Magnetic Properties of Materials (Ch. 14-17, 재료과학 Ch. 20)

Dae Yong JEONG

Inha University

Magnetics (Recall your memory)

Earth is a huge magnetic.

Current (charge movement) magnetic field :

Motor

Magnetic field change current generation :

generator

“Electro-magnetic” wave : always together

Maxwell Eq. for Electro-magnetic properties

0

B

E

t

DJH

t

BE

Current flow magnetic flux

magnetic field change electric current flow and displacement change

Source of electric property charge (material)

Source of magnetic property No material

Magnetics (Recall your memory)

Question

Electric current,

Electron (charge) is a real material with (-) charge.

Electron and hole can be separated into each element.

But, magnetic current??

Always magnetic wave, field, flux

Are there any materials which have only (N) pole or (S) pole?

(N) and (S) are always together.

Magnetics (Recall your memory)

Materials

Many Metallic (magnetic)

High power electric vehicle

…

Ceramic magnetic (electrically insulator)

Plastic magnetic for sticker on Restaurants near campus:

composite of polymer and ceramic magnetic

Rust : Fe3O4 (FeO-Fe2O3) iron ferrite

Any polymeric magnetics? RARE

Magnetic Properties

왜 어떤 물질은 자석에 붙고, 어떤 물질은 붙지 않을까?

외부 자기장의 변화에 따라 어떤 반응을 보이는가?

5

11.1. Basic concept and Equation

Current magnetic field

Maxwell Eq. (경험법칙)

nm IAuμ Current

Area circled by current

Unit vector

normal to the

surface

Magnetic

moment

전류가 흐르면 자기장

(물질이 아닌 개념)이 형성됨

물질로 이해를 하면

(magnetic dipole이 moment

를 가진다)

μm

μn

A

I

Characteristics of Magnetic dipole moment

외부에서 자기장을 magnetic dipole에 걸어주면 (즉

자기력선 안에 magnetic dipole를 놓아두면)

magnetic dipole은 힘을 받아서 자기력선의 방향으로

배열됨. (magnetic dipole moment가 변화한다.)

Magnetic dipole 은 마치 자석처럼 역할을 함.

Magnetic dipole moment의 크기(세기)는 자석에서 나오는 자기력선 개수로 생각할 수 있음.

(자석이 세다 자기력선이 촘촘하게 나온다. 즉 자기력선의 면적밀도가

높다)

μm

A

I

B

B

Origin of magnetic dipole momentum in Materials

orbiting electron Spinning electron

(up/down)

Electron movement current magnetic dipole moment

Electron (material) movement ??

Lm

e

e2orb

2

e

period

eI

dt

dQ

2

22 r

erIorb

2)( rmrvmL e

rv

e 전자(물질)이 가지는

orbital angular

momentum

Sm

e

e

pin s

e

s

e

z

e

zm

em

m

eS

m

e

2

em

e

2

Z방향으로의 momentum

Bohr magneton

9.27 10-24 A m2 or J T-1.

-e

ω r A

I

L

μorb

=

Sz S

μz μspin

B

z

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

EX)

The isolated Fe atom has 4 unpaired spins and a spin magnetic moment of

4

11.1. Equation Current Generate the magnetic dipole (가상개념) moment

Field 개념을 도입하여 이해하면 어떠할까? (~ Electric field ; E = V/m) 영구자석은 외부에서 직접 전류를 흘러주지 않아도 자석이잖아요?

Current를 Magnetic field로 연계시켜 이해

즉, Magnetic field (H)를 가했더니 Magnetic dipole이 형성되고

최종적으로: Dipole에 의해서 여러 magnetic properties이 나타난다.

l

NIH

Current-turn/length

Ampere-turn/meter A/m or Oe

Magnetic induction Magnetic field가 가해지면 magnetic dipole moment이 형성

형성되는 dipole moment크기는 ‘(자기력선/단위 면적)= magnetic flux density 이 얼마나 큰가”로 이해할 수 있을 것임.

In vacuum

HBo 0 mH /10257.1104 57

0

er)(Henry/met /

)Vacuum(in ty permeabili :0

mHWb/A-m

투자율

11.1. Equation

HB Magnetic flux density: # of magnetic field line/unit area

er)(Henry/met / )(ty permeabili :

/]mweber[ 22

mHWb/A-m

teslamWb

투자율

Relative permeability 0

r

(a) Consider a long solenoid. With free space as medium inside, the

magnetic field is B0.

(b) A material medium inserted into the solenoid develops a

magnetization M.

11.1. Equation

외부 magnetic field를 재료에 가해주면, Magnetization 된다.

재료내부 magnetic dipole moment가 변화 (즉, 외분 전류에 의해

재료에 가상 전류가 생성된다고 이해)

Due to applied field (vacuum) + enhanced flux density MHB oo

HM m

HHHHB romomoo 1

essDimensionl :litysusceptibi magnetic :m

11.1. Magnetic Units

From Electronic properties of materials, Fourth Edition, Hummel (© Springer, 2010)

11.3. Magnetic material classification 외부 magnetic field (H) 변화에 따라, 어떤 Magnetization (M) 변화를 보이는가? 어떤 B의 변화를 보이는가?

MHB oo

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Diamagnetism

Diamagnetism (c) No momentum in materials itself

Apply external M-field to reduce the external M-field

Material generates M-moment opposite direction.

