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: ( )MHBrrr

+= 0μ

External magnetic field:→

→→

= HM χ

H

Magnetization average magnetic moment of magnetic material

Susceptibility tensor representing anisotropic material

→

M

χ

( )→→

=+= HHB μχμ 10

where: ( )χμμ += 10 permability of the material

Maxwell’s equations

0==∇ BdivBrr

or

jHrotHrrrr

==×∇

∫ =l

ildHr

or

tBErotE∂∂

−==×∇r

rrr

Ut

sdBt

ldES

=∂∂

−=∂∂

−= ∫∫φr

orr

or

riHπ2

=

[oe]

[oe]

liNH =

[A/m]

[A/m]

Demagnetization field

24

rdVdH πρ

=

rsH /2.0=

⎟⎟⎠

⎞⎜⎜⎝

⎛++−=∇−=

dzdM

dydM

dxdM

M zyxm

ro

rρ

To compute the demagnetization field, the magnetization at all points must be known.

MNHd

rr−= when magnetic materials becomes magnetized by application of

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

[emu/cm4]

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/cm2]

[oe= emu/cm3]

Demagnetization field

poles density, magnetic „charge” density

mMMB

ρμμ

=∇−=⎟⎟⎠

⎞⎜⎜⎝

⎛ −∇

→→→

o

rr

o0

0

Demagnetization tensor N

zzzyzxyzyyyxxzxyxx

π400000000

000020002

ππ

3/40003/40003/4

ππ

π

DStotal HHH −=

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 4πdemagnetizing factor on magnetization components out of plane. A sphere showsa 4/3 π factor in all directions. A long cylinder has no demagnetization along its axis, but shows 2π in the x and y directions of its cross sections.

HS - the solenoid field

(4π)

Electron spin

Orbital momentum prL rrr×= ωmrrmvL 2==

2rTeSiL πμ =⋅=Magnetic moment of electron

Tπω 2

=πωπμ

2

2reL =

me

LL

2=

μ)1(

2+= llhL

π

)1(4

+= llm

ehL π

μ

Lr

rr Lμ pr

i

Electron Spin

emum

ehB

201093.04

−×==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 μB .

Electron spin

Exchange coupling

338

2

/1700)1086.2(

2.2)0( cmemuTM BS =

×== −

μ

The saturation of magnetization MS 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 woskowegocylindra 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 zopiłkami żelaza.

Lata trzydzieste XX wieku -BASF – pierwsze taśmy z tworzyw sztucznych pokryte tlenkami żelaza.

Historia – pierwszy zapis dźwięku1898 – Valdemar Poulsen

2 m/s

Elektro-magnes

Mikrofon

blabla

.

la..

Fala dźwiękowa

Sygnał elektryczny

Zapis magnetyczny

Głowica zapisu

Nośnik informacji – struna fortepianowa(drut stalowy).

Elektro-magnes

GłośnikBla 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 nmdługość

dysk

20 nm

Magnetyczny zapis w informatyce

Zapis binarny (0, 1) → kierunek namagnesowania ←/→

Warunek stabilności – pole koercji (pole potrzebne do przemagnesowania) materiału ferromagnetycznego HC musi być dostatecznie duże – im węższe bity tym większe musi być pole HC

Im większe pole HC tym trudniej zapisać informację – wymagane są bardzo małe odległości pomiędzy głowicą zapisu i dyskiem (obecnie 0.1μm, większe wartości prądu płynące przez elektromagnes.....

Gęstość zapisu przy podanych rozmiarach bitów wynosi około 30Gbit/inch2.

1nm = 10-9m1nm = 10-6mm1nm = 0.000001mm1Å = 10-7mm

1

0

M

HHC-HC

Dążymy do uzyskania maksymalnej gęstości zapisu !!!!!!!

Co oznacza gęsty zapis?Bity – obszary o namagnesowaniu ←/→ powinny mieć jak najmniejszą długość i szerokość.

Szerokość bitu

Długość bituCo 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 driveThe 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 Ni80P20(Tc<Troom). 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 diskFor high density recording the macroscopic properties such as coercivity (Hc), remanence (Mr), coercive squerness (S*) and remanence squerness (S) determine read-back signal variables such as pulse shape, amplitude and resolution arising from magnetic transitions.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

fxMxM r arctan2)(

πThe 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

dMf

π

δδ 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 Hc of the medium,•smaller Mr reduce the read signal detected by AMR or GMR.

Tradycyjne media jeden bit złożony z 1000 ziaren

Grains in bit cell

Microscopic propertiesCoercivity Hc - 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, biasvoltage, 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 effectThe 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 allowsdisk-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 103 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 stabilityFor 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−=

Wff exp0⎠⎝ kT

ΔW is energy barier, Ku 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):

Ku=2×105 J/m3. Bit stored 10 years at room temperature

(f<3.33×10-9Hz at T=300 K), than diameter of spherical grain is 9 nm.

where ΔW = KuV (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 Ni81Fe19 (permalloy) films P1 and P2.These films are all deposited on the top of substrate which consists of insulators (Al2O3 and TiC). The gapwidth is defined by the thickness of Al2O3 insulation layer between P1 and P2 hich is below 100 nm.

Micrograph of the write/read head taken by SEM from the ABS side.

Aim for applicationMagnetic properties optimization of

ML (Fe97Al3)85N15/Al2O3 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)