Modern Ferrites, Volume 2 E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 1089

Veröffentlichungsjahr: 2022

Beschreibung

MODERN FERRITES, Volume 2 A robust exploration of the basic principles of ferrimagnetic and their applications In Modern Ferrites: Volume 2, renowned researcher and educator, Vincent G. Harris delivers a comprehensive overview of ferrimagnetic phenomena and discussions of select applications of modern ferrite materials in emerging technologies and applications. Volume 2 explores fundamental properties of ferrite systems, including their structure, chemistry, and magnetism, as well as practical applications, such as permanent magnets; inductors, inverters, and filters; and their use in emerging applications as metamaterials, multiferroics, and biomedical technologies. In addition to the properties of ferrites, the included resources explore the processing, structure, and property relationships in ferrites as nanoparticles, thin and thick films, compacts, and crystals. The authors discuss how these relationships are key to realizing practical device applications laying the foundation for next generation communications, radar, sensing, and biomedical technologies. This volume includes: * A comprehensive review of ferrite discoveries and impacts upon ancient cultures, their scientific evolution, and societal benefits; * Discussion of the origins of magnetism in ferrimagnetic oxides including superexchange theory, GKA-rules, and recent developments in density functional theory; * In-depth examination of ferrite power conversion and conditioning components and their processing as low temperature co-fired ceramics; * Ferrite-based electromagnetic interference suppression and electromagnetic absorption; * Nonlinear microwave devices; multiferroic and emerging magnetoelectric devices; * Biomedical applications of ferrite nanoparticles Perfect for RF engineers and magnetitians working in the fields of RF electronics, radar, communications, and spintronics as well as other emerging technologies. Modern Ferrites will earn a place on the bookshelves of engineers and scientists interested in the ever-expanding technologies reliant upon ferrite materials and new processing methodologies. Modern Ferrites Volume 1: Basic Principles, Processing and Properties is also available (ISBN: 9781118971468).

Leseprobe

Modern Ferrites, Volume 2

Emerging Technologies and Applications

Edited by

Vincent G. Harris College of Engineering Northeastern University Boston, MA, USA

This edition first published 2023

© 2023 John Wiley & Sons, Ltd.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Vincent G. Harris to be identified as the author of this work has been asserted in accordance with law.

Registered Offices

John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

Editorial Office

The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print-on-demand. Some content that appears in standard print versions of this book may not be available in other formats.

Trademarks: Wiley and the Wiley logo are trademarks or registered trademarks of John Wiley & Sons, Inc. and/or its affiliates in the United States and other countries and may not be used without written permission. All other trademarks are the property of their respective owners. John Wiley & Sons, Inc. is not associated with any product or vendor mentioned in this book.

Limit of Liability/Disclaimer of Warranty

While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

A catalogue record for this book is available from the Library of Congress

Hardback ISBN: 9781394156139; ePub ISBN: 9781394156153; ePDF ISBN: 9781394156160; oBook ISBN: 9781394156146

Cover image: Wiley

Cover design by Wiley

Set in 9.5/12.5pt STIXTwoText by Integra Software Services Pvt. Ltd, Pondicherry, India

“Peace can only come as a natural consequence of universal enlightenment…”

Nikola Tesla

Contents

Cover

Title page

Copyright

Dedication

Preface

List of Contributors

1 Magnetism in Ancient Societies to the Present

2 Goodenough–Kanamori–Anderson Rules of Superexchange Applied to Ferrite Systems

3 Ferrite Inductor Cores for MHz-Frequency Applications

4 Hexaferrite Permanent Magnets and Applications

5 Low-Temperature Co-Fired Magnetoceramics for RF Applications

6 Electromagnetic Interference Suppression and Electromagnetic Absorption

7 Nonreciprocal and Nonlinear Behavior of Ferrites and Applications in RF Devices

8 Ferrite-Based Magnetoelectronics

9 Ferrite-Based Multiferroic Devices

10 Biomedical Applications of Nanoparticle Ferrites

Index

End User License Agreement

List of Tables

CHAPTER 01

Table 1.1 History of key technological...

CHAPTER 02

Table 2.1 Structural and magnetic properties...

Table 2.2 Common substitutional cations...

CHAPTER 03

Table 3.1 Main applications of soft

Table 3.2 DC and AC resistivity...

Table 3.3 DC and AC resistivity...

CHAPTER 04

Table 4.1 Numerical values of the...

Table 4.2 Magnetic properties of high...

Table 4.3 Room temperature magnetic properties...

Table 4.4 Magnetic properties of high...

Table 4.5 Magnetic properties of high...

Table 4.6 Magnetic properties of some...

CHAPTER 05

Table 5.1 The melting points of...

Table 5.2 Typical characteristics of LTS...

Table 5.3 Average particle sizes of...

Table 5.4 Properties of low-temperature...

