Fundamentals of Magnetism

Lecture 1

Magnetic domain image of iron from

Principia Rerum Naturalium (1734) given by

E.Swedenborg

Magnetized state of Fe

Demagnetized state of Fe

Definitions of magnetic fields

Induction:

(

)

M

H

B

r

r

r

+

=

0

μ

External magnetic field:

→

→

→

= H

M

χ

H

Magnetization

average magnetic moment of

magnetic material

Susceptibility

tensor representing anisotropic material

→

M

χ

(

)

→

→

=

+

=

H

H

B

μ

χ

μ

1

0

where:

(

)

χ

μ

μ

+

=

1

0

permability of the material

Maxwell’s equations

0

=

=

∇

B

div

B

r

r

o

r

j

H

rot

H

r

r

r

r

=

=

×

∇

∫

=

l

i

l

d

H

r

o

r

t

B

E

rot

E

∂

∂

−

=

=

×

∇

r

r

r

r

U

t

s

d

B

t

l

d

E

S

=

∂

∂

−

=

∂

∂

−

=

∫

∫

φ

r

o

r

r

o

r

r

i

H

π

2

=

[oe]

[oe]

l

iN

H

=

[A/m]

[A/m]

Demagnetization field

2

4

r

dV

dH

πρ

=

r

s

H

/

2

.

0

=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

−

=

∇

−

=

dz

dM

dy

dM

dx

dM

M

z

y

x

m

r

o

r

ρ

To compute the demagnetization field, the magnetization at all points must

be known.

M

N

H

d

r

r

−

=

when magnetic materials becomes magnetized by application of

external magnetic field, it reacts by generating an opposing field.

[emu/cm

4

]

The magnetic field caused by magnetic poles can be obtained

from:

The fields points radially out from the positive or

north poles of long line. The

s

is the pole strength

per unit length [emu/cm

2

]

[oe=

emu/cm

3

]

Demagnetization field

poles density, magnetic „charge” density

m

M

M

B

ρ

μ

μ

=

∇

−

=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛ −

∇

→

→

→

o

r

r

o

0

0

Demagnetization tensor N

zz

zy

zx

yz

yy

yx

xz

xy

xx

π

4

0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

2

π

π

3

/

4

0

0

0

3

/

4

0

0

0

3

/

4

π

π

π

D

S

total

H

H

H

−

=

For ellipsoids, the demagnetization tensor is the same at all the points within the
given body. The demagnetizing tensors for three cases are shown below:

The flat plate has no demagnetization within its x-y plane but shows a 4

π

demagnetizing factor on magnetization components out of plane. A sphere shows
a 4/3

π factor in all directions. A long cylinder has no demagnetization along its

axis, but shows 2

π in the x and y directions of its cross sections.

H

S

- the solenoid field

(4

π)

Electron spin

Orbital momentum

p

r

L

r

r

r

×

=

ω

m

r

rmv

L

2

=

=

2

r

T

e

S

i

L

π

μ

=

⋅

=

Magnetic moment of electron

T

π

ω

2

=

π

ω

π

μ

2

2

r

e

L

=

m

e

L

L

2

=

μ

)

1

(

2

+

=

l

l

h

L

π

)

1

(

4

+

=

l

l

m

eh

L

π

μ

L

r

rr

L

μ

pr

i

Electron Spin

emu

m

eh

B

20

10

93

.

0

4

−

×

=

=

π

μ

The magnetic moment of spining electron is called the

Bohr magneton

3d shells of Fe are unfilled and have uncompensated electron spin magnetic

moments

when Fe atoms condense to form a solid-state metallic crystal, the electronic

distribution

(density of states)

, changes

.

Whereas the isolated atom has

3d:

5+, 1-; 4s:1+, 1-,

in the solid state the distribution becomes

3d: 4.8+, 2.6-; 4s:

0.3+,0.3-.

Uncompensated spin magnetic moment of Fe is

2.2

μ

B

.

Electron spin

Exchange coupling

3

3

8

2

/

1700

)

10

86

.

2

(

2

.

