Table Of ContentForeword
This volume in the Electromagnetism series presents a modern, in-depth,
comprehensive and self-contained treatment of the characterization and
measurement of magnetic materials. These materials are ubiquitous in
numerous industrial applications that range from electric power genera-
tion, conversion and distribution to magnetic data storage. Currently,
there does not exist any book that covers the physical properties of
magnetic materials, their characterization and modern measurement
techniques of various parameters of these materials in detail. This book
represents the first successful attempt to give a synthetic exposition of all
these issues within one volume.
The author, Dr Fausto Fiorillo, is a well-known expert in the field. He has
an extensive experience in the area of magnetic measurements as well as
intimate and firsthand knowledge of the latest technological innovations
and has thus managed to put together an extraordinary amount of
technical information in one volume. The salient and unique features
of the book are its scope and strong emphasis on the metrological aspects
of magnetic measurements. The book also reflects the broad expertise
and extensive knowledge accumulated over the years by the highly
visible and respected research group of the IEN Galileo Ferraris Materials
Department based in Turin, Italy.
I maintain that this book will be a valuable reference for both experts and
beginners in the field. Electrical engineers, material scientists, physicists,
experienced researchers and graduate students will find this book to be a
valuable source of new facts, novel measurement techniques and
penetrating insights.
Isaak Mayergoyz, Series Editor
vii
Preface
Magnets and measurements are everywhere. Magnetic materials are
key pieces of a complex puzzle and are fundamental in satisfying basic
demands of our society such as the generation, distribution, and
conversion of energy, the storage and retrieval of information, many
types of media and telecommunications. With their use in so many critical
applications, these materials play a crucial role in our daily life and the
present pace of research provides good reason for believing that their
importance will continue to increase. With an annual global market
valued at approximately EUR s the economic relevance of magnetic
materials in industry is clear. Just as magnetic materials are important so
accurate measurements are indispensable to science, industry, and
commerce and are the prerequisite for any conceivable development in
the production and trading of goods. They have relevant costs (about 5%
of GNP in industrial countries) and require highly specialized organiza-
tions (such as the National Metrological Institutes) to develop and
maintain the standards. Taken together these two elements are both
scientifically and economically significant. This is the only book that takes
that approach.
Magnetism has a popular reputation of being a difficult subject. Part
of this notion is as a result of the unfortunate duality of unit systems,
which has greatly complicated life for students, researchers, and
practitioners for many years. Nowadays, the SI system, recommended
by the Conf&ence Poids et Mesures under the MKSA label since 1946, is
establishing itself as the dominant system, despite resistance from many
workers in the field. The SI system is preferentially adopted in most
technical journals and recent books on the subject. There are plausible
reasons for preferring the CGS system, not least the avoidance of
redundant fields in free space, but diffusion of knowledge on magnetism
and magnetic materials will certainly benefit from generalized adoption
of the SI system.
The topic of magnetic measurements is traditionally treated in
textbooks as a branch of electrical measurement and the peculiar role of
the materials and their physical properties are seldom emphasized.
xiii
xiv Preface
Textbooks on magnetic materials typically devote a chapter to experi-
mental methods, but they obviously follow a concise approach to this
matter, which is seen as a corollary to the treatment of physical topics.
No modern treatise devoted to magnetic measurements and character-
ization of magnetic materials is therefore available nowadays. The
standard text in the field is the two-volume book by H. Zijlstra
latnemirepxE Methods ni Magnetism (North-Holland), which was published
in 1967. Since the publication of that work there have been many changes
such as the discovery of novel compositions and properties and the
improved phenomenological understanding of the behavior of the
materials. In addition, the digital revolution has brought about wide-
spread changes in the way that measurements are taken both in research
laboratories and in industry. Never has there been a greater need for a
book that summarizes the principles and the present state of the art in the
field of magnetic measurements. This book fills that need whilst bearing
in mind materials scientists, the practical impact on everyday test activity,
quality control in the laboratory and the education of scientists engaged in
the basic characterization of materials.
This is a consistent book drawn from the author's own long
experience in the lab. It looks at measuring problems from a practical
viewpoint and, by placing the treated topics within a clear physical
framework it will be useful both to those approaching the subject for
the first time as well as to experienced researchers. It is intended for
technicians in the lab and materials scientists in industry, university, and
research centers. It aims at answering the basic questions and dilemmas
people engaged in this field are faced with, enabling the reader to find
straightforward answers without tiresome recourse to scattered literature.
