Using Magnetic Fields and Storing Data.pdf

Using Magnetic Fields and Storing Data

CHAPTER PREVIEW

If you were asked to give an example of a magnetic material instinctively you would probably

say iron. It is a good example, but in its pure form iron is not a very useful magnet. Ceramics

can be magnetic too and they were the ﬁrst magnets known to humans. About 600,000 t of

ceramic magnets are produced each year making them, in terms of volume, commercially more

important than metallic magnets. The largest market segment is hard ferrites (permanent

magnets) that are used in a range of applications including motors for electric toothbrushes

and windshield wipers in automobiles, refrigerator door seals, speakers, and stripes on the back

of the ubiquitous credit and ATM cards. Soft ferrites can be magnetized and demagnetized

easily and are used in cell telephones, transformer cores, and, now to a somewhat lesser extent,

magnetic recording.

Ferrite is a term used for ceramics that contain Fe 2 O 3 as a principal component.

Magnetism has probably fascinated more people, including Socrates and Mozart (listen to

Così fan tutte ), over the years than any other materials property. For over four thousand years

the strange power of magnets has captured our imagination. Yet it remains the least well

understood of all properties. In this chapter we will start by describing some of the basic

characteristics of magnetic materials, which often contain one of the ﬁrst row transition metals,

Fe, Co, or Ni. The electron arrangement in the 3d level of these atoms is the key. The manga-

nates are a very interesting class of magnetic ceramic. Although they are not new, the recent

discovery that they exhibit colossal magnetoresistance (just like the giant magnetoresistance

observed in metal multilayers only much bigger) has renewed interest in these materials. Struc-

turally the manganates are very similar to the high-temperature superconductors (HTSCs). The

similarity may be more than coincidental.

33.1 A BRIEF HISTORY OF

MAGNETIC CERAMICS

polished bronze plate. The rounded bottom of the spoon

swivels on the plate until it points south. Although this

compass has been found to work it was used apparently

for quasimagical rather than navigational purposes.

Magnetite is found in many parts of the world and is

an important iron ore used for steel making. The word

magnet comes from the Greek word magnes , which itself

may derive from the ancient colony of Magnesia (in

Turkey). Magnetite was mined in Magnesia 2500 years

ago. Today, large deposits of magnetite are found at Kiruna

in Sweden and in the Adirondack region of New York.

Commercial interest in ceramic magnets really started

in the early 1930s with the ﬁling of a Japanese patent

describing applications of copper and cobalt ferrites. In

1947 J.L. Snoeck of N.V. Philips Gloeilampenfabrieken

performed a detailed study of ferrites, and the following

year Louis Néel published his theory of ferrimagnetism.

This latter study was particularly important because most

of the ceramics that have useful magnetic properties are

ferrimagnetic. The ﬁrst commercial ceramic magnets were

produced in 1952 by researchers at the Philips Company,

Applications of magnetism began with ceramics. The ﬁrst

magnetic material to be discovered was lodestone, which

is better known now as magnetite (Fe 3 O 4 ). In its naturally

occurring state it is permanently magnetized and is the

most magnetic mineral. The strange power of lodestone

was well known in ancient times. In c. 400 BCE Socrates

dangled iron rings beneath a piece of lodestone and found

that the lodestone enabled the rings to attract other rings.

They had become magnetized. Even earlier (

c. 2600 BCE)

a Chinese legend tells of the Emperor Hwang-ti being

guided into battle through a dense fog by means of a small

pivoting ﬁ gure with a piece of lodestone embedded in its

outstretched arm. The ﬁ gure always pointed south and was

probably the ﬁrst compass. The term lodestone was coined

by the British from the old English word lode , which

meant to lead or guide .

Figure 33.1 shows an ancient Chinese compass. The

spoon or ladle was carved out of lodestone and rests on a

∼

598 .............................................................................................................. USING MAGNETIC FIELDS AND STORING DATA

Direction of

current

Nucleus

e -

Direction of

electron motion

Direction of

electron spin

(A) (B)

FIGURE 33.2 Generation of atomic magnetic moments by

(a) electron orbital motion around the nucleus; (b) electron spin

around its axis of rotation.

netic dipoles are small internal magnets with north and

south poles.

FIGURE 33.1 An ancient Chinese compass.

Orbital motion . Equiva-

lent to a small current

loop generating a very

small magnetic ﬁeld. The

direction of the magnetic

moment is along the orbit

axis as illustrated in

Figure 33.2a.