Table 5.5 Effect of the amount...

CHAPTER 06

Table 6.1 Structural and compositional...

Table 6.2 Magnetic properties of hexagonal...

CHAPTER 07

Table 7.1 Applied bias field and...

Table 7.2 Jammer effectiveness reduction due...

CHAPTER 08

Table 8.1 Chemical formula, stacking sequence...

Guide

Cover

Title page

Copyright

Dedication

Table of Contents

Preface

List of Contributors

Begin Reading

Index

End User License Agreement

Pages

i

ii

iii

iv

v

vi

vii

viii

ix

x

xi

xii

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

Preface

Modern Ferrites Volume 2: Emerging Technologies and Applications is the second book in a two-volume set on Modern Ferrites. Volume 2 addresses not only conventional ferrites as inductors, permanent magnets, electromagnetic shielding, and absorbers, but also their role in the emerging fields of magnetoelectrics, multiferroics, medical magnetism, nonlinear microwave devices, and ferrite-based metamaterials.

The motivation for undertaking these volumes on Modern Ferrites is to create a modern-day text on ferrites to supplement the tomes of the masters, including those of Smit and Wijn, von Aulock, Soohoo, Lax and Button, Goldman, and others. Our aspirations are bold. The contributing authors are experts chosen from the international community who have distinguished themselves throughout their careers and provide here exceptional products to the reader. Some have invited aspiring younger colleagues as coauthors who show singular potential. Our principal goal is to provide a text covering both basic principles and emerging applications of particular societal value while maintaining the standards of excellence embraced by those who came before us.

A project like this is always the result of a group effort, and this text is no different. I am thankful and indebted to my family, students, staff, and friends who assisted in the preparation of this text. A special thanks goes to Ms. Mary Zeng who has assisted me and other authors in editing, formatting, referencing, and submission of chapters to Wiley Publishing Company. Thank you, Mary.

Wiley Publishing Company’s Ms. Sandra Grayson and Ms. Juliet Booker, and others on the editorial staff, were of immense value in guiding this project through to its completion and showing uncommon patience with its editor.

Finally, I thank each of the contributing authors and coauthors for their hard work and commitment in sharing with our readers their life lessons and experiences in ferrite research.

In closing, sadly, during the production of this text, our community has lost some of its most valued leaders – persons who were exceptional scholars, mentors, educators, and friends. These individuals include Dr. Gerald Dione (2020) of MIT Lincoln Labs, a renowned expert in all aspects of magnetic oxides, including the physics as well as engineering of magnetoceramics; Dr. John Douglas Adam (1943–2018), formally of Westinghouse and Northrop Grumman Corporation, the principal inventor of many important nonlinear ferrite devices and developer of advanced ferrite LPE-growth techniques; Prof. Takanori Tsutaoka (1959–2019) of Hiroshima University, an expert and innovator of high-frequency magnetic materials, composites, and metamaterials; and Prof. Boris Kalinikos of St. Petersburg’s Electrotechnical University and Colorado State University at Fort Collins, who had made several important contributions to the understanding of nonlinear properties of ferrites and loss mechanisms and had through many of his contributions laid the foundations to the emerging field of Magnonics (a growing subfield of Spintronics). I speak for many in saying that we stand on the shoulders of these giants. May their souls rest in peace, knowing that they have left behind more than technical papers and discoveries – a legacy of grateful students, valued friendships, and treasured memories.

Alas, we have come to the end of this long road… the asphalt has turned to sand.

Here, our product is laid bare for your judgment. May you find value in our endeavor.

V.G.H.

List of Contributors

Volume 2

John D. Adam (deceased)Ph.D., Metamagnetics Inc., Westborough, MA, USA

Parisa AndalibResearch Professor, Northeastern University, Boston, MA, USA

Ogheneyunume FitchorovaSenior Research Scientist, Kostas Research Institute at Northeastern University, LLC, Burlington, MA, USA

Anton L. GeilerPresident, Metamagnetics Inc., Marlborough, MA, USA

Vincent G. HarrisUniversity Distinguished Professor and W. L. Smith Chair Professor, Northeastern University, Boston, MA, USA

Orestis KalogirouProfessor and President at Hellenic NARIC, Aristotle University of Thessaloniki, Thessaloniki, Greece

Tsuyoshi KimuraProfessor, University of Tokyo, Kashiwa, Chiba, Japan

Marina KoledintsevaPh.D., Metamagnetics Inc., Westborough, MA, USA

Jean-Marie Le BretonProfessor, Université de Rouen, St. Etienne du Rouvray, France

Douglas K. LinkhartPrincipal RF Engineer, Metamagnetics Inc., Marlborough, MA, USA

Yingli LiuProfessor, University of Electronic Science and Technology of China, Chengdu, Sichuan, China

Virginie NachbaurAssociate Professor, Université de Rouen, St. Etienne du Rouvray, France

