

crystals for low concentrations of RE ions and SrF crystals

2

3+

for RE ions in the earlier part of the rare-earth series,

involves an interstitial F ion occupying one of the six empty

cubes adjacent to the substitutional rare-earth ion, as shown in

3+

Figure 1.2. Each of the pairs of ions {RE -F ) gives a site of

i

tetragonal (C ) symmetry, and it is this charge compensation

4v

arrangement which is of most interest in this research. Other

[image:37.595.55.530.309.760.2]

(38)

involving cubic (0 ) and trigonal (C ) symmetry have also been

h 3v

(27) reported in the literature. A recent review is by Baker

/ /

/

I

~0-RE~H

0 I

--0-

~

/

"

/

(39)

CHAPTER 2 THEORY

2.1 CRYSTAL-FIELD THEORY

The Hamiltonian for a rare-earth ion in fr crystal field has

(20)

been well documented by Wybourne , and may be written as:

[

h2 N 2 N Ze2 N 2

J

k k

'JC

= - -

L

v · -

I -

+

I

~ +

I

~(E) ~i • ~i +

I

B (c-) . , (2 .1)

2me i=l J. i=l ri i<j rij i k,q,i q q J.

where the symbols have their usual meanings. The free ion terms in the bracket are the .kinetic energies of all the electrons, the electron-nuclear potential energy, the repulsive Coulomb potential energy of the interaction between pairs of electrons, and the electron spin-orbit energy respectively. Basis states frequently used for the eigenfunctions of the Hamiltonian, are those formed by Russell-Saunders (LS) coupling, since the first three terms of the Hamiltonian commute with both the total orbital angular momentum operator L and the total spin angular momentum operator

s.

The spin-orbit interaction commutes with the total angular momentum operator J=L+S, but not with L or S

2S+l

individually, and so splits the L terms into levels 2S+l

characterised by different values of J (i.e. L ) •

J

If there

(40)

momentum it is often more realistic to use the j - j coupling scheme. For the rare-earth ions, the spin-orbit coupling is of moderate strength and an intermediate coupling scheme is appropriate with the eigenvectors formed from linear

2S+l 2S+l

combinations of the L terms. The dominant L term in

J J

the combination is usually used as a label even though

s

and L are no longer good quantum numbers.

The last term of the Hamiltonian, the crystal-field term, can lift the degeneracy of the intermediate coupling free ion levels further, although two-fold Kramers degeneracy must remain for a configuration containing an odd number of equivalent

( 32)

electrons Provided the. crystal field is invariant under the operations of a point group, the eigenfunctions of the crystal-field levels can be labelled according to their transformation properties by the irreducible representations (irreps)

r

of that point group. Although the previous S, L and

j

J labels are no longer good quantum numbers they are often included in the labelling scheme as indicators of the parentage of an eigenfunction.

(33)

Bethe developed crystal-field considering purely electrostatic

theory fields

in 1929 perturbing

by the wavefunctions of the ion. The surrounding _ligands were replaced by point charges and the potential energy for an

(34)

(41)

(20)

Wybourne expanded the crystal field in terms of the Racah (k)

spherical tensors C which are related to the spherical

harmonics Y by:

k,q

c

(k) =

q q

( _2k+l41T ]

~

y _k,q ( 2 • 2)

The matrix elements of these operators may be calculated using (20)

the detailed formulae given by Wybourne The effects of intermediate coupling can be accounted for in first-order perturbation using the electrostatic and spin-orbital wavefunctions as zero-order wavefunctions by noting that

<o:JIIU(k)llo:'J'>

= L

ij

c . c . <

s .

L' Jll

u (

k) II

s

'L 'J I > ,

1 J 1 1 J J ( 2 • 3)

where the c and c 's are the ISL> eigenvector components of the

i j

(k) intermediate coupling states lo:J>, and U

(k)

reduction of the matrix elements of U in:

q

=

<

l u (

k)

I

> < Q.

II c (

k )

II

Q, >

q

arises from the

( 2. 4)

The radial information is contained in the crystal-field k

parameters (B ) which are usually treated

q

as adjustable

(42)

-configuration, k will be even and not greater than 6, and the values of k and q will be restricted by the point symmetry of

the rare-earth ion site.