Spin . Origin of the

fourth quantum number,

m s , that we used in

Chapter 3. The magnetic

moment is along the

spin axis as shown in

Figure 33.2b and will be

either up ( m s =+1/2) or

in an antiparallel down

direction ( m s =−1/2).

The magnetic moment

due to electron spin is,

when present, dominant

the same company that

introduced the compact

audiocassette in 1963.

MAGNETIC MOMENTS

The fundamental magnetic moment is the Bohr magne-

ton, μ B , which has a value of 9.27 × 10 −24 A·m 2 .

The orbital magnetic moment, μ orb , of a single elec-

tron is

33.2 MAGNETIC

DIPOLES

[

(

)

]

μμ

orb

ll 1

(Box 33.1)

l is the orbital shape quantum number (see Chapter 3).

The spin magnetic moment of an electron is

The Danish physicist Hans

Christian Oersted discov-

ered that an electric current

(i.e., moving electrons)

gives rise to a magnetic

force. In an atom, there

are two possible sources

of electron motion that can

create a magnetic dipole

and produce the resultant

macroscopic magnetic pro-

perties of a material. Mag-

[

(

)

]

μμ

(Box 33.2)

In ceramics where the magnetic behavior is due to the

presence of transition metal ions with unpaired electron

spins in the 3d orbital the magnetic moment of the ion

due to electron spin, μ ion , is

[

(

)

]

(Box 33.3)

ion

= ∑

TABLE 33.1 Magnetic Moments of Isolated Transition Metal Cations

Calculated moments

Measured

Cations

Electronic conﬁ guration

using Eq. B3

moments ( m B )

Sc 3 + , Ti 4 +

3d 0

0.00

0.0

V 4 + , Ti 3 +

3d 1

1.73

1.8

V 3 +

3d 2

2.83

2.8

V 2 + , Cr 3 +

3d 3

3.87

3.8

Mn 3 + , Cr 2 +

3d 4

4.90

4.9

Mn 2 + , Fe 3 +

3d 5

5.92

5.9

Fe 2 +

3d 6

4.90

5.4

Co 2 +

3d 7

3.87

4.8

Ni 2 +

3d 8

2.83

3.2

Cu 2 +

3d 9

1.73

1.9

Cu + , Zn 2 +

3d 10

0.00

0.0

................................................................................................................................................ 599

33.2 MAGNETIC DIPOLES

TABLE 33.2 Terms and Units Used in Magnetism

Parameter Deﬁ nition

Units/value

Conversion factor

Magnetic ﬁ eld strength

A/m

1 A/m

π×

10 − 3

oersted (Oe)

H c

Coercive ﬁ eld

A/m

H cr

Critical ﬁ eld

A/m

Magnetization

A/m

Magnetic ﬂ ux density

Wb m − 2

kg A − 1 s 2

V s m − 2

Magnetic induction

10 4

gauss (G)

Permeability of a vacuum

π×

10 − 7 H/m

1 H

1 J s 2 C − 2

Permeability

H/m

1 H/m

1 Wb m − 1 A − 1

Relative permeability

Dimensionless

Susceptibility

Dimensionless

ion

Net magnetic moment of an atom or ion

A·m 2

Spin magnetic moment

A·m 2

orb

Orbital magnetic moment

A·m 2

Bohr magneton

9.274

10 − 24 A·m 2

Curie temperature

0 K

=−

273°C

Néel temperature

T c

Critical temperature for superconductivity

Curie constant

over that due to orbital motion. Table 33.1 lists values of

μ ion calculated for some ﬁrst row transition metal ions

using Eq. Box 33.3. You can see that, in general, the cal-

culated values agree well with the experimental values.

This agreement shows that we are justiﬁed in considering

only the contribution of the spin magnetic moment to the

overall magnetic moment.

When an electron orbital in an atom is ﬁlled, i.e., all

the electrons are paired up, both the orbital magnetic

moment and the spin magnetic moment are zero.

where N is the number of turns of wire per meter. The

magnetic induction or magnetic ﬂux density, B , is related

to H by

=μ 0 H

(33.2)

μ o is a universal constant.

When a material is placed inside the coil, as shown in

Figure 33.3b, it becomes “magnetized.” The magnetic

33.3 THE BASIC EQUATIONS, THE

WORDS, AND THE UNITS

Table 33.2 lists the important parameters used in this

chapter and their units. The situation regarding units is

more complicated for magnetism than for almost any other

property. The reason is that some of the older units, in

particular the oersted (Oe) and the gauss (G), are still in

widespread use despite being superceded, in the SI system,

by A/m and T, respectively.