The various aspects of standardization of measurements are illustrated
and constantly referred to. This goes hand in hand with a discussion on
the metrological issues, which include intercomparison, traceability, and
measuring uncertainty problems.
The book is organized in three parts and 10 chapters. Part I is
made of three introductive chapters. Chapter 1 illustrates the general
physical concepts and introduces the quantities constantly referred to
along the treatise. Chapter 2 consists in a synthetic presentation of
soft magnetic materials and includes a description of the preparation
methods and a discussion on their physical properties. Chapter 3 is
focused on the operation of permanent magnets, the related energetic
aspects, and the classical electrical analogy of the magnetic circuits.
No attempt is made to delve into the specific physical properties of
permanent magnets. Contrary to the case of soft magnets, where scant
recent review literature exists, the reader can easily retrieve information
ecaferP vx
on the physics of permanent magnets in a good number of comprehen-
sive up-to-date books.
Part II is devoted to the discussion on generation and measurement
of magnetic fields, a necessary step in any characterization process, but
one which also has value in different contexts, including environmental
studies and medical applications. Generation techniques are presented
in Chapter .4 Distinction is made there between coil-based sources
(DC, AC, and pulsed fields) and generation by means of permanent
magnets and electromagnets. It is stressed how the field generating
capabilities of permanent magnet based sources can be strongly
enhanced with the use of extra-hard rare-earth based compositions.
Chapter 5 provides a comprehensive review of the physical principles
exploited in the measurement of magnetic fields and of the solutions
adopted in actual measuring devices. It is stressed that the basic problem
of precise absolute measurement and traceability to the base IS units
can be solved by use of quantum resonance magnetometers, where
the determination of the field strength is reduced to a frequency
measurement.
The characterization of magnetic materials is discussed in Part III.
After a preliminary introduction on general measuring problems and
methodologies (Chapter 6), theory and practice in the measurement of
the properties of soft and hard magnets are treated. Reference is made,
whenever appropriate, to written measuring standards (e.g. IEC, ASTM,
SIJ standards). The discussion on the characterization of soft magnets
is carried out by separately discussing the measurements under DC,
low-frequency, medium-to-high frequency and radio frequency excitation
(Chapter .)7 In hard magnetic materials, distinction is made instead
between closed magnetic circuit testing, where electromagnets are used at
the same time as field sources and soft return paths for the magnetic flux,
and open sample testing (Chapter .)8 The latter methods often combine
versatility with measuring sensitivity and are nowadays increasingly
applied in the characterization of permanent magnets, besides being
the natural choice for thin films and weak magnets. After a discussion in
Chapter 9 regarding the measurement of intrinsic material parameters
(Curie temperature, saturation magnetization, and magnetic anisotropy),
Chapter 01 examines the very often neglected topic of measuring
uncertainty and its crucial relationship with the metrological issues
raised by intercomparisons and traceability to the relevant base and
derived SI units. Specific examples regarding magnetic measurements are
provided.
The IS system of units has been adopted throughout the whole text.
When data and graph scales expressed in CGS had to be taken from
xvi ecaferP
the literature, the appropriate conversion to IS was made. Because of
its persisting use, the measure of the magnetic moment has been provided
also in e.m.u., in association with the corresponding SI unit (A m2).
Conversion rules for translating SI equations in Gaussian equations
and vice versa and a comprehensive conversion table are given in
Appendix A.
Whilst comprehensive this book is not meant to be exhaustive. A
major part of it is devoted to methods for the determination of material
properties having relevant interest for applications, i.e., the parameters
associated with magnetic hysteresis. In this respect, the measuring
written standards are constantly referred to guidelines. Magneto-optical,
magnetostrictive, and superconductive effects are among the topics not
discussed here. If the reader wishes to explore these further they can be
found in many recent textbooks. For example, magnetostriction measure-
ments are described to full extent in the E. du Tr6molet de Lacheisserie
book noitcirtsotengaM (CRC Press, 1993). Magneto-optical methods and
phenomena are exhaustively discussed in the outstanding work, citengaM
sniamoD by A. Hubert and .R Sch/ifer (Springer, 1998).
stnemgdelwonkcA
In preparing this book, I received contributions, suggestions, encourage-
ment, and help from many friends and colleagues. I am indebted to all of
them. I am especially grateful to Giorgio Bertotti, who assisted me in
many ways, willingly engaging in many clarifying discussions, and
allowing me to benefit from his deep knowledge of electromagnetism and
magnetic phenomena. The series editor, Isaak Mayergoyz, fully sup-
ported my effort, fostering my confidence in the project and generously
handling my outrageously delayed delivery of the manuscript.