The crystal-field Hamiltonian appropriate for

c

symmetry 4v

is:

( 2 • 5)

however, it is often more convenient in dealing with the cubic fluorite lattice to express the tetragonal crystal-field as the sum of cubic and axial terms:

4 6

Since the cubic crystal-field parameters B and B are

than, or at least comparable with the axial parameters

,._6

and B , the crystal-field wavefunctions can be labelled

0

( 2 • 6)

larger "2 _._4 B

,

B

0 0

by the

cubic 0 and tetragonal C irreps

r

and Y respectively. For

h 4v i j

configurations with an odd number of electrons, J is half integer and the crystal-field energy levels may be characterised

(2) by the

r

, r

6 7

( 2)

and

r

8 ( 4)

(43)

by the C irreps into which these decompose, viz y , y and

4v 6 7

y +y • 6 7

The

M

basis states are commonly used to form the

J

eigenfunctions of the y and y irreps of the C group. In the

6 7 4v

( 35)

notation of Hellwege (i.e. M

=

ll (mod q)) the y and y

J 6 7

irreps correspond to the ll = ±1/2 and +3/2 crystal quantum numbers respectively.

Group theory can be used to determine the non-zero matrix elements

J

~;~~idT

a requirement of which is that the triple

*

product f X f X f contains the identity irrep f , where f and

f op i 1 i

r

are the irreps of two levels connected by an operator

f

transforming as the

r

op

irrep of the point group. This may

equivalently be written in the more convenient form:

r

₀P

x

ri

:J

rf .

( 2 • 7)

Since the Hamiltonian transforms as

r

,

the

c

crystal-1 4v

field energy matrix can be reduced to two matrices whose wavefunctions transform as the y andy irreps respectively.

(44)

2.2 THEORY OF THE TRANSVERSE ZEEMAN EFFECT

The interaction of the electronic magnetic dipole moment

with ary external magnetic field {~) can be written, in

first-{20) order in the field, as a sum of N electrons

and in the LS coupling scheme this becomes

where g = 2.00232 and

_S

₌

eh _2m is the Bohr magneton. s

{2. 8)

( 2. 9)

The parallel and perpendicular (i.e. transverse) Zeeman

effects are calculable from the magnetic part of the

Hamiltonian, ~~ = SB (L +g S )

z

s z

and

=

SB {L +g

S )

X X S X

respectively, using the tensor operator methods of Racah.

Formulae for the parallel and perpendicular Zeeman matrix

{20)

elements are given by Wybourne However, there are errors

of sign in two of the perpendicular Zeeman formulae (6.34 and

6.39 of reference(20)), and the corrected formulae are:

<fNaSLJJ

I

(L +2S )

I

fNaSLJJ ±1> = 9

2 [ (J+J ) (J±J +1)]

~

Z X X Z Z Z (2.10)

and

<fNaSLJJ _z

I

(L +2S ) lfNaSLJ'J ±1> _y _y _z

a± i<fNaSLJJ

I~

+2S ) lfNaSLJ'J +1>

(45)

Formulae with the orbital angular momentum reduction factor included (so that k~+g ~ is the Zeeman operator}, are given by

s (68)

M?-cFarlane

The parallel and perpendicular magnetic splitting values,

~I and

s

_{1 , of the crystal-field energy levels are defined by the} llE

relationship S =

BB'

where llE is the energy separation between the components of a Kramers doublet in a magnetic field.

When a magnetic field is applied perpendicular to the c axis of a unaxial crystal, the point symmetry at the ion site in

the crystalline lattice will be reduced to one of the subgroups of the zero magnetic field point group. In general this reduction will be to

c

I but if the magnetic field is parallel

1

to an axis of symmetry in the transverse plane, a higher subgroup may be appropriate. The energy levels of the ion can then be classified according to the irreps of that subgroup point symmetry. As the crystal is rotated about the c axis, the irrep labels for the levels may be compared for the magnetic field along the various axes of symmetry. The irrep labels may be either preserved or switched under the rotation, and the corresponding levels are historically labelled type A or type B

(9)

respectively

For an ion in tetragonal C symmetry, the two sets of axes

4v

(46)

symmetry, make angles of ~/4 with each other. When a magnetic

field coincides with either of these sets of axes, that is the x

(or y) axis or an axis midway between the x,y axes, the point

"

symmetry at the ion will be C or C respectively. Here we

s s

adopt the true crystal-field symmetry at the ion rather than the

(1)

method of Judd et al. who started with a higher point

symmetry, D

4h

by omitting the odd-parity terms of the C

4v

crystal-field Hamiltonian. For an ion with an odd number of

electrons, the Kramers components can be labelled by the y and

3

y irreps of the C group. The crystal-field energy levels can

4 s

be classified as types A or B using the method shown in detail

(1)

by Judd and Runciman The only difference in the analysis

when considering the

c

group instead of the C group is that

s 2h

the rotation R of TI about y is replaced by a reflection

a

in the

xz plane (of the C group). However, since

4v

J+M

a!JM>

=

(-1) IJ,-M>

(1)

(2.12)

for an odd-parity configuration , the resulting irrep labels

will be similar.