2

)

0

(

cm

emu

T

M

B

S

=

×

=

=

−

μ

The saturation of magnetization

M

S

for body-centered cubic Fe crystal can

be calculated if lattice constant

a=2.86 Å

and two iron atoms per unit cell.

Magnetyczny (analogowy) zapis dźwięku

1877

-

T. Edison

– nagranie i odtworzenie dźwięku z woskowego

cylindra zapis niemagnetyczny.

1898

-

V. Poulsen

– telegrafon – zapis na drucie stalowym

(

Φ = 1mm) prędkość zapisu 2m/s.

1900

-Prezentacja telegrafonu na Światowej Wystawie w Paryżu.

Lata dwudzieste XX wieku

-

L. Blattner

– Blattnerphone - zapis

na taśmie stalowej (grubość 0.05mm, szer. 3mm)
prędkość zapisu 1m/s.

1927

-

F. Pflumer

– zapis na taśmie papierowej pokrytej klejem z

opiłkami żelaza.

Lata trzydzieste XX wieku

-

BASF

– pierwsze taśmy z tworzyw

sztucznych pokryte tlenkami żelaza.

Historia – pierwszy zapis dźwięku

1898 – Valdemar Poulsen

2 m/s

Elektro-
magnes

Mikrofon

bl

a

bl

a.

la

..

Fala dźwiękowa

Sygnał elektryczny

Zapis magnetyczny

Głowica zapisu

Nośnik informacji –

struna fortepianowa

(drut stalowy).

Elektro-
magnes

Głośnik

Bla bla...

2 m/s

Głowica odczytu

Odczyt informacji (głowica indukcyjna) :

Do odczytu informacji wykorzystywane jest zjawisko indukcji magnetycznej – generowanie
siły elektromotorycznej w obwodzie prądu pod wpływem zmian strumienia magnetycznego –
przecinania linii sił rozproszonego pola magnetycznego pochodzącego od różnie
zorientowanych magnetycznie obszarów

.

Jak zwiększyć gęstość zapisu informacji?

Zastąpić materiał lity (stalowy drut lub taśmę) drobinami materiału
ferromagnetycznego naniesionymi na niemagnetyczne podłoże (wpierw
papier później tworzywa sztuczne – taśmy magnetofonowe).

In the early 1930s researchers at the Ludwigshafen works created a sensation with
another pioneering invention: the Magnetophon, which had been developed in
cooperation with AEG. It was presented at the Berlin Radio Exhibition in 1935.

Pierwsze magnetofony firmy AEG prezentowane na światowej
wystawie sprzętu radiowego (Berlin 1935).

zapis

odczyt

350 nm
szer.

45 nm
długość

dysk

20 nm

Magnetyczny zapis w informatyce

Zapis binarny (0, 1)

→ kierunek namagnesowania

←

/

→

Warunek stabilności – pole koercji (pole potrzebne do
przemagnesowania) materiału ferromagnetycznego H

C

musi być

dostatecznie duże – im węższe bity tym większe musi być pole H

C

Im większe pole H

C

tym trudniej zapisać informację – wymagane są

bardzo małe odległości pomiędzy głowicą zapisu i dyskiem (obecnie
0.1

μm, większe wartości prądu płynące przez elektromagnes.....

Gęstość zapisu
przy podanych
rozmiarach bitów
wynosi około
30Gbit/inch

2

.

1nm = 10

-9

m

1nm = 10

-6

mm

1nm = 0.000001mm
1Å = 10

-7

mm

1

0

M

H

H

C

-H

C

Dążymy do uzyskania maksymalnej

gęstości zapisu !!!!!!!

Co oznacza gęsty zapis?
Bity – obszary o namagnesowaniu

←

/

→

powinny mieć jak

najmniejszą długość i szerokość.