I would like to acknowledge that this project could only be pursued
thanks to the special cooperating milieu, the broad expertise on the
physics of magnetic materials, and the array of experimental researches
developed by fellow scientists at the Materials Department of IEN.
I found advice and support in all of them. I am also indebted to elder
scientists in my lab who educated me in the early years of my careen The
late Andrea Ferro Milone introduced me to materials science and Piero
Mazzetti taught me the basic virtues of the experimental physicist. Aldo
Stantero helped me in many ways and on innumerable occasions for more
than twenty years. His untimely death was an untold loss to me and to the
lab at IEN. Giorgio Bertotti, Vittorio Basso, Carlo Appino, and Alessandro
Magni read substantial parts of the manuscript and Oriano Bottauscio
provided me with crucial help by expressly performing numerous
electromagnetic field computations. The field maps presented in Chapters
4 and 8 are due to him. Vittorio Basso, Cinzia Beatrice, Enzo Ferrara, and
Eros Patroi kindly supplied me with their own experimental data and
Marco Co'isson clarified to me specific aspects of magnetoimpedance
measurements. Anna Maria Rietto carried out careful experiments to
elucidate a few important details in the magnetic lamination testing with
the Epstein test frame and Luciano Rocchino assisted me in assessing the
problems related to reference field sources and their traceability to the
base units. Sigfrido Leschiutta enhanced my sensitivity to metrological
issues and the role of metrology in the physical sciences. I also need to
thank all the many colleagues in Europe and elsewhere with whom I
shared cooperative research activity and discussions on various scientific
iiv-x
xviii Acknowledgments
matters. It is finally a pleasure to acknowledge the help provided by
Christopher Greenwell and Sharon Brown at Elsevier, who assisted me in
the various stages of the book production, and Lucia Bailo, Francesca Fia,
and Emanuela Secinaro at the Publication Department of IEN, for their
help in literature retrieval.
CHAPTER 1
Basic Phenomenology in
Magnetic Materials
1.1 MAGNETIZED MEDIA
In September 1820 H. C. Oersted demonstrated that electrical currents
and magnets displayed equivalent effects. In a matter of weeks, A. M.
Amp6re, elaborating on Oersted's discovery and making his own
experiments, boldly interpreted the magnetism of materials as electricity
in motion, i.e. the result of hidden microscopic currents, circulating
around "electrodynamic molecules". The pedestal of electromagnetism
was built in those few weeks, to be crowned in less than 50 years by the
towering achievement of Maxwell's equations. Nowadays, we know that
these currents exist, but they are quantum-mechanical in nature. They
naturally slip into the classical Maxwellian scenario through the concept
of permanent magnetic moment and the useful intermixing of classical
and quantum concepts in the description of their relationship with
the electronic angular momenta. A material sample is fundamentally
described, from the viewpoint of magnetic properties, as a collection of
magnetic moments, resulting from the motion of the electrons. Classically,
orbiting electrons generate microscopic currents and are endowed with a
magnetic moment m = -(e/2me).L, if e and m e are charge and mass of the
electron, and L is the angular moment. Quantum mechanics makes the
view of electronic magnetic moment physically consistent, besides
providing the additional basic concept of magnetic moment associated
with spin angular momentum.
When writing the classical equations of electromagnetism and
assigning a meaning to the value of the physical quantities involved,
we look at the material as a continuum. This means that all atomic
scale intricacies are lost. In particular, the internal currents of quantum-
mechanical origin are retained as averages over elementary volumes A ,V
sufficiently small to be defined as local over the typical scale of the
problem, but large enough with respect to the atomic scale. These currents
CHAPTER 1 Basic Phenomenology in Magnetic Materials
(Amperian currents), resulting from electron trajectories at the atomic
scale, do not convey any flow of charge across the body. Let us call jM(r)
the associated current density. Because of its solenoidal character, jM(r) can
be expressed as the curl of another vector function M(r)
jM(r) = V X M(r). (1.1)
Remarkably, it can be demonstrated that the vector function M(r)
represents the magnetic moment per unit sample volume 1.1.