In summary, the preservation or switching of the labels

depends on the particular M values associated with the Kramers

(47)

components. In a rotation of n/4 about the z axis, so that the magnetic field direction goes from one axis of symmetry to another, the signs of some of the M states will change

J

~

(1)

d • e 4 z \ a

·I

M>

accor 1 ng to l

~ ~

.L. A A

These changes in sign have the effect oj reversing the energies of the y

3

and y 4

levels for the

type B doublets, while for the type A doublets the sign changes are cancelled when the contributing Zeeman matrix is formed and hence the energies do not reverse. It is concluded that the tetragonal C y and y doublets are of type B and type A

4v 7 6

respectively, aqd this result holds irrespective of the parity (1)

of the configuration. Judd et al. summarise the type assignments of levels for a number of point group symmetries.

The intensity variations in the transverse Zeeman spectra can be analysed in terms of the electric dipole selection rules

II

for the C and C groups and the direction of the electric

s s

vector, ~' of the incident electromagnetic radiation. From an experimental point of view, it is convenient to consider the direction of propagation of light as paral 1 to the magnetic field direction (i.e. the z axis of the C point group) .

s

Therefore, the electric field vector will be perpendicular to the static field

!r

and the electric dipole operator will

A A A

transform as the y (x or y) irrep of the C point group (see

1 s

Section 4.2.3}. Hence, .the allowed transitions for both the C

(48)

"

and

c

groups will correspond to those labelled by a _in

s

" A A A

Table 2.l(b), and these are the y ->Y and y ->Y transitions.

3 3 4 4

This means that A(Y )->B{Y ) and B(Y ) ->A (Y ) are the

6 7 7 6

transitions which show the striking intensity alternations in the

transverse Zeeman patterns for ions in sites of C symmetry.

4v

These results are summarised schematically in Figure 2.1.

The D group may be analysed by precisely the same method.

4

The D point group, however, differs in that the A->A and B->B 2d

transitions show the large intensity variations as the crystal

is rotated in a transverse magnetic field. This can be shown as

follows. When a magnetic field is applied along the y axis, the

reflection symmetry ad is broken leaving only a

c

symmetry

2

operation. However, when the field along the axis midway

between the x,y axes, the point symmetry is now

c

.

The

s

"

magnetic energy levels may still be labelled by the y and y

3 4

irreps of the respective

c

and

c

point groups, and the

2 s

(49)

type B

Figure 2.1

(a)

(x)

C + C'

4v s

ION

c axis (z)

/

B

c4v

Y7

type A y6

(y)

C' s

A

Ys

A

Y4

A

Ys

(b)

c4v

Y7

C + C"

4v s

c axis

(z)

B

(y)

C" s

A

Y~t

A

Y.3

The allowed transitions are shown for ~parallel to the direction of light.

A summary of the transverse Zeeman effect for ions in sites

[image:49.597.44.502.70.624.2]

(50)

TABLE

point

2.1 Electric dipole selection rules for the

c

and

c

groups.

(a)

c2

" Ya

A

y'*

For !!:;1!!,

"

2 s

(b)

A A

cs

A

"

Ya y'* Ya y'*

A

7T 0 _Ya 0 7T

A

0 7T _y'* 7T 0

the allowed transitions for B along the C axis 2

are y -> y and y ->y , while along the C axis they are Y ->Y

3 4 4 3 s 3 3

A A

and y ->y in agreement with the analysis of Judd and Runciman.

4

The analysis here has the advantage that the symmetry of the

leading odd crysta field term does not need to be determined

for the transverse symmetry axes. Also, the method of Judd and

Runciman conceals the way that the true point symmetry at the

ion alters when the magnetic field is along the different

symmetry axes.