Konstantin RozanovDirector, Institute for Theoretical and Applied Electromagnetics (ITAE), Moscow, Russia

Gopalan SrinivasanProfessor, Oakland University, Rochester, MI, USA

Nian SunProfessor, Northeastern University, Boston, MA, USA

Charalampos A. StergiouCentre for Research and Technology Hellas - CERTHThessaloniki, Greece

Mingzhong WuProfessor, Colorado State University at Fort Collins, Fort Collins, CO, USA

Yu WangPh.D., University of Electronic Science and Technology of China, Chengdu, Sichuan, China

1 Magnetism in Ancient Societies to the Present Circa 1400 BCE to 2020 CE

Vincent G. Harris

Center for Microwave Magnetic Materials and Integrated Circuits; Department of Electrical and Computer Engineering, and Department of Chemical Engineering Northeastern University, Boston, MA 02115–5000, USA

1.1 Introduction

Magnetic materials, in the form of lodestone, have been known to ancient cultures for many centuries. Both Greek and Chinese cultures have been widely recognized for their rich heritage in the historical foundations of magnetism for early lodestone instruments and related descriptive literature dating to several centuries before the common era (BCE). Here, we present published findings that supplement these many reports and support the use of magnetic materials by Mesoameric cultures some 800–1000 years before the Greek and Chinese societies [1].

Lodestone is the descriptor assigned by historians to ancient magnetic ores of igneous, metamorphic, and sedimentary rocks consisting of not only mostly magnetite but also maghemite, hematite, and other more exotic oxide phases of lessor volume fractions. The principal phase, magnetite, having formula Fe3O4, is the iron oxide form of spinel ferrite, (A)[B]2O4, where A and B are Fe2+ and Fe3+ cations occupying tetrahedrally and octahedrally oxygen-coordinated sites in the structure: (Fe3+)[Fe2+Fe3+]2O4–2. Fragments of spontaneously magnetized lodestone have only been found near the earth’s surface and not buried below its crust [2]. This observation fostered the belief that its permanent magnetic properties likely derive from lightning strikes.

When a naturally magnetized lodestone fragment is suspended in a fluid, it naturally orients toward a magnetic pole thus enabling the design and development of a magnetic compass.

1.2 Discovery and Ancient Applications of Lodestone: 1400 BCE–CE

1.2.1 Magnetism in Ancient Mesoameric Societies

1.2.1.1 Olmec: Circa 1400 BCE to 400 BCE

Challenging the general attribution of the origins of magnetism to the ancient Greek and Chinese societies, recent findings support the earliest discovery and applications of magnetism to the ancient Mesoameric societies, i.e. the Olmec society of North America (c. 1400 BCE to 400 BCE), which is now located in the modern Mexican state of Veracruz [1].

An ancient Olmec magnetic artifact is shaped as an engineered bar composed of hematite impregnated with Fe2–xTixO3 lamellae [3] and is dated to more than a thousand years before the Greek and Chinese discoveries of magnetism. If true, this artifact would represent the first use of magnetic materials for navigation, or other forms of directional seeking, in world history.

Figure 1.1a contains a photograph of this artifact that shows what appears to be an engineered bar whose functionality remains the subject of much conjecture among historians.

Figure 1.1 (a) Olmec artifact (M-160) from reference 1 (dimensions in centimeters). (b, left) Top face and cross section of M-160 (dimensions in millimeters) and representation of the “floater” experiment showing the observed orientation 35.5° west of magnetic north. (b, right) Total magnetic moment vector M and components of M-160 [1].

1.2.1.2 Monte Alto: Circa 400 BCE to 200 CE

Another ancient Mesoameric society, the Monte Alto (c. 400 BCE to 200 CE), flourished in present-day Guatemala and produced sculpted potbellied figures (see Figure 1.2) that resemble those of the earlier Olmec civilization. It is unknown why Monte Alto sculptors incorporated magnetized ores into their work. Fu et al. [4] postulated the ability of such sculptures of leading authorities of the time to deflect a compass needle would have appeared quite impressive to any audience.

Figure 1.2 Photograph of a representative potbellied sculpture of the Mesoameric era. Findings by Fu et al. [4] and others support a magnetic signature of the sculpture. The origins and purpose of the magnetic signature is as yet unclear.

The Monte Alto people were known to trade widely throughout North America. Lodestone tools able to detect magnetic anomalies, which had exotic or even perceived mystical properties, would have proven particularly valuable [4]. It is believed that magnetism had spread broadly throughout North America at this time.

1.2.1 Magnetism in Ancient Greek Societies

1.2.2.1 Archaic: Circa 800 –480 BCE

Chronologically, following the Mesoameric societies are reports of the ancient Greek societies, circa 800 BCE to 500 BCE.