Szerokość bitu

Długość bitu

Co ogranicza gęstość zapisu?
•Nośnik informacji – materiał magnetyczny
•Zapis informacji – głowica zapisu
•Odczyt informacji – głowica odczytu

History of HDD

• 1956 – HDD of IBM, random access method of

accounting and control (RAMAC)

• 1980 – induction thin film head
• 1990 – write induction coil, read AMR sensor
• 1996 – GMR sensor

HDD for 50 years and now

First Hard Disk Drive with 24" Diameter Disks Compared with Modern 2.5" HDD. The first HDD was

introduced in 1956 with

50 disks of 24" diameter holding a total of 4.4 Mbytes

of data. The purchase price of

this HDD was

$10,000,000 per Gbyte

. For comparison in the foreground a modern HDD is shown holding

160

Gbyte of data on two 2.5" diameter disks

at a purchase price of

less than $1 per Gbyte

.

Dimensions scaling

Areal data storage density vs. time for inductive and

MR read heads

Disc drive

The slider carrying the magnetic

write/read head. The slider is

mounted on the end of head

gimbal assembly (HGA)

The air-bearing surface (ABS)

allowing the head to fly at a distance

above the medium about 10 nm

The magnetic disks (up to 10) in

diameter 1 – 5.25 inches. 5.400 –

15.000 RPM it is related to about

100 km/h

Thin film disks

Substrate – Al Mg (or glass) + electroplated Ni

80

P

20

(T

c

<T

room

). NiP undercoat layer make disk hard and smooth.

Cr underlayer is used to control microstructure and magnetic

properties the main magnetic recording layer of CoPtCr

doped with B. The magnetic layer is covered by a carbon

overcoat layer and lubricant. The last two layers are

necessary for the tribological performance of the head-disk

interface and for the protection of the magnetic layer.

Disk layer structure

Evolution of bit size

Macroscopic properties of the disk

For high density recording the macroscopic properties such as

coercivity

(H

c

),

remanence

(M

r

)

, coercive squerness

(S

*

)

and

remanence squerness

(S)

determine read-back signal variables such

as pulse shape, amplitude and resolution arising from magnetic

transitions.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

=

f

x

M

x

M

r

arctan

2

)

(

π

The parameter

(f )

is called as

transition slope parameter.

In an ideal

situation, in the absence of demagnetizing fields (arising from

adjacent bit cells), the transition would be abrupt.
Assuming that the contributions to the transition parameter from

characteristics of the write head are negligible and that the recording

medium has a coercive squerness

S

*

= 1

a simplified relation can be

derived from the Williams Comstock model:

(

)

c

r

H

d

M

f

π

δ

δ

2

+

=

(4)

(5)

To minimize

the transition slope f

, Eq.5 indicates that this can be achieved by:

•decreasing the magnetic spacing

d

and thickness of recording medium

δ,

•increasing the

H

c

of the medium,

•smaller

M

r

reduce the read signal detected by AMR or GMR.

Tradycyjne media jeden bit z

łożony z 1000 ziaren

Grains in bit cell

Microscopic properties

Coercivity

H

c

-

control and modification:

• magnetocrystalline anisotropy (grain shape anisotropy),

•selection of alloying elements (Al, Cr, Pt, Ta, B,...)

•determination of influence:

•deposition conditions and parameters: substrate temperature, bias

voltage, sputtering power (deposition rate), sputtering gas pressure

(Ar)

•microstructure: film stresses, grain size, texture (grain orientation),

grain boundaries, crystal defects.

If the grain structure is noticably voided, leading to reduced magnetic intractions and

lower transition noise

.

Superparamagnetic effect

The superparamagnetic effect originates from the shrinking volume of magnetic grains that compose the storage properties of hard disk
media. The magnetic grains represent the data bits that are stored as alternating magnetic orientations. To increase data-storage densities
while maintaining acceptable performance, designers have shrunk the media's grain diameters and decreased the thickness of the media.
The resulting smaller grain volume makes them increasingly susceptible to thermal fluctuations, which decreases the signal sensed by the
drive's read/write head. If the signal reduction is great enough, data could be lost over time to this superparamagnetic effect.

TEM of the grain structures in magnetic media. (magnification = 1 million)

The pictures are transmission electron micrographs (TEM) of two different disk media which illustrates how the grain structure has
evolved over time.

The TEM on the left is a magnetic media that supports a data density of about 10 gigabits/inch2 with an average grain

diameter of about 13 nanometers

.

The magnetic media on the right supports a data density of 25 gigabit/inch2 with an average grain

diameter of about 8.5 nanometers.

