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538 Part C Materials Properties Measurement

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Part C 9

540 Part C Materials Properties Measurement

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Part C 9

541

Magnetic Pro

10. Magnetic Properties

Magnetic materials are one of the most promi-

nent classes of functional materials, as introduced

in Sect. 1.3. They are mostly inorganic, metallic or

ceramic in nature and typically multicomponent

when used in applications (e.g. alloys or inter-

metallic phases). Their structure can be amorphous

or crystalline with grain sizes ranging from a few

nanometers (as in high-end nanocrystalline soft

magnetic materials) to centimeters (as in grain-

oriented transformer steels). They are available as

powders, cast, sintered or composite materials,

ribbons or even thin ﬁlms and ﬁnd a huge variety

of applications in transformers, motors, genera-

tors, medical system sensors, and microelectronic

devices.

The aim of this chapter is to give advice as to

which methods are most applicable to determine

the characteristic magnetic properties of any of the

materials mentioned above. Magnetic thin-ﬁlm

structures have recently gained signiﬁcant scien-

tiﬁc and economic importance. Not only can their

properties deviate from the respective bulk mater-

ials but novel phenomena can also occur, such as

giant and tunnel magneto-resistance, which lead

to their application in read heads and their likely

future application to nonvolatile magnetic solid-

state memory (MRAM). Therefore, we have added

a section that explains the important peculiarities

special to thin ﬁlms, in which we summarize the

most relevant measurement techniques.

Section 10.1 will give a short overview to enable

the reader to differentiate between the various

manifestations of magnetism, different mater-

ials and their related properties. For a deeper

understanding, of course, textbooks should be

used (see the references given in Sect. 10.2).

Section 10.2 covers the standard measurement

techniques for soft and hard magnetic mater-

ials. The tables at the beginning of Sect. 10.2.1

are a valuable guide to choose the best tech-

nique for any given property to be measured.

It is anticipated that this chapter will cover the

overwhelming needs for a routine characterization

of soft and hard magnetic materials in their various

forms. Section 10.3 introduces an elegant, novel

and extremely fast technique, the so-called pulse

ﬁeld magnetometer, to measure the hysteresis

loop of hard magnetic materials and thereby

to determine the remanent magnetization, the

anisotropy ﬁeld and coercivity, respectively. This

method has been developed only recently and is

not yet comprehensively covered in textbooks. It

is therefore described in more detail with a critical

discussion of possible measurement errors and

calibration requirements. Finally, as mentioned

above, Sect. 10.4 addresses features peculiar to

magnetic thin ﬁlms and recommends techniques

for their magnetic characterization. It comprises

an overview of magneto-resistive effects occurring

in magnetic thin ﬁlms or multilayers where the

electrical resistivity depends on external magnetic

ﬁelds. These devices ﬁnd important applications

as read heads in hard-disc drives and as sensors

in the automotive and automation industries.

The standard measurement to determine the ﬁeld

response (change in resistance within a given

ﬁeld range) is simply a resistivity measurement,

as described in Chap. 9, except that it needs to

be done in an external magnetic ﬁeld. These

electrical techniques are therefore not covered in

this chapter.

In bulk and thin-ﬁlm ferromagnets properties

such as remanent magnetization and coercivity

often depend on the time scale used in the mea-

surement (Sects. 10.1.6, 10.3.3). Time-dependent

measurements needed, e.g., to predict the stabil-

ity of the material in applications are not explicitly

described in this chapter since, in principle, any

sensitive magnetometer can be used for these

measurements. In research, sophisticated meth-

ods are used to resolve magnetization dynamics on

pico- or even femtosecond time scales. A detailed

description of these more specialized methods is

beyond the scope of this handbook.