This quantity takes the name "magnetization". If the previous elementary
volume contains a certain number of moment carriers, it is M(r)=
~V~/imi~
where the summation runs over the moments contained in such
a volume. Thanks to Eq. (1.1), we are in a position to describe the magnetic
effects ensuing from steady external currents when media are involved. If
such currents are made to circulate in the absence of media, the induction
vector B (often called "B-field") is given by the Biot-Savart law, which is
expressed in differential form as
V x B =/~0je, (1.2)
where ej is the density of the supplied currents and ~ = 4Ir x 01 -7 N/A 2 is
the magnetic constant (sometimes called permeability of vacuum).
Analysis of the Biot-Savart law additionally shows that the B vector is
solenoidal, i.e. it obeys the equation B.V = .0 It can be shown that this
equation and Eq. (1.2) determine B uniquely for given .ej We recall here that
the operative definition of the vector B is provided by Lorentz's law, which
describes the coupling of electrical and magnetic fields with electrical
charges. It states that a charge q moving at velocity t is subjected to a force
F = E(q + t x .)B (1.3)
In the presence of magnetic media, both the externally supplied currents
and the internal microscopic averaged currents will contribute to the
B-field. The two base equations will be
B.V -- 0, V x B --/~0(je + jM). (1.4)
When dealing with experiments on magnetic materials and their applica-
tions, we endeavor to drive the magnetic state of the material by means
of external currents, i.e. acting on the quantity -ej We can single out ej in
Eq. (1.4), introducing through Eq. (1.1) the magnetization M, a quantity
directly accessible to experiments, in place of the awkward internal
currents .Mj In this way we define the so-called H-field
Vx ~- -M =VXH--je. (1.5)
1.1 MAGNETIZED MEDIA 5
H is the quantity conventionally defined as the magnetic field as it is the
quantity susceptible to direct control by means of the external currents.
On the other hand, B appears to be the ffmdamental field vector because
it is characterized by the condition B.V = 0 everywhere, in the free space
and inside the matter, and Lorentz's equation everywhere applies to it.
According to Eq. (1.5), the general relationship connecting the vectors B,
H, and M is
B = p, oH +/zoM. (1.6)
In the SI unit system the magnetization M is expressed, like the magnetic
field, in A/m, putting in evidence the Amperian origin of the
magnetic moment. In the absence of media, M = 0 and B =/~H, i.e.
magnetic field and induction (i.e. H-field and B-field) are equivalent
quantities, as they are related by the proportionality constant/z0.
In many kinds of experiments, we exploit the Faraday-Maxwell law
V x E = -OB/Ot, where E is the electric field, in order to determine.the
magnetic behavior of the material. We detect in this case the electromotive
force generated in a linked search coil by the time variation of the
induction. Normally, we wish to get rid of the term /z0H in Eq. (1.6),
because we are only interested in the contribution/z0M deriving from the
material. This contribution is called magnetic polarization, J =/z0M, a
quantity having the same dimensions as B (tesla, T) and the same
properties as M. We then write B =/z0H + J. This general relationship will
be specialized to the magnetic properties of the investigated medium by
means of some constitutive equation J(H) or B(H). In ferromagnetic
materials, these relationships can be very complex and very difficult to
predict. In some well-defined instances, it is meaningful to define the
relationships B =/zH =/Zr/z0H and M -- xH, where/z is the permeability,
is the relative permeability, and X is the susceptibility. The quantifies/zr
/d, r
and X are related by the equation
1 + .X (1.7)
~r m
Note that, in the old Gaussian system, the base Eq. (1.6) is written as
B = H + 4rrM, (1.8)
i.e. field, induction, and magnetization have all the same dimensions
(though different names, oersted (Oe) for H and gauss (G) for 4rrM and
B). In this book, the SI system will be used throughout and little
reference will be made to the increasingly obsolete Gaussian units. A
complete set of conversion formulae is nevertheless provided, together
with a discussion on their logical foundation, in Appendix A.