Historically, disk drive designers have had only two ways to maintain thermal stability as the media's

grain volume decreases with increasing areal density: 1) Improve the signal processing and error-correction codes (ECC) so fewer grains
are needed per data bit, and 2) develop new magnetic materials that resist more strongly any change to their magnetization, known
technically as higher coercivity. The later is complicated by the laws of physics, as higher coercivity alloys are more difficult to write on.
While improvements in coding and ECC are ongoing, Hitachi GST's discovery of AFC media is a major advancement because it allows
disk-drive designers to write at very high areal densities on a surface that offers greater stability than conventional media.

Nośnik informacji – ferromagnetyczna cienka warstwa (z
anizotropią w płaszczyźnie warstwy) o granularnej (ziarnistej)
strukturze. Takie dyski są obecnie powszechnie stosowane.

1 bit (obszar, w którym ziarna mają
określony kierunek magnetyzacji)
składa się z około 10

3

ziaren.

Rozmycie granicy pomiędzy bitami
nie może być duże. Tak więc wzrost
gęstości zapisu można uzyskać
poprzez zmniejszenie rozmiaru
ziaren.

Czy można bezkarnie zmniejszać rozmiar cząstek?
Dla małych cząstek (d<3nm w temperaturze pokojowej) kierunek
namagnesowania cząstki ferromagnetycznej w wyniku wzbudzeń
termicznych fluktuuje (zmienia kierunek) – cząstka
superparamagnetyczna. Oznacza to utratę zapisanej informacji
(limit superparamagnetyczny).

Signal to noise (S/N) ratio

Highly intergranular coupled magnetic thin films with long correlation lengths

tends to form zizag domain walls in recorded transitions (bits) which results in

noises. Threrefore the reduction of intergranular exchange coupling becomes

important.

There are three major approaches to noise reduction:

•physical grain segregation,

•compositional segregation,

•Small grains with very narrow size distributions.

For example – higher Cr content and higher sputter temperatures leads to Cr

segregation to grain boundaries, forming non-magnetic phases in CoPtCrTa and

CoPtCrTB. The low solubility of B in the cobalt alloys leads to compositional

segregation.

The ideal thin-recording-magnetic layer should be composed of grains with

high-anisotropy, which are smaller than the recording bit cell, uniform in size

and magnetically isolated.

Thermal stability

For high density recording the grains are small in comaprison to the bit cell. In a simplified model,

assuming isolated grains, the thermally induced switching of magnetization has to overcome an

energy barier. The switching probability

f

is given by an Arrhenius equation:

⎟

⎞

⎜

⎛

Δ

−

=

W

f

f

exp

0

⎠

⎝

kT

ΔW

is energy barier,

K

u

is the uniaxial anisotropy constant, V is grain volume. If the grains

become very small, the magnetization switch very easily which leads to

superparamagnetic

efect.

Estimation of minimum grain size (example):

K

u

=2

×10

5

J/m

3

.

Bit stored 10 years at room temperature

(f<3.33

×10

-9

Hz at T=300 K),

than diameter of spherical grain is

9 nm.

where

ΔW = K

u

V (6)

Granular media vs. patterned media

Self organized particle media

Chemical method for preparation FePt

nanoparticles

TEM micrograph of self-assembled

FePt nanoparticles (size 3 to 10nm)

Write/read head of HDD

Inductive write head

The yoke consists of structured Ni

81

Fe

19

(permalloy) films P

1

and P

2

.These films are all

deposited on the top of substrate which

consists of insulators (Al

2

O

3

and TiC). The gap

width is defined by the thickness of Al

2

O

3

insulation layer between P

1

and P

2

hich is

below 100 nm

.

Micrograph of the write/read head

taken by SEM from the ABS side.

Aim for application

Magnetic properties optimization of

ML (Fe

97

Al

3

)

85

N

15

/Al

2

O

3

for shields and poles of HDD heads

SEM cross section of the head

Schematic representation of a longitudinal recording

process

Magnetic force micrograph (MFM)of

recorded bit patterns. Track width is

350 nm recorded in

antiferromagnetic coupled layers

(AFC media)