Part C 10

542 Part C Materials Properties Measurement

10.1 Magnetic Materials ............................... 542

10.1.1 Diamagnetism, Paramagnetism,

and Ferromagnetism .................... 542

10.1.2 Antiferromagnetism,

Ferrimagnetism

and Noncollinear Magnetism ......... 543

10.1.3 Intrinsic and Extrinsic Properties.... 544

10.1.4 Bulk Soft and Hard Materials ......... 544

10.1.5 Magnetic Thin Films...................... 544

10.1.6 Time-Dependent Changes

in Magnetic Properties .................. 545

10.1.7 Deﬁnition of Magnetic Properties

and Respective Measurement

Methods ..................................... 545

10.2 Soft and Hard Magnetic Materials:

(Standard) Measurement Techniques

for Properties Related to the B(H) Loop .. 546

10.2.1 Introduction ................................ 546

10.2.2 Properties

of Hard Magnetic Materials............ 549

10.2.3 Properties

of Soft Magnetic Materials ............. 555

10.3 Magnetic Characterization

in a Pulsed Field Magnetometer (PFM).... 567

10.3.1 Industrial Pulsed Field

Magnetometer ............................. 568

10.3.2 Errors in a PFM............................. 569

10.3.3 Calibration [10.1] .......................... 573

10.3.4 Hysteresis Measurements

on Hard Magnetic Materials........... 575

10.3.5 Anisotropy Measurement .............. 576

10.3.6 Summary:

Advantages and Disadvantages

of PFM ........................................ 579

10.4 Properties of Magnetic Thin Films .......... 579

10.4.1 Saturation Magnetization,

Spontaneous Magnetization .......... 579

10.4.2 Magneto-Resistive Effects ............. 583

References .................................................. 585

10.1 Magnetic Materials

Empirically, materials are classiﬁed according to their

response to an applied magnetic ﬁeld, i. e. the mag-

netization induced by the external ﬁeld. A more

fundamental understanding results from considering the

microscopic mechanisms that determine the behavior of

materials in the magnetic ﬁeld.

10.1.1 Diamagnetism, Paramagnetism,

and Ferromagnetism

Diamagnetism is a property of all materials. It results

from an additional orbital angular momentum of elec-

trons induced in a magnetic ﬁeld. In analogy to the

induction of eddy currents in a conductor it manifests it-

self as a magnetization oriented in the opposite direction

to the external ﬁeld; by deﬁnition this is equivalent to

a negative susceptibility (deﬁnitions are given below).

Paramagnetism means a positive magnetic suscep-

tibility, i. e. the induced magnetization is along the

direction of the external magnetic ﬁeld. It is observed

in materials which contain atoms with nonzero angu-

lar momentum, e.g. transition metals. The susceptibility

scales with 1/T (Curie’s law). Paramagnetism is also

found in certain metals (e.g. aluminum) as a con-

sequence of the spin of conduction electrons (Pauli

spin susceptibility). The related susceptibility is essen-

tially independent of temperature. The paramagnetic

susceptibility is generally several orders of magni-

tude larger than the diamagnetic component; therefore,

diamagnetism is not observable in the presence of

paramagnetism.

Ferromagnetism describes the fact that certain solid

materials exhibit a spontaneous magnetization, M

even in the absence of an external magnetic ﬁeld. It

is a collective phenomenon resulting from the sponta-

neous ordering of the atomic magnetic moments due

to the exchange interaction among the electron spins.

It is observed in a few transition metals (e.g. 3d, 4f)

where itinerant electrons play the essential role for the

exchange coupling mechanism, but also in their oxides,

halides etc., where the exchange interaction is medi-

ated by localized electrons of oxygen, sulfur etc. atoms

located between neighboring metal atoms (indirect ex-

change, superexchange). Recently ferromagnetism has

been observed in semiconductors (e.g. GaAs, TiO

)

doped with a few percent of a transition element

like Mn, Fe or Co which provides localized magnetic

moments and free charge carriers which mediate the

exchange interaction among the localized moments. If

ferromagnetic order in these materials can be main-

tained above room temperature (which is currently not

certain) they might become useful for future electronic

devices based on the spin of electrons besides their

charge (spintronics).

Part C 10.1

Magnetic Properties 10.1 Magnetic Materials 543

Many ferromagnetic objects do not show a net mag-

netization without an external magnetic ﬁeld. This is

a consequence of magnetic domains, which are formed

to reduce the energy connected with the dipolar ﬁelds

(the stray ﬁeld and demagnetizing ﬁeld). When an exter-

nal magnetic ﬁeld is applied domains gradually vanish

due to the motion of domain walls and rotation of the

magnetization inside the domains. These processes are

partly reversible and irreversible. In sufﬁciently high

ﬁelds technical saturation is achieved. The correspond-

ing saturation magnetization, however, must not be

mistaken for the spontaneous magnetization. The rea-

son is that, at any temperature T > 0, an external ﬁeld

will increase the magnetization above the spontaneous

value inside the domains (i. e. M

at H = 0) by sup-

pression of spin waves (the para-process). Hence, the

experimental determination of the spontaneous magne-

tization in general requires a speciﬁc extrapolation of

high-ﬁeld data to zero ﬁeld.

Spin-wave excitations are the reason for the de-

crease of the spontaneous magnetization with increas-

ing temperature, which in general follows Bloch’s law,

i. e. the decrease of the spontaneous magnetization from

its ground-state value at T =0 is proportional to T

3/2

The phase transition from long-range ferromagnetic

order to the paramagnetic state at a critical tempera-

ture (the Curie temperature, T

) is governed by power

laws for the spontaneous magnetization close to T

= A(1 −T/T

)

, for the magnetic susceptibility,

χ =χ

(1 −T/T

)

−γ

and for other quantities. The crit-

ical exponents (β and γ ) are of universal character and

depend only on the dimensionality of the sample in real

space (e.g. 3-D for a bulk material, or 2-D for ultrathin

ﬁlms) and in spin space (e.g. 3-D if all orientations of

the magnetization are allowed, 2-D if the magnetization

vector is conﬁned to a plane, and 1-D in the case of

extremely strong uniaxial anisotropy).

In general, the magnetization of a ferromagnetic ob-

ject is preferentially oriented along certain axes that

correspond to an energy minimum, which are known as

easy axes of magnetization. The directions of the re-

spective energy maxima are called hard axes or hard

directions. This property, magnetic anisotropy,isthe

key to many technical applications of ferromagnetic

materials; e.g. a binary memory element requires a uni-

axial anisotropy characterized by two stable states. The

strength of the anisotropy is expressed by anisotropy

constants K

; it can be measured by the external ﬁeld

required to rotate the magnetization from an easy direc-

tion to a hard one. Materials with small/large anisotropy

constants are called magnetically soft/hard.

Two interactions are responsible for magnetic

anisotropies: dipolar interactions between atomic mo-

ments are directly connected with the shape of a given

ferromagnetic body (shape anisotropy), while spin–

orbit interaction is the origin of all other anisotropies:

magneto-crystalline, magneto-elastic, surface/interface

anisotropies, which are intimately related to the local

symmetry of the atomic conﬁguration.

10.1.2 Antiferromagnetism, Ferrimagnetism

and Noncollinear Magnetism

In certain materials atomic moments are strictly ordered

without showing any resulting magnetization. This hap-

pens if neighboring magnetic moments are antiparallel

to each other due to a negative exchange interaction

between the spins; this phenomenon is called antifer-

romagnetism and is mainly found in transition-metal

oxides, halides etc. (MnO, CoO, NiO, α-Fe

etc.),

but also in metal alloys such as FeMn or IrMn. Anti-

ferromagnetism vanishes above a critical temperature

called the Néel temperature. Due to their zero net mag-

netic moment, antiferromagnets are hardly affected by

external magnetic ﬁelds. This has recently led to tech-

nical applications in so-called spin-valves where the

antiferromagnet pins the magnetization of an adjacent

ferromagnetic layer in a magneto-resistive sensor.

A special form of antiferromagnetism is observed in

metallic chromium: the local magnetization varies sinu-

soidally along certain lattice directions. This is called

a spin-density wave and is not always commensurate

with the crystal lattice.

Ferrimagnetism is a more general version of antifer-

romagnetism: neighboring moments are antiparallel but

of different sizes, resulting in a ﬁnite net magnetization.

It is found in compounds of 3d transition metals and

rare-earth elements (e.g. ferrites, garnets, amorphous

3d–4f alloys and multilayers).

Other forms of magnetic order are found mainly

in rare-earth compounds: magnetic moments can form

helical structures (helimagnetism) and even more com-

plex structures giving rise to noncollinear magnetism

meaning that magnetic moments are not aligned along

a deﬁned axis. Such a magnetic order can result from

different or competing exchange interactions and very

strong magnetic anisotropies.

Competing ferromagnetic and antiferromagnetic

coupling between neighboring moments in a crystalline

lattice or purely antiferromagnetic interactions on a tri-

angular lattice can lead to frustration; this means that

the individual spins cannot follow the exchange cou-

Part C 10.1

544 Part C Materials Properties Measurement

pling to all neighbors simultaneously. The consequence

is a spin conﬁguration similar to a frozen paramag-

net called a spin-glass state. It manifests itself by

thermal hysteresis below the freezing temperature and

pronounced relaxation effects, indicating the presence

of highly degenerate states. Typical materials showing

such behavior are dilute alloys of 3d metals (Mn, Fe,

Co) in a nonmagnetic matrix (Au, Cu).

10.1.3 Intrinsic and Extrinsic Properties

Intrinsic magnetic properties are those characteristic

of a given material (e.g. spontaneous magnetization,

magneto-crystalline anisotropy constant etc.), while ex-

trinsic properties are strongly affected by the speciﬁc

shape and size of the magnetic object as well as by

their microstructure. The most important example is the

magnetic shape anisotropy caused by the dipolar energy

via the demagnetizing ﬁeld: for a three-dimensional fer-

romagnetic object characteristic quantities such as the

remanent magnetization and saturation ﬁeld are mainly

determined by the shape and much less by the intrinsic

magnetic anisotropy.

Another extrinsic effect is the role of mechanical

strain in a specimen; this may be introduced during the

production process. Stress and strain may signiﬁcantly

alter the shape of the magnetization loop via magne-

tostrictive effects.

10.1.4 Bulk Soft and Hard Materials

The magnetic softness or magnetic hardness of a mater-

ial is a key factor for many applications. For instance,

magnetically soft materials are needed for transformers,

motors and sensors, i. e. where the magnetization should

fully align with even very small external magnetic

ﬁelds. This requires very low coercivity and the high-

est possible susceptibility (or permeability), which is

equivalent to weak anisotropy and large magnetization.

Also, very low magnetostriction is needed to prevent

mechanical strain from building up magneto-elastic

anisotropies. As an example, in some speciﬁc binary

or ternary alloys of 3d metals the magneto-crystalline

anisotropy can be very close to zero, making them

magnetically very soft. In particular, Ni

(permal-

loy) has nearly zero magneto-crystalline anisotropy and

very weak magnetostriction. A large number of spe-

cial alloys of Fe, Co and Ni with the addition of

Cr, Mn, Mo, Si and other elements have been de-

veloped that allow for a compromise between high

permeability (e.g. 78 permalloy = Fe

21.2

78.5

0.3

supermalloy = Fe

15.7

0.3

,mu-metal=

) and high magnetization (e.g. permen-

dur = Fe

49.7

0.3

). For all these alloys proper

heat treatment is essential for optimum soft magnetic

properties.

For high-frequency applications soft magnetic fer-

rites still play an important role.

Magnetically hard materials, in turn, are needed

for permanent magnets, magnetic information-storage

media (memories) and other applications. They should

posses strong anisotropies and large coercivity so their

magnetic state cannot be easily altered by external mag-

netic ﬁelds. Besides high coercivity and large remanent

magnetization their maximum energy product (BH)

max

is a key quantity. While alloys of 3d metals with alu-

minum dominated the marked until 1975 (e.g. Alnico V

= Al

) they have gradually been re-

placed by materials based on intermetallic rare-earth

cobalt compounds (e.g. SmCo

,Sm

(Co, Fe)

)and

more recently by Nd

, which does not contain

relatively expensive cobalt. The magnetic properties of

these materials critically depend on the metallurgical

production process, which affects the granular structure

needed for high coercivity and large energy product; the

latter has increased by more than an order of magnitude

since the development of rare-earth-containing perma-

nent magnets. For less-demanding applications ferrite

magnets are still in use.

For magnetic recording media (mainly hard-disk

drives) somewhat different requirements have to be met.

Here alloys of the type CoCrPt in the form of thin ﬁlms

are mainly used today.

10.1.5 Magnetic Thin Films

For several reasons ferromagnetic thin ﬁlms constitute

a special class of magnetic materials.

1. The reduced dimensionality of a thin ﬁlm makes the

axis perpendicular to the ﬁlm plane a natural sym-

metry axis, which gives rise to speciﬁc magnetic

anisotropies, e.g. the so-called shape anisotropy

with an easy plane and a perpendicular hard axis.