In this context, Thales of Miletus has been widely attributed as the first reporter of magnetism from these regions and eras. Aristotle attributed the first of what would be called scientific discussions on magnetism to Thales, who lived from about 625 BCE to about 545 BCE [5], is historically recognized as the first individual known to have entertained and engaged in scientific philosophy and is often attributed to the discovery of mathematics and is often referred to as the Father of Science.

Thales of Miletus

Although none of Thales’s writings have been preserved, Aristotle, circa 384 BCE to 322 BCE, noted in On the Soul that Thales described the magnet as possessing a “soul” because it moves iron. This description has been corroborated by Laertius, circa 300 CE, in Lives of Eminent Philosophers [5, 6]. The first attempts to provide a rational explanation for magnetism came concomitantly from Empedocles of Akragas (c. 495 BCE to 435 BCE), Democritus of Thracia (c. 460 BCE to 370 BCE), and from Diogenes of Apollonia (c. 450 BCE) [5, 6].

These philosophers attributed magnetism to the movement of iron particles on a “fluid” through air to the surface of lodestone entering surface “pores.” The forces of flow were implied to exist between both iron and lodestone but only iron particles were identified to physically flow to the lodestone and not lodestone particles to the iron. This one-way mechanistic particle flow interpretation of magnetism held for nearly six centuries [6].

During these eras, amber, i.e. fossilized tree resin, had been shown that upon rubbing with a cloth attracted small particles. This was known as the amber effect. Plato, circa 428 BCE to 348 BCE, speculated incorrectly that the amber effect, an attraction between electrostatic dipoles, and magnetism, an attraction between magnetostatic dipoles, shared a common origin [5, 6].

Plutarch, circa 46 CE to 119 CE, was first to postulate the attractive powers of magnets and amber derived from different phenomena [6]. Impressively for the day, Plutarch hypothesized the interpretation that would evolve to be termed “magnetic effluvium” and “electric effluvium” where the term effluvium was interpreted as a discharge. The concept of different discharges, one necessitated as Empedocles’s magnetic fluid, another as the electric fluid, was required as the relative strength of magnetism was many times stronger than that created by amber [6].

Plato and Plutarch

1.2.3 Magnetism in Ancient Chinese Societies

1.2.3.1 Zhou Dynasty: Circa 1046 BCE to 221 BCE

Concurrent with, and independent of the Greek societies, the Chinese reference magnetism in the fourth century BCE. As stated in the Book of the Devil Valley Master: “When the people of Cheng go out to collect jade, they carry a south-pointer with them so as not to lose their way.” [7]

The “south-pointer” can only be reasonably interpreted as a lodestone compass. Compasses of that era used lodestone as a natural permanent magnet that aligned itself with Earth’s magnetic field exhibiting north–south polarity.

1.2.3.2 Qin Dynasty: Circa 221 BCE to 206 BCE and Han Dynasty: Circa 206 BCE to 220 CE

The history of the compass was further developed during the Qin (221 BCE to 206 BCE) and Han dynasties (206 BCE to 220 CE). In the Qin dynasty, Lüshi Chunqiu explicitly asserted, circa 200 BCE, that “lodestone makes iron come or it attracts it,” and the earliest Chinese mineral diviners had experimented with tools that today would be describe as compasses [8].

Lüshi Chunqiu (Courtesy of the National Palace Museum, Taipei, Taiwan, Republic of China)

The earliest Chinese compasses include lodestone-shaped spoons or ladles that sat atop a flat, square-shaped plate, made of bronze, which served as a representation of Earth. The lodestone spoon balanced on its curved base and pointed toward the polar south [9] (see Figure 1.3).

Figure 1.3 Photograph of an early spoon compass circa 60 CE [11].

The spoon compass was first mentioned by Wang Chong in Lun Heng, a book of essays on astronomy and meteorology, written during the Han dynasty. There he described this compass as: “When the south pointing spoon is thrown upon the ground, it comes to rest pointing at the south” [10, 11].

1.2.4 Magnetism Ancient Indian Societies

1.2.4.1 Mahajanapadas: Circa 600 BCE–CE

Angutara Nikaya, a Buddhist scripture, mentions 16 great kingdoms, or Mahajanapadas, in India at the beginning of the sixth century BCE. These emerged during the Vedic Age (c. 1500 BCE to 500 BCE). The history of the emergence of Mahajanapadas is linked to the development of eastern Uttar Pradesh and western Bihar where agriculture thrived due to the availability of fertile lands and the abundance of iron ores. This resulted in the development of iron weapons and the subsequent expansion of Janapadas [12]. The ancient Indian text Sushruta Samhita was the first to describe the use of lodestone (i.e. magnetite) as a surgical tool used to remove arrow heads embedded in a person’s body. This is the earliest account of employing magnetism in human health care [13, 14].

1.3 Discovery and Applications of Magnetism: CE to Circa 1800 CE

1.3.1 Magnetism in Chinese Tang and Song Dynasties

1.3.1.1 Tang Dynasty (618 CE to 907 CE)

By the time of the Tang dynasty, and the beginning of the Northern Song dynasty (960 CE to 1127 CE), Chinese scholars devised a way to magnetize iron needles by rubbing them with magnetite and then suspending them in water. They also observed that needles heated to a high temperature and cooled in the north–south orientation (i.e. along the earth’s magnetic axis) would become magnetic. These more refined compasses could be floated in water as wet compasses, mounted on a shaft as dry compasses, or suspended from a thread, etc. Consequently, due to their portability, they were of greater practicality for purposes of navigation [15].

During the Song dynasty, many ships sailed as far as Saudi Arabia such that the compass was introduced to the Arab and European societies. The spread of the compass to Europe opened travel and led to the discovery of the New World.

1.3.1.2 Song Dynasty (960 CE to 1279 CE)

The eleventh-century Chinese scientist Shen Kuo (1031–1095) wrote in the Dream Pool Essays in 1088 that the magnetic needle compass improved the accuracy of navigation by employing the astronomical true north [15, 16].

Shen Kuo

Shen Kuo provided the first detailed description of a magnetized needle compass. This invention enabled global exploration and international commerce. Remarkably, the floating needle compass of 1088 CE has not changed fundamentally in its components and construction to present-day compass manifestations.

1.3.2 Magnetism in Ancient Arabic Societies: The Islamic Golden Age

Dry compasses appeared circa 1269 CE in Medieval Europe and 1282 CE in the Islamic Golden Age [17]. Circa 1300 CE, Al-Ashraf Umar II (1242–1296), a Yemeni physicist, astronomer, and geographer, and Ibn Simô¢un, a Cairene astronomer, wrote individually treatises on the magnetic compass [18]. Al-Ashraf Umar II is known for writing the first description of the use of a magnetic compass for determining the qibla, i.e. the direction toward the Mosque in Mecca used by Muslims to determine the appropriate direction for prayer [18, 19].

1.3.3 Magnetism in European Eras: 1000 CE to 1800 CE

Later, compass designs included metallic iron needles. Magnetized needles and compasses were first described in Medieval Europe by the English theologian Alexander Neckam (1157 CE to 1217 CE) circa 1190 CE. Neckam preserved the earliest European reports of the magnetized needle as a guide to mariners [20, 21].

Alexander Neckam

Pierre de Mariciurt

In the thirteenth century, Peter Peregrinus (aka, Pierre de Mariciurt) [22] wrote the first treatise describing the properties of magnets and pivoting compass needles as Epistola de magnete. This tome, divided into two parts, part 1 focusing on inductive reasoning of definite experiences describing fundamental laws of magnetism and discussing for the first time the polarity of magnets and part 2 describing devices of the day utilizing the properties of magnets and their practical applications (e.g. the “wet” floating and “dry” pivoting compass) [23].

The mariner’s compass was further advanced by Italian inventor Flavio Gioja circa 1300 CE [24].

1.3.3.1 The Renaissance: Circa 1400–1700

Leonardo Garzoni’s (1543–1592) work, the Due trattati sopra la natura, e le qualità della calamita, is the first known example of a modern treatment of magnetic phenomena. Written circa 1580 CE, but never published, it was widely distributed in its time. In particular, Garzoni was referred to as an expert in magnetism by Niccolò Cabeo, whose Philosophia Magnetica (c. 1629 CE) is believed to be a worthy reproduction of Garzoni’s work [25–27].

In 1600 CE, William Gilbert (1544–1603) published his De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on the Great Magnet the Earth) [28]. In this work, he described many of his experiments from which he concluded that Earth was itself magnetic and that this was the reason compasses pointed north (previously, some believed that it was the pole star, Polaris, or a large magnetic mass at the north pole that attracted the compass) [29].

William Gilbert

Although lodestone finds great utility in terrestrial, nautical, and celestial navigation, it was not until the mid-twentieth century that modern variants of lodestone, i.e. spinel ferrites, garnets, and hexaferrites, would be studied for their magnetic and electronic properties for use in power generation, conditioning, and conversion, thus setting society on a course of tremendous technological advance.

Nearly a thousand years after the discovery of the floating lodestone needle compass, ferrites were rediscovered and developed to address other technological needs ranging from communication, computation, transportation, energy and medical applications, and consumer electronics.

1.4 Development of Modern Magnetism: 1800 CE to Circa 2020 CE

1.4.1 Development of Classical Electromagnetism (1800 CE to 1900 CE)

Hans Christian Ørsted

André-Marie Ampére

Johann Friedrich Carl Gauss

Jean-Baptiste Biot and Félix Savart

Michael Faraday

The modern understanding of the relationship between electricity and magnetism began in 1819 with the work by Hans Christian Ørsted (1777–1851) who serendipitously noticed the twitching of a compass needle by a nearby electric current and inferred an induced magnetic field was generated by the current. André-Marie Ampère (1775–1836) followed in 1820 with the postulate that any induced magnetic field was related to an electrical current, provided that the electric field does not change with time [30]. Johann Friedrich Carl Gauss (1777–1855) and Jean-Baptiste Biot (1774–1862) and Félix Savart (1791–1841), also in 1820, derived the Biot–Savart law that quantitatively relates the magnetic field amplitude to a current-carrying wire (for example) and is analogous to Coulomb’s law for electricity [31]. Michael Faraday (1791–1867), in 1831, reported that a time-varying magnetic flux through a loop of wire induces a voltage. Faraday also established that magnetism could affect the polarization of light providing the foundation for nonreciprocity in today’s RF and optical devices [32]. He similarly discovered the principles of electromagnetic induction (near simultaneously with the American scientist Joseph Henry who also popularized the electromagnet as a practical device) [31, 33, 34] and mutual induction – the basis for modern power converters and transformers [35], as well as diamagnetism, and the fundamentals of electrolysis. His inventions of rotary machines included the first ever generator of electricity and electric motor technology that enabled and accelerated the industrial revolution [36, 37].

These founding fathers of electromagnetism laid the early foundational stones for examination by Maxwell.

James Clerk Maxwell

James Clerk Maxwell (1831–1879), circa 1861, expanded upon those ideas and produced his astonishing revolutionary formulas, unifying all electricity, magnetism, and optics into the modern field of electromagnetism. With the development of his four principal equations for electromagnetism, Maxwell demonstrated that electric and magnetic fields travel through space as waves moving at the speed of light. He proposed that light is an undulation in the same medium as that hosting electric and magnetic phenomena [38]. The unification of light and electrical phenomena led to his prediction of radio waves. Maxwell is regarded as the founder of the modern field of electrical engineering [39].

Nikola Tesla

In more practical developments, in 1887, Nikola Tesla (1856–1943) developed an induction motor that ran on alternating current, a power system that was rapidly expanding in Europe and the United States because of its advantages in long-distance, high-voltage transmission. The motor used polyphase current, which generated a rotating magnetic field that turned the motor, a principle that Tesla conceived of in 1882 [40–42]. His electric motor was a simple self-starting design that did not require a commutator, thus avoiding sparking and high maintenance [43, 44].

Hendrik Lorentz

Approaching the turn of the century, Hendrik Lorentz (1853–1928) derived the modern formula for electromagnetic force that included contributions from both electric and magnetic fields. Lorentz began by distinguishing between matter and the luminiferous aether and applying Maxwell’s equations at a microscopic scale. Using Oliver Heaviside’s version of Maxwell equations for a stationary ether and applying Lagrangian mechanics, he derived the now widely used Lorentz law for electromagnetic force [45].

In 1892, Lorentz further introduced a new time concept, i.e. local time, that depended on universal time and a person’s particular location to describe electromagnetic phenomena in reference frames that moved relative to the said luminiferous aether [46]. In 1900, Henri Poincaré called local time Lorentz’s “most ingenious idea” [47]. In 1892, attempting to explain the Michelson–Morley experiment (which disproved that light waves were carried on the luminiferous aether) [48], Lorentz proposed that moving bodies contract in the direction of motion [49]. In 1899, Lorentz added time dilation to his transformations and published what Poincaré in 1905 named Lorentz transformations [50]. Lorentz’s covariant formulation of electrodynamics, in which electrodynamic phenomena in different reference frames are described by identical equations with well-defined transformations, recognized that the outcomes of electrodynamic experiments do not depend on the relative motion of the reference frame. These ideas proved foundational to the work of Albert Einstein in his development of the theories of special and general relativity [51].

1.4.2 Classical Magnetism: Enter the Electron (1900–1925)

Pierre Curie and Pierre Weiss

Pierre Curie (1859–1906) was a pioneer in crystallography, magnetism, piezoelectricity, and radioactivity. Before his studies on magnetism, he designed and perfected sensitive torsion balances for measuring magnetic coefficients. With these tools, Curie studied ferromagnetism, paramagnetism, and diamagnetism and discovered the effect of temperature on paramagnetism which is known as Curie’s law. He also discovered that ferromagnetic materials exhibit a critical temperature transition, above which the materials lose ferromagnetic behavior. This is now known as the Curie temperature. In addition to ferromagnetic materials, the Curie temperature is used to study plate tectonics, treat hypothermia, and understand extraterrestrial magnetic fields, among other effects [52].

Pierre Weiss (1865–1940) developed the domain theory of ferromagnetism in 1907 [53]. Weiss also developed the Weiss domains, the Weiss mean field theory (MFT), and the Curie–Weiss law. Of these, MFT was perhaps his most significant contribution. The main idea of MFT is to replace all interactions relative to any one body with an average molecular field. This reduces any many-body problem to an effective one-body problem. The ease of solving MFT problems means that insight into the behavior of a complex system can be readily obtained with little effort. MFT has been widely applied to fields outside of physics, including statistics, graphical models, neuroscience [54], artificial intelligence, epidemic models [55], queueing theory [56], and computer-network performance and game theory [57]. Alongside Auguste Picard, Pierre Weiss is considered one of the discoverers of the magnetocaloric effect (1917) [58].

J. J. Thomson

Joseph John (J. J.) Thomson (1856–1940) published a number of influential papers addressing problematic issues of electromagnetism at the turn of the twentieth century. He examined the electromagnetic theory of light of James Clerk Maxwell, introduced the concept of electromagnetic mass of a charged particle, and demonstrated that a moving charged particle increases in mass [59]. In 1897, Thomson suggested that one of the fundamental units contributing to the structure of atoms was more than 1000 times smaller than the atom then thought to be a singular unit. Thomson discovered this through his careful experiments on the properties of cathode rays following his discovery that such rays travel much further through air than expected if the rays consisted of atom-sized particles [60, 61]. His experiments suggested that cathode rays were more than 1000 times lighter than the hydrogen atom and that their mass did not vary from their atomic source. He concluded the rays were composed of very light, negatively charged particles that later scientists would name the electron [62]. The charge of the electron was measured with precision by Robert A. Millikan’s oil drop experiment in 1909 [63].

1.4.3 Electron Spin

An essential property of an electron is its spin. Spin is an intrinsic form of angular momentum necessary to the origins of magnetism. Spin is one of two types of angular momentum in quantum mechanics, the other being orbital angular momentum. Where the spin angular moment refers to the intrinsic spin of the electron (spin ½), the orbital angular moment component derives from a classical analog of a charge orbiting about its nucleus akin to a charge traveling through a loop of wire, giving rise to an axial magnetic field through its center.

Wolfgang Pauli, George Uhlenbeck, and Samuel Goudsmit

Wolfgang Pauli (1900–1958) in 1924 proposed the doubling of available electron states by introducing two-valued “hidden rotation” [64]. In 1925, George Uhlenbeck and Samuel Goudsmit suggested the physical interpretation of a particle spinning on its own axis [65]. The mathematical theory was worked out by Pauli in 1927 [66].

1.4.4 Wave Mechanics

Louis de Broglie and Erwin Schrödinger

Louis Victor Pierre Raymond, 7th Duc de Broglie (1892–1987), commonly referred to as Louis de Broglie, was a French physicist and aristocrat who made groundbreaking contributions to quantum theory. In 1924, he postulated the wave nature of electrons and suggested that all matter possessed wave properties. This concept is known as the de Broglie hypothesis, an example of wave–particle duality, and forms a central tenet of the theory of quantum mechanics. de Broglie won the Nobel Prize for Physics in 1929, after the wave-like behavior of matter was experimentally verified [67].

The de Broglie hypothesis was later used by Erwin Schrödinger (1887–1961) in his formulation of wave mechanics. In 1926–1927, Schrödinger published a series of influential papers on wave mechanics and presented what is known as the Schrödinger equation and derived it for time-independent systems and showed that it gave correct energy eigenvalues for the hydrogen atom. He went on to show the equivalence of this approach with that of Heisenberg’s and extended his approach to time-variant systems, introducing complex solutions to wave equations in order to prevent higher order (i.e. fourth and sixth orders) differential equations and ultimately reducing them to first-order differential equations, making quantum mechanics accessible to common practitioners [68].

1.4.5 Quantum Theories of Magnetism

In 1927, Walter Heitler and Fritz London successfully applied Schrödinger’s theory to address bonding in dihydrogen (i.e. H2). This theory introduces the first principles of how two hydrogen atom wave functions join to form a covalent bond [69]. Linus Pauling built upon the HL theory and the work of Lewis (of ionic bonding theory) to establish resonance and orbital hybridization, two key foundations of valence bond theory (VBT) that led to his Nobel Prize in Chemistry in 1954. Today, modern VBT is complemented by molecular orbital theory (MOT) as pillars of quantum chemistry. The principal difference between these theories is that VBT treats electron pairs as localized to the parent atoms, whereas MOT treats electron pairs as molecular orbitals that may extend over the entire molecule. Importantly, MOT is more readily adaptable to predicting magnetic properties.

MOT was developed through the efforts of Friedrich Hund, Robert Mulliken, John C. Slater, and John Lennard-Jones [70]. The first quantitative use of MOT was the 1929 work of Lennard-Jones [71] who predicted a triplet ground state for the dioxygen molecule that explained its paramagnetism.

The success of MOT spawned ligand field theory, which was developed during the 1930s and 1940s as an alternative and enhancement to crystal field theory.

Werner Karl Heisenberg

Werner Karl Heisenberg (1901–1976) contributed significantly to quantum magnetism in calculating the exchange term, Jjk, which appears in the context of chemical bonding, spectroscopy, and MFT (see Curie–Weiss) to be of central import in explaining ferromagnetism. In order to calculate the effect, he used the many-electron wave function to be a Slater determinant so that it is antisymmetric, thus making sure all electrons obey Pauli’s principle. Heisenberg proceeded to calculate the magnetization of such systems such that Jjk > 0, with the triplet state having the lowest energy. This state, in which the two neighbor spins are aligned in the same direction, is energetically favorable and represents the case for all ferromagnetic materials such as Fe, Co, Ni, and some rare earth elements.

Modern theories of magnetism extensively use a Hamiltonian called the “Heisenberg exchange Hamiltonian” to investigate the magnetic properties of materials. The exchange term, J, was put to use by many notable physicists, most notably Néel who postulated that the exchange could take on negative values and thus give rise to antiferromagnetic (or ferrimagnetic) order in which nearest-neighbor spins antialign [72]. Other theories that employ common concepts include superexchange [73]. These phenomena have their origin in the Heisenberg exchange mechanism that have been validated by neutron scattering developed by contributions of Shull et al. [74].

Paul Adrien Maurice Dirac

The first step in the development of a new quantum theory was taken in 1925 when Paul Adrien Maurice Dirac (1902–1984) received a paper from Werner Heisenberg who revisited the old quantum theory of Bohr and Sommerfeld and changed the equations so that they were constrained by directly observable quantities, leading to a matrix formulation. Dirac’s attention was drawn to an enigmatic mathematical relationship of noncommuting dynamical variables.

In 1928, Dirac derived his relativistic equation of motion for the wave function of the electron [75]. This work led Dirac to predict the existence of antiparticles such as the positron, the electron’s antiparticle [76], which was later observed by Carl Anderson in 1932 [77]. Dirac’s equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon.

Dirac is regarded as the founder of quantum electrodynamics (QED), being the first to use that term. He also introduced the idea of vacuum polarization (1930) [78]. This work was key to the development of QED by the next generation of theorists, in particular Julian Schwinger [198], Richard Feynman [79], Shin’ichirō Tomonaga [80], and Freeman Dyson [81], in their formulation of modern QED.

In 1931, Dirac proposed that the existence of a single magnetic monopole in the universe would explain the quantization of electrical charge [82]. To date, no direct evidence supports their existence.

1.4.6 Density Functional Theory (1970s–Present)

Density functional theory (DFT) is a powerful computational quantum mechanical modeling method used in physics, chemistry, and materials science to investigate the electronic structure (or nuclear structure) principally of the ground state of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of many-electron systems can be determined by using functionals, i.e. functions of other functions. In the case of DFT, these are functionals of spatially dependent electron density.

DFT is among the most popular and versatile methods available in condensed-matter physics, computational physics, and computational chemistry.

Although DFT has been commonly applied to problems in solid-state physics as the 1970s, it was not considered sufficiently accurate for calculations in quantum chemistry until the 1990s, when approximations were greatly refined to better approximate exchange and correlation interactions.

Recent advances in DFT applied to magnetic oxide systems derive from basic observations in applying the Hubbard model. The Hubbard model, introduced in 1963 [83], is based on the tight-binding approximation in which electrons are viewed as occupying standard orbitals “hopping” between atoms during conduction. The competition between the hopping integral and the onsite repulsion accounts for the transition from conductor to insulator in many transition metal oxide systems, including many magnetic oxides such as the ferrites. As previously mentioned, the superexchange interaction (J) between cations mediated by an anion is often found to be negative. As J is negative, the ground state is the antialignment of near-neighbor cation spins [84], i.e. antiferromagnetic or ferrimagnetic states. This has been confirmed by neutron diffraction experiments [85].

Walter Kohn, Pierre Hohenberg, and Lu Jeu Sham

DFT was put on a firm theoretical footing by Walter Kohn and Pierre Hohenberg with the conception of the two Hohenberg–Kohn (HK) theorems [86]. The original HK theorems applied only to nondegenerate ground states in the absence of a magnetic field [87, 88]. The first HK theorem demonstrated that ground-state properties of many-electron systems are uniquely defined by electron densities that depend on spatial coordinates. This theorem identifies a path to reducing the many-body problem of N electrons through the use of functionals of the electron density. The second HK theorem defined an energy functional and proved the ground-state electron density for minimization of that functional. In a later work, the HK theorem was further developed to produce the Kohn–Sham DFT to address the intractable many-body problem of interacting electrons in a static potential [89]. The effective potential includes the external potential and the effects of Coulomb interactions between the electrons, e.g. the exchange and correlation interactions. Modeling the latter two interactions become the challenge of KS DFT.