The properties of most interest to us in the description

of magnetic behavior are

These terms are, of course, related to each other and by

considering the role of H to macroscopic measures such

as M and B .

The usual starting point to arrive at expressions for

N turns

and

is to consider a coil of wire in a vacuum as illus-

trated in Figure 33.3a. A current, I , passed through the

wire generates a magnetic ﬁeld H

(A) (B)

FIGURE 33.3 Generation of a magnetic ﬁ eld by current ﬂ owing in

a coil of wire (a) in a vacuum; (b) with a material present.

(33.1)

600 .............................................................................................................. USING MAGNETIC FIELDS AND STORING DATA

moment produced in the material by the external ﬁeld

changes B :

nature of the dipoles and their origin is very different. In

the case of a dielectric, the dipoles are electric; there is a

separation of positive and negative charges. These dipoles

can be permanent or induced. In a magnetic material, the

dipoles are, of course, magnetic in origin and are due to

electron motion.

A note on terminology : In most materials science text-

books, as we have done here, H is deﬁned as the magnetic

ﬁeld or the applied magnetic ﬁeld and B as the magnetic

ﬂux density. In many physics textbooks B is referred to as

the magnetic ﬁeld and H is often ignored. The physics

convention is adopted for purely historical reasons, but it

does have the advantage of reducing the number of terms

we need to consider. Also H has nothing to do with a

material whereas B is a measure of the response of a mate-

rial to an applied magnetic ﬁeld. Another point to note is

that B and H are both vector quantities and because the

magnetic properties of a material are anisotropic (differ-

ent along different directions in the crystal) they should

actually be represented by a second-rank tensor.

=μ 0 H

+μ 0 M

(33.3)

M represents the response of the material to H , which is

linear, and the ratio gives

χ=

M / H

(33.4)

By simple substitution we get

=μ 0 (1

+χ

) H

(33.5)

B/H is then the permeability:

B/H

=μ 0 (1

+χ

)

=μ

(33.6)

The ratio of the permeabilities gives us the relative

permeability:

(33.7)

=+ =

33.4 THE FIVE CLASSES OF

MAGNETIC MATERIAL

There are many quali-

tative similarities between

magnetic parameters and

those we used to describe

dielectrics in Chapter 31.

In the former case, the

material is responding to

an applied magnetic ﬁeld,

and in the latter case, it is

responding to an applied electric ﬁeld.

There are ﬁve main types

of magnetic behavior and

these can be divided into

two general categories:

c AND m

Susceptibilities are generally used when the response to

an applied magnetic ﬁeld is weak (of interest only to

physicists!). Permeabilities are used when the response

is large—of great interest to engineers!

Induced

Spontaneous

Table 33.3 summarizes the properties of the ﬁve classes.

We can ﬁnd examples of each in ceramics.

H and the electric ﬁeld strength

(V/m). Both are the

external driving force, which causes the orientation of

either magnetic or electric dipoles resulting in magne-

tization or polarization, respectively.

33.5 DIAMAGNETIC CERAMICS

Most ceramics are diamagnetic. The reason is that all the

electrons are paired during bond formation and as a result

the net magnetic moment due to electron spin is zero.

Table 33.4 l ists

B and the polarization P (C/m 2 ). Both correspond to

the total ﬁeld after dipole orientation.

. Both are dimensionless

“constants” that describe the magnitude of a material’s

response to the applied ﬁeld. They are both properties

of a material and depend on the types of atoms, the

interatomic bonding, and, the crystal structure.

and dielectric constant,

for several diamagnetic materials. Cu,

Au, and Ag are diamagnetic even though their atoms have

unpaired valence electrons. When the atoms combine to

form the metal the valence electrons are shared by the

crystal as a whole (to form the electron gas) and, on

average, there will be as many electrons with m s

μ o and the permittivity of a vacuum

ε 0 are constants.

They are reference values to establish the strength of

a materials response to H or

1/2

as with m s

1/2.

Most diamagnetic ceramics are of no commercial sig-

niﬁcance and of little scientiﬁc interest, at least not for

their magnetic behavior.

The one exception is the

ceramic superconductors,

which are perfect diamag-

nets below a critical mag-

netic ﬁeld.

=−

, respectively.

The similarities described above are not surprising.