2. The reduced dimensionality also causes modiﬁca-

tions of fundamental magnetic properties such as

the saturation magnetization, its temperature depen-

dence, the Curie temperature and others. These size

effects become more pronounced with decreasing

ﬁlm thickness.

3. Magnetic properties at surfaces and interfaces are

generally different from the corresponding bulk

Part C 10.1

Magnetic Properties 10.1 Magnetic Materials 545

properties. These surface effects become more inﬂu-

ential with decreasing ﬁlm thickness and may even

become dominant for ultrathin ﬁlms,i.e.ﬁlmsof

only a few atomic layers. Indeed, new materials with

a combination of properties that does not occur in

nature can be created in this way, e.g. multilayers or

superlattices of a ferromagnetic and a nonmagnetic

component.

4. Certain magneto-transport phenomena such as

the giant magneto-resistance (GMR)ortunnel

magneto-resistance (TMR) effects can best be ob-

served and exploited in very thin ﬁlms. As these

effects ﬁnd more practical applications (e.g. in hard-

disk read heads) thin and ultrathin magnetic ﬁlms

receive increasing attention.

The growing interest in magnetic ﬁlms and their

technical application naturally increases the demand for

methods and instruments to characterize their magnetic

properties as completely as possible. Established instru-

ments suitable for the study of bulk magnetic materials

are of limited value because of the high sensitivity

required for measurements of the small material quan-

tities typical for thin ﬁlms. Suitable methods will be

described in Sect. 10.4.

10.1.6 Time-Dependent Changes

in Magnetic Properties

Ferromagnetic materials frequently show a continuous

change of their macroscopic magnetization in the course

of time even in a constant or zero applied magnetic

ﬁeld. This is usually termed the magnetic aftereffect

or magnetic viscosity and may occur on a time scale

of seconds, minutes or even thousands of years. The

underlying physical reason is that a ferromagnetic ob-

ject with a net magnetic moment in the absence of

an external magnetic ﬁeld is generally in a thermo-

dynamically metastable state. This is indicated by the

presence of hysteresis. The equilibrium state will be

asymptotically approached by domain nucleation and

wall motion. Domain-wall motion is a relatively slow

process due to the effective mass or inertia that can be

attributed to a magnetic wall; since it is thermally acti-

vated it also depends strongly on temperature. For the

same reason the coercivity of a sample depends on the

measurement time if magnetization reversal occurs via

domain walls. This needs to be taken into account when

comparing data obtained by quasistatic measurements

with those extracted from high-speed measurements

(Sect. 10.3.3).

In the absence of domains walls and for a uni-

formly magnetized sample the magnetization responds

to the torque exerted by an external magnetic ﬁeld by

a precession of the magnetization vector around the

effective ﬁeld, which is well described by the Landau–

Lifschitz–Gilbert equation. As a consequence, in these

cases the maximum rate of change of the magnetization

is limited by the precession frequency of the magne-

tization vector, which for common materials like Fe,

Co, Ni and their alloys is between 1 GHz and 20 GHz

in moderate applied magnetic ﬁelds. It is evident that

magnetization dynamics on a timescale of nanoseconds

and below is relevant for magnetic devices in high-

frequency applications.

10.1.7 Deﬁnition of Magnetic Properties

and Respective Measurement

Methods

The most important magnetic quantities are deﬁned in

the following in conjunction with their primary mea-

surement methods.

The magnetic ﬁeld H,orﬂux density B,(which

are equivalent in free space) are measured with Hall

probes, inductive probes (e.g. ﬂux-gate magnetome-

ters for very low ﬁelds) or nuclear magnetic resonance

(NMR) probes for very high accuracy.

Magnetic moments are measured by different types

of magnetometers.

•

Via the force exerted by a magnetic ﬁeld gradient

(e.g. Faraday balance, or alternating gradient mag-

netometer (AGM))

•

Via the voltage induced in a pickup coil by the mo-

tion of the sample, e.g. the vibrating-sample magne-

tometer (VSM,Fig.10.7) is a widely used standard

instrument, or a superconducting quantum interfe-

rence device (SQUID, Figs. 10.48, 10.49) magneto-

meter for highest sensitivity

Quantity Symbol Unit

Magnetic ﬁeld H [A/m]

Magnetic ﬂux density, B [T]

magnetic induction

Magnetic ﬂux Φ [Wb]

Magnetic moment m [Am

]

Magnetization (=m/V ) M [A/m]

Magnetic polarization (=μ

M) J [T]

Susceptibility (= M/H) χ [−]

Part C 10.1

546 Part C Materials Properties Measurement

The (average) magnetization of a magnetic object is

usually determined by dividing the magnetic moment

by the volume of the sample. Care must also be

taken concerning the vector component of the mag-

netic moment that is detected. This is crucial in the

case of samples with a signiﬁcant magnetic anisotropy

which can even result from the shape of the specimen

(Sect. 10.1.1).

All these instruments need careful calibration. This

is important because the effective calibration factors de-

pend more or less on the size and shape of the specimen.

Magnetic moments related to different chemical el-

ements in a specimen can be measured selectively by

means of magnetic x-ray circular dichroism (MXCD)or

XMCD based on the absorption of circularly polarized

x-rays from a suitable synchrotron radiation source. In

principle, this method allows the separation of orbital

and spin magnetic moments.

If only the relative value of the magnetization is

of interest and not its absolute value, then a number

of different methods can be used to measure, for in-

stance, M as a function of temperature or of the applied

magnetic ﬁeld. Such methods include magneto-optic

effects (e.g. the magneto-optic Kerr effect (MOKE))

or the magnetic hyperﬁne ﬁeld measured by using the

Mößbauer effect, perturbed angular correlations (PAC)

of gamma emission, or nuclear magnetic resonance

(NMR). While MOKE is frequently used for character-

izing magnetic materials, nuclear methods due to their

relative complexity are restricted to special applications

where standard techniques do not provide adequate

information. NMR is widely exploited in magnetic res-

onance imaging (MRI) as a diagnostic tool in medicine.

The methods most commonly used for character-

izing different magnetic materials are discussed in the

following sections.

10.2 Soft and Hard Magnetic Materials: (Standard) Measurement

Techniques for Properties Related to the B(H) Loop

10.2.1 Introduction

During the past 100 years many different methods

have been developed for the measurement of mag-

netic material properties and sophisticated ﬁxtures,

yokes and coil systems have been designed. Many of

them vanished when new materials required extended

measuring conditions. With progress in electronic mea-

suring techniques other instruments were superseded.

Fluxmeters and Hall-effect ﬁeld-strength meters, for

example, replaced ballistic galvanometers and rotating

coils. Comprehensive explanations of the older meth-

ods can be found in [10.2]. New methods are ready

to enter magnetic measuring technique. One new op-

portunity is for the pulse ﬁeld magnetometer (PFM),

which is discussed in Sect. 10.3. This device can com-

plement the capabilities of a hysteresisgraph for hard

magnetic materials, although it should be mentioned

that the instrumentation is not less demanding. The dif-

ﬁculties involved require a careful interpretation of the

results.

Table 10.1 gives an overview of the measuring

methods described in the subsequent chapters. The tech-

niques are classiﬁed according their main application

for hard or soft magnetic materials, although some of

them may also be applicable in the other group.

Table 10.2 compares the capabilities of various

methods. Of course, it can only cover typical conﬁgu-

rations and applications and give rough indications. In

many cases, the measuring conditions may be adjusted

to meet special demands. The magnitude of the quan-

tities, which limit the measuring ranges, can either be

determined by the instrumentation or by the require-

ments resulting from the specimen properties.

The tables can certainly not give a complete survey

of all requested quantities and methods that are used to-

day. The selected techniques are common in industrial

and scientiﬁc research or in quality control.

Some basic methods in magnetic measurement are

taken as known. Fluxmeters are used in many measuring

set ups to integrate voltages that are induced in mea-

suring coils to obtain the magnetic ﬂux. Today various

analog or digital integration methods are used. A dis-

cussion of them can be found in [10.3].

The same applies for ﬁeld-strength meters that use

the Hall effect. These instruments, usually called Gauss-

or Teslameters, are widespread. A description of their

working principle is given in many educational books.

In many cases it is impossible to determine the ma-

terial properties of components in a shape that is deﬁned

by the production conditions or application. In these

cases, relative measuring methods are often applied.

These usually compare measurable properties or com-

binations of properties with those of a reference sample.

Sections 10.2.2 and 10.2.3 focus on methods that

provide directly material properties, allow traceable

Part C 10.2

Magnetic Properties 10.2 Soft and Hard Magnetic Materials: Measurement Techniques 547

Table 10.1 Measuring methods for properties of magnetic materials

Measuring method Soft/hard Quantities

Hysteresisgraph for hard magnetic materials H J(H), B(H), B

, H

,(BH)

max

, μ

rec

Vibrating-sample magnetometer (VSM) H, (S) J

, J(H), B

, H

,(BH)

max

, μ

rec

, J(T), T

Torque magnetometer H, (S) Anisotropy constants

Moment-measuring coil (Helmholtz) H J (at working point)

Pulse ﬁeld magnetometer (PFM) (Sect. 10.4) H J

, J(H), B(H), B

, H

,(BH)

max

DC hysteresisgraph S J

, B(H), B

, H

, μ(H), μ

, μ

max

, P

for soft magnetic materials – ring method

DC hysteresisgraph (permeameter) S J

, J(H), B(H), B

, H

, μ

max

, P

for soft magnetic materials – yoke methods

Coercimeter S, (H) H

AC hysteresisgraph – ring method S B(H), B

, H

, μ

, P

, μ

(H), μ

(B), P

(H), P

(B), P

( f ), J

Epstein frame S P

, J(H), B

, H

, μ

Single-sheet tester (SST) S P

, J(H), B

, H

, μ

Wattmeter method S P

Voltmeter–ammeter method S P

, μ

Saturation coil S J

, μ

Magnetic scales (Faraday, Gouy) S μ(H), μ

, μ

max

, χ(H), χ

, χ

max

, J

, T

Impedance bridges S μ =μ



−iμ



, Q, tan δ

=μ

saturation polarization; T

: Curie temperature; B

= J

: remanence; H

: coercivity (coercive ﬁeld strength) for J(H)

hysteresis loop; H

: coercivity (coercive ﬁeld strength) for B(H) hysteresis loop; (BH)

max

: maximum energy product; μ =μ

permeability; χ =μ −1: susceptibility; μ

: relative permeability; μ

,χ

: initial permeability/susceptibility; μ

max

,χ

max

:maxi-

mum permeability/susceptibility; μ

rec

: recoil permeability; μ

: amplitude permeability; μ =μ



−iμ



: complex permeability; P:

hysteresis loss; P

: total loss; Q: Q-factor, quality factor; δ: loss angle; f : frequency

Table 10.2 Characteristics of measuring methods for magnetic materials

Measurement

principle

Measurement

range (limiting

quantities)

Measurement

sensitivity

Measure-

ment

repro-

ducibility

range (%)

Materials

specimen

type

Specimen

geometry,

dimensions

Methods

merit

Methods

demerit

Hysteresisgraph

for hard

magnetic

materials

max

1.6–2.4MA/m

max

:1.2–1.5T

H:0.1kA/m

J:1mT

H: 1–3

J: 0.5–2

Bulk

permanent

magnets

Cylinders,

blocks,

segments,

(large) rings

Many

quantities,

standard-

ized, easy

operation

Restricted

for non-

plane-parallel

specimens

Vibrating-

sample

magnetometer

(VSM)

max

:1.2–4MA/m

max

:1Am

max

:10

−6

Vsm

H:0.1kA/m

m:10

−9

j:10

−15

Vsm

H, J: 1–3 Ferro- and

param-

agnetic

material,

amorphous

or nanocrys-

talline

alloys

Powders,

thin ﬁlms,

ribbons,

small

massive

samples

High

sensitivity,

wide

specimen

temperature

range

Demagnetization

factor to be

considered

Torque

magnetometer

max

0.8–10MA/m

L:10

−4

–10

−2

1) L:

−9

–10

−7

1) L: 1–5 Ferro- and

param-

agnetic

material

Discs,

spheres,

small

particles,

ﬁlms, single

crystals

High sen-

sitivity,

low tem-

peratures

possible

Restricted

specimen

shape, some-

times delicate

instrumentation

Part C 10.2