The same technique can be used for the hexagonal symmetry

groups D , C and D The results obtained using the true

6 6v 3h

point symmetry at the ion are analogous to those obtained by

(1)

Judd and Runciman However, while the method used here is

more direct, Judd and Runciman's approach does show more

[image:50.597.66.529.73.730.2]

(51)

3.1 CRYSTALS

CHAPTER 3 EXPERIMENTAL

The rare-earth doped alkaline-earth fluoride crystals were

either purchased

from Optovac Inc.

(U.S.A.)

or grown in this

department

by Mr

R.A. Ritchie using a

38 kilowatt radio

frequency furnace manufactured by Arthur D. Little Company.

The

locally made unoriented crystals were grown from

alkaline-earth

fluoride

crystal starting material (Optovac Inc.

stock) by the

Bridgeman-Stockbarger method.

The dopant was added in the

rare-earth fluoride form and small amounts (typically 2%

by weight)

of lead fluoride were added as an oxygen scavenger.

Rare-earth

concentrations of 0.05% and 0.1% were used

for

most crystals,

this being a

compromise between having sufficient rare-earth

dopant to give observable spectral line intensities yet

not

so

much

that cluster sites predominate.

The crystals were grown

over a period of 18 hours in a helium atmosphere, by lowering a

graphite crucible containing

the crystal material through a

temperature gradient.

(52)

calcium or strontium fluoride melt. The seed could be aligned

0

to within 10 of the required orientation by means of the {111) cleavage planes using the crosshairs of a cathetorneter. The diameter of the crystal was controlled by altering the furnace

(36)

temperature. R.J. Kennedy found the least strained crystals were obtained at pulling rates of between 20-25 mrn/hour, and 5 rev/min rotations of the seed produced more uniform diameter crystals. Crystals up to 8 ern in length were grown and these

0

were annealed at -700 C for half an hour before being cooled to room temperature. A more detailed account of Czochralski crystal growing with the aforesaid radio-frequency furnace has

(36)

been given by Kennedy

Crystals oriented in a <100>, <110> and <111> direction were also purchased from Optovac Inc. The alignment of Optovac crystals has been found by X-ray diffraction photographs in the

0

Laue back reflection mode to be within 2 of the required

{37)

(53)

3.2 OPTICAL SPECTROSCOPY OF CaF :Er 2

-3.2.1 INSTRUMENTATION

The absorption and fluorescence spectra were recorded photoelectrically with a Jarrell-Ash Model 25-103 double monochromator. This instrument has a one meter focal length Czerny-Turner configuration with an effective aperture of f/8.7. The gratings have 1180 lines/mm and are blazed for 5000

A.

The scanning energy range for this particular model, is from

-1 -1 -1

21900 em to 11500 em with a reproducibility of

±1

em over

-1

any 5000 em region. The resolution of the spectrometer was measured at various slitwidth settings using the 3131

A

Hg doublet, and is tabulated in Table 3.1. Most spectra were

recorded with slitwidths between 30 ~m and 100 ~m.

Table 3.1 Resolution of the Jarrell-Ash double monochromator measured at various slitwidths using the 3131

A

Hg doublet.

Nominal Slitwidths Resolution entrance/intermediate/exit (em-1

)

(microns)

20/20/12 .1

20/20/20 .2

30/30/30 . 4

40/40/40 . 5

50/50/50 . 7

_I

60/60/60 1.0

[image:53.597.67.529.154.465.2] [image:53.597.91.443.591.799.2]

(54)

Using the accurately known mercury spectral lines, the calibration of the instrument was measured over the whole spectral range. Then during each experimental session, the 3131.55

A

and 3131.83

A

Hg lines were recorded in second order, and the appropriate wavenumber corrections made to the recorded spectra. All energies are reported in air wavenumber units.

An R.C.A. type 31034 photomultiplier tube,

thermo-0

electrically cooled to 5

c,

was used as a detector. This tube has an extended S-20 spectral response. The photomultiplier's output was amplified using a Jarrell-Ash d.c. electrometer, and the output displayed on a Bristol chart recorder.

3.2.2 ABSORPTION EXPERIMENTS

A 100 watt quartz-iodine lamp operated from a voltage regulated power supply was used as a source to obtain the absorption spectra. A series of Corning filters were used to provide a pass band in the wavenumber reg ion to be scanne-d, to eliminate radiation from unwanted orders and to provide minimal heating at the crystal. In particular, the CS 1-69 filter was used to eliminate infrared radiation.

4 4 -1

The Z > F and