In both cases, we are con-

cerned with the relation-

ship between an external

ﬁeld and the dipoles within

a material. Despite these

similarities the physical

MAXWELL EQUATIONS

The magnetic, electric, and optical properties of a mate-

rial are all related mathematically through the Maxwell

equations.

33.5 DIAMAGNETIC CERAMICS ........................................................................................................................................ 601

TABLE 33.3 Magnetic Classiﬁcation of Materials

Critical

Temperature

Spontaneous

Class

temperature

variation of c

magnetization

Structure on atomic scale

Diamagnetic

None

−

10 − 6

−

10 − 5

Constant

None

Atoms have no permanent dipole

moments

Paramagnetic

None

10 − 5

10 − 3

χ=

C / T

None

Atoms have permanent dipole

moments; neighboring moments

do not interact

Ferromagnetic

Large (below

C )

Above

C ,

Below

C , M s ( T )/ M s (0)

Atoms have permanent dipole

χ=

C /( T

−θ

), against T /

C follows a

moments; interaction produces

with

θ≈θ

universal curve; above

parallel alignment

C , none

Antiferromagnetic

As paramagnetic

Above

N ,

None

Atoms have permanent dipole

χ=

C /( T

±θ

moments; interaction produces

with

θ≠θ

N ,

antiparallel alignment

below

N ,

decreases,

anisotropic

Ferrimagnetic

As ferromagnetic

Above

C ,

Below

C , does not

Atoms have permanent dipole

χ≈

C /( T

±θ

follow universal curve;

moments; interaction produces

with

θ≠θ

above

C , none

antiparallel alignment; moments

are not equal

33.6 SUPERCONDUCTING MAGNETS

The net effect is that the whole of the magnetic ﬂux

appears to have been sud-

denly ejected from the

material and it behaves as

a perfect diamagnet. This

phenomenon is known as

the Meissner effect and is

usually demonstrated by

suspending a magnet above

a cooled pellet of the

superconductor.

There is an upper limit

to the strength of the mag-

netic ﬁeld that can be

applied to a superconduc-

tor without changing its

diamagnetic behavior. At a critical ﬁeld H cr the magnetiza-

tion goes toward zero and the material reverts to its normal

state. For most elemental superconductors M rises in mag-

nitude up to H cr and then abruptly drops to zero; this is

Ty p e I b e h av io r.

A few elemental and most compound superconductors,

including all HTSCs, exhibit Type II behavior. Above a

certain ﬁeld, H c1 , magnetic ﬂux can penetrate the material

without destroying superconductivity. Then at a (usually

much) higher ﬁeld, H c2 , the material reverts to the normal

state. These two behaviors are compared in Figure 33.4.

When a Type II superconductor is in the “mixed” state

it consists of both normal and superconducting regions.

The normal regions are called vortices, which are arranged

parallel to the direction of the applied ﬁeld. At low tem-

perature the vortices are in a close-packed arrangement

and vibrate about their equilibrium positions, in the same

way that atoms in a solid vibrate. If the temperature is high

enough the vortex motion becomes so pronounced that the

LONDON PENETRATION DEPTH

Although there is no magnetic ﬁeld in the bulk of a

superconductor it does penetrate below the surface to a

depth of between 0.2 and 0.8

When a superconductor in

its normal (i.e., nonsuper-

conducting) state is placed

in a magnetic ﬁeld and

then cooled below its criti-

cal temperature the induced

magnetization, M , exactly

opposes H and so from Eq.

33.3, we can write

CRITICAL MAGNETIC FIELDS FOR YBCO

H c1 (T)

|| c

∼

0.1

|| a , b

∼

0.01

H c2 (T)

200

|| c ﬁeld along the c axis of the unit cell

|| a , b ﬁeld in the basal plane

These H c2 values are enormous. The world’s most pow-

erful magnet is about 40 T.

|| c

∼

|| a , b

∼

(33.8)

TABLE 33.4 Magnetic Susceptibilities for Several

Diamagnetic Materials

Material

c (ppm)

Al 2 O 3

− 37.0

− 9.0

BeO

− 11. 9

− 280.1

− 6.7

CaO

− 15.0

CaF 2

− 28.0

C (diamond)

− 5.9

C (graphite)

− 6.0

− 5.5

− 76.8

− 28.0

− 23.0

LiF

− 10.1

MgO

− 10.2

− 3.9

− 19.5

NaCl

− 30.3

602 .............................................................................................................. USING MAGNETIC FIELDS AND STORING DATA

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: