Landolt-Brnstein Group III
: Condensed Matter
Volume 12 

Magnetic and Other Properties of Oxides and Related Compounds 
Subvolume A Part A
: Garnets and Perovskites

Introductory material 
1	
Garnets 1

1.1	
Crystallographic and structural data of garnets 1

(W.
 TOLKSDORF, U. WOLFMEIER)
1.1.0	
Introduction 1

1.1.0.1	
General remarks 1

1.1.0.2	
List of symbols and abbreviations 1

1.1.1	
Locations and environments of ions in the unit cell of the garnet lattice 2

1.1.2	
Oxygen coordinates, interionic spacings and bond angles of compounds with 4

garnet structure (Refinements)

1.1.3	
Lattice parameters of garnets 22

1.1.4	
Site selectivity 41

1.1.5	
Influence of preparation 44

1.1.6	
Thermal expansion 45

1.1.7	
References for 1.1 48

1.2	
Iron garnets (P. HANSEN, K. ENKE, G. WINKLER) 53

1.2.1	
Introduction 53

1.2.1.1	
General remarks 53

1.2.1.2	
List of symbols and abbreviations 55

1.2.2	
Magnetic properties 58

1.2.2.1	
Magnetic moments and molecular field data 58

1.2.2.1.1	
Saturation magnetization and Curie temperature 58

A. 
Rare-earth iron garnets and mixed rare-earth iron-gallium/aluminum garnets 59

B. 
Garnets of composition Y3Fe5-xMxO12 and (Y, Ca)3(Fe, M)5O12	63

C. 
Special compositions	66

D. 
Ion distribution and thermal history	71

E. 
Compositions with a compensation point	72

F. 
Antiferromagnetic garnets	74

G. 
Pressure dependence of the Curie temperature	74



1.2.2.1.2	
Molecular field- and exchange constants 75

1.2.2.1.3	
Critical exponents 77

1.2.2.2	
Susceptibility and permeability 77

1.2.2.2.1	
Susceptibility 78

1.2.2.2.2	
Permeability 80

1.2.2.3	
Magnetocrystalline anisotropy 81

1.2.2.3.1	
Cubic anisotropy 81

A. 
Rare-earth iron garnets R3Fe5O12	82

B. 
Garnets of composition Y3Fe5-xMxO12	86

C. 
Garnets doped with small amounts of magnetically anisotropic transition-metal 89

ions

D. 
Garnets of special composition	94

E. 
Pressure dependence of K1 for Y3Fe5O12 96



1.2.2.3.2 
Uniaxial anisotropy 96

A. 
Temperature and concentration dependence of the uniaxial anisotropy constant 97

B. 
Dependence of the uniaxial anisotropy constant on various other parameters 101



1.2.2.4 
Ferromagnetic resonance (FMR) 104

1.2.2.4.1 
Resonance field 104

A. 
Rare-earth-substituted garnets 105

B. 
Garnets with small substitutions of magnetically anisotropic transition-metal 106

ions and the garnet Ca3Fe2Ge3O12



1.2.2.4.2 
FMR linewidth 110

A. 
Rare-earth-substituted garnets (single crystals) 111

B. 
Garnets of composition Y3Fe5-xMxO12 (single crystals) 113

C. 
Pressure dependence (single crystals) 115

D. 
Polycrystalline garnets 116



1.2.2.4.3 
g-factor 119

1.2.2.5 
Magnetostatic modes, spin waves, and relaxation 120

1.2.2.5.1 
Magnetostatic modes and spin waves 120

A. 
Magnetostatic modes 121

B. 
Spin waves 122

C. 
Interaction of spin waves with light 123



1.2.2.5.2 
Relaxation 125

A. 
Single-crystal garnets 125

B. 
Polycrystalline garnets 127



1.2.2.6 
Nuclear magnetic resonance (NMR) 130

1.2.2.7 
Mssbauer spectroscopy 132

1.2.2.8 
Magnetic domains (stripe and bubble domains) 140

1.2.2.8.1 
Static properties 140

A. 
Collapse field and diameter 142

B. 
Wall energy and material length 143



1.2.2.8.2 
Dynamic properties 147

A. 
Collapse diameter, collapse time and velocity 147

B. 
Mobility 152



1.2.3 
Magnetoelastic properties 155

1.2.3.1 
Magnetostriction 155

A. 
Rare-carth garnets of composition Y3-xRxFe5O12 156

B. 
Garnets of composition Y3Fe5-xMxO12 with M = Ga3+, Sc3+ 159

C. 
Garnets doped with small amounts of magnetically anisotropic ions 161

D. 
Garnets of special compositions 164



1.2.3.2 
Magneto-elastic waves 164

1.2.4 
Elastic properties 165

1.2.4.1 
Elastic constants and Young's modules 165

1.2.4.2 
Parallel pumping of elastic waves 166

1.2.5 
Optical and magnetooptical properties 167

1.2.5.1 
Optical properties 168

1.2.5.1.1 
Absorption of light 169

A. 
Absorption spectra (near IR to UV) 172

B. 
Absorption spectra of lattice vibrations 180

C. 
Local vibrational modes 181

D. 
Dielectric tensor (diagonal elements) 182

E. 
Influence of annealing on absorption 183


Reflection of light 183

Refractive index 185

Crystal field splitting of electronic levels 186

Magnetooptical properties 188

Faraday rotation 189

A. 
Yttrium and dysprosium iron garnets, and garnets doped with bismuth and with 195

ions replacing iron

B. 
Gadolinium iron garnets doped with bismuth and with ions replacing iron 198

C. 
Calcium-bismuth iron-vanadium garnets 200

D. 
Yttrium and gadolinium iron garnets doped with Co2+, Co3+, and Fe2+ 201

E. 
Other iron garnets 202

F. 
Temperature dependence of the Faraday rotation 202

Magnetic circular dichroism (MCD) 203

A. 
Yttrium iron garnet 204

B. 
Yttrium iron garnet doped with bismuth and gallium 205

206 
207 
209 
211 

214 
215 
216 
217 
218 
218 
219 
219 
219 
220 
220 
221 
221 
223 
224 


Thermal conductivity (thermal resistance) and heat capacity 224

Magnetocaloric effect 227

Electrical properties 230

References for 1.2 235

Non-iron garnets (W. GUNSSER, U. WOLFMEIER, J. FLEISCHHAUER) 265

Introduction 265

General remarks 265

List of symbols and abbreviations 266

Magnetic susceptibility 268

Paramagnetic susceptibility above the ordering temperature 268

Susceptibility data in the vicinity of an ordering temperature 271

Summary of susceptibility parameters and transition temperatures 272

Magnetization and magnetic structure 276

Magnetic moments of gadolinium and neodymium gallium garnets 276



1.3.3.2	
Magnetic moments of terbium aluminum and terbium gallium garnets 280

1.3.3.3	
Magnetization of dygprosium aluminum and dysprosium gallium garnets 282

1.3.3.4	
Magnetic moments of erbium gallium, holmium gallium and aluminum garnets, and 286

manganese chromium-germanium garnets

1.3.3.5	
Magnetic neutron scattering in dysprosium aluminum garnet 287

1.3.3.6	
Magnetic neutron scattering and magnetic structure of terbium and holmium 288

aluminum garnets

1.3.4	
Results of magnetic resonance experiments 289

1.3.4.1	
Electron paramagnetic resonance of transition metal ions in diamagnetic garnets 289

1.3.4.2	
Electron paramagnetic resonance of rare-earth ions in diamagnetic garnets 293

1.3.4.3	
Electron paramagnetic resonance of impurities in paramagnetic garnets 294

1.3.4.4	
Nuclear magnetic resonance and electron double resonance (ENDOR) 295

1.3.5	
Optical and magnetooptical properties 298

1.3.5.1	
Crystal field parameters 298

1.3.5.2	
IR, UV and Raman spectra, and index of refraction 302

1.3.5.3	
Information on colour centres and references 313

1.3.5.4	
Further references for results from optical measurements 317

1.3.5.5	
Faraday rotation 323

1.3.6	
Mssbauer effect in garnets 325

1.3.7	
Electron spin-lattice relaxation of paramagnetic ions in garnets 327

1.3.8	
Thermal properties 328

1.3.8.1	
Molar heat capacity 328

1.3.8.1.1	
Molar heat capacity of gadolinium gallium garnet 329

1.3.8.1.2	
Molar heat capacity of dysprosium aluminum garnet and dysprosium gallium 332

garnet

1.3.8.1.3	
Specific heat of further rare-earth gallium and aluminum garnets and some 337

germanium and vanadium garnets

1.3.8.2	
Thermal conductivity (and resistivity) 340

1.3.8.3	
Ultrasonic attenuation 346

1.3.8.4	
Debye temperature 350

1.3.8.5	
Thermal expansion 351

1.3.8.6	
Derived thermodynamic functions 352

1.3.9	
Elastic, thermoelastic and photoelastic properties 356

1.3.10	
Magnetostriction 357

1.3.11	
Electric properties 359

1.3.12	
References for 1.3 360

2	
Crystallographic and magnetic properties of perovskite and perovskite-related 368

compounds (S. NOMURA)

2.0	
Introduction 368

2.0.1	
General remarks 368

2.0.2	
References to text books, review articles and proceedings 369

2.0.3	
List of symbols and abbreviations 370

2.1	
Descriptions of stoichiometric ABX3 and McXMf3 structures 372

2.1.1
 - 2.1.6See section 3.1.1 - 3.1.6 in Vol. 4A 
2.1.7	
Data: Crystallographic properties 373

2.2	
Descriptions of perovskite-related structures 414

2.2.1
 - 2.2.3See section 3.2.1 - 3.2.3 in Vol. 4A 
2.2.4	
Data: Crystallographic properties of non-ABX3 compounds 414

2.3 
Magnetic order: localized electrons 429

2.3.1-2.3.3 
See section 3.3.1 - 3.3.3 in Vol. 4A

2.3.4 
Data: Magnetic properties of perovskite and perovskite-related compounds 429

2.4 
Localized versus collective electrons 475

2.4.1
 - 2.4.4 See section 3.4.1 - 3.4.4 in Vol. 4A
2.5 
The McXMf3 alloys 475

2.5.1 
See section 3.5.1 in Vol. 4a 
2.5.2 
Data: Magnetic and crystallographic properties of McXMf3 or M3M'X compounds 475

2.5.2.1 
Crystallographic properties 475

2.5.2.2 
Magnetic properties 476

2.6 
References for 2 480

2.6.1 
Textbooks, review articles, and proceedings 480

2.6.2 
Research papers 482



1.2.5.1.2 
1.2.5.1.3 
1.2.5.1.4 
1.2.5.2 
1.2.5.2.1 
1.2.5.2.2 
1.2.5.2.3 
1.2.5.2.4 
1.2.5.2.5 
1.2.5.3 
1.2.5.3.1 
1.2.5.3.2 
1.2.6 
1.2.6.1 
1.2.6.2 
1.2.7 
1.2.8 
1.3 
1.3.1 
1.3.1.1 
1.3.1.2 
1.3.2 
1.3.2.1 
1.3.2.2 
1.3.2.3 
1.3.3 
1.3.3.1 
Kerr effects

A. Polar Kerr rotation

B. Equatorial Kerr effects

C. Kerr ellipticity

Magnetic linear birefringence (MLB) and non-magnetic linear birefringence 
A. Orientational dependence

B. Temperature dependence

C. Field dependence

D. Stress dependence

E. Piezooptic effect
Magnetic linear dichroism (MLD)
Photoinduced effects
Decrease of permeability

A. Time dependence

B. Concentrational dependence

C. Temperature dependence

D. Spectral dependence
Change of magnetic anisotropy

l.2.5.3.3 Change of optical properties
Thermal properties