From The Structures and Properties of Materials, Vol. 4, R. M. Rose, L. A. Shepard and J. Wulff(© John Wiley & Sons, 1966)

Paramagnetic Materials

(a) In a paramagnetic material each individual atom possesses a permanent

magnetic moment, but due to thermal agitation there is no average moment per

atom and M = 0.

(주의: Dielectric에서 paraelectric은 자체가 dipole을 가지지 않음.)

(b) In the presence of an applied field, individual magnetic moments take alignments

along the applied field and M is finite and along B.

A paramagnetic material

placed in a non-uniform

magnetic field experiences a

force towards greater fields.

This attracts the paramagnetic

material (e.g. liquid oxygen)

towards a permanent magnet.

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Ferromagnetic Materials

MB o

Ferromagnetism: α-ferrite, Co, Ni, Gd… magnetic momentum itself

After applying M-field, align the magnetic momentum. removal M-field, remain alignment Cf) paramagnetic No alignment due to thermal fluctuation

H << M

Small external M-field Large Magnetization

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Antiferromagnetic Materials In this antiferromagnetic BCC crystal

(Cr) the magnetic moment of the

center atom is cancelled by the

magnetic moments of the corner

atoms (an eighth of the corner atom

belongs to the unit cell). MnO

eTemperatur Neel :

T

C

T

C

From Electronic properties of materials, Fourth Edition, Hummel (© Springer, 2010)

Ferrimagnetic Materials

Ferrimagnetism: Fe3O4 (ferrite), Garnet (M3Fe5O12)… Anti-parallel alignment but different magnitude of magnetic momentum

None zero Net magnetic moment

Without M-field (H) : Net Magnetization

Hysteresis

Inverse Spinel structure

Large saturated magnetization and electrical insulating (less edge current less heating) high frequency applications

FeO-Fe2O3 • O-2: not magnetic momentum • Fe+3: octahedral cancellation Fe+3:

tetrahedral • Fe+2: tetrahedral contributes net

magnetization

Fe2+ : Mn2+: Ni2+: Cu2+: Co2+ different magnetization

α-ferrite for crystal structure of pure iron.

Ferrite is for general ceramic ferrimagnetic materials.

From Engineering Materials and Their Applications, Fourth Edition, (© John Wiley & Sons, 1990)

From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Normalized saturated magnetization vs. reduced temperature T/TC where TC is

the Curie temperature (Pure: Fe 1043 K).

11.4. Temp effect on Magnetism (ferro, ferri)

Fig 8.30 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

Schematic illustration of magnetic domains in the grains of an unmagnetized

polycrystalline iron sample. Very small grains have single domains.

11.5. Grain –Domain Polycrystalline magnetic

Fe는 근본적(전자구조)으로 강자성체라고 하는데…

왜 우리 주위에서 쉽게 보는 못은 자석(영구)이 아닌가?

11.5. Domain (microstructure) Domain

the region where magnetic momentum is aligned along the same direction.

(ferromagnetism, ferrimagnetism)

Domain wall (Bloch wall)

Fig 20-11, 20-12

~ 50nm thickness

From The Structures and Properties of Materials, Vol. 4, R. M. Rose, L. A. Shepard and J. Wulff(© John Wiley & Sons, 1966)

11.5. Hysteresis (ferro, ferri)

어렸을 때 경험

준비물: 큰 못, 작은 핀, 막대자석

못은 서로 붙지 않는다. (왜?)

막대자석을 못에 가까이 대면, 못이 자석에 붙는다. 못에 작은 핀도 붙는다. (왜?)

못을 자석에 붙여 놓고 짧은 시간 후에: 못을 자석에서 떼어내면, 못에 붙어 있던 작은 핀도 못에서 떨어진다. (왜?)

못을 자석에 붙여 놓고 오랜 시간이 흐른 후에: 못을 자석에서 떼어내어도, 작은 핀은 여전히 못에 붙어 있다. (왜?)

더욱 시간이 지나면, 못에 붙어 있던 작은 핀도 못에서 떨어진다.(왜?)

철에 바늘이 붙어 있음

자석에 바늘이 붙어 있음

Fig 8.31 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

M vs. H behavior of a previously unmagnetized polycrystalline iron specimen. An example grain in the

unmagnetized specimen is that at O. (a) Under very small fields the domain boundary motion is reversible.

(b) The boundary motions are irreversible and occur in sudden jerks. (c) Nearly all the grains are single

domains with saturation magnetizations in the easy directions. (d) Magnetizations in individual grains have to

be rotated to align with the field, H. (e) When the field is removed the specimen returns along d to e. (f) To

demagnetize the specimen we have to apply a magnetizing field of Hc in the reverse direction.

11.5. Hysteresis (ferro, ferri)

Hysteresis Magnetic field change the magnitude of

magnetic momentum

Lager magnetic field rotates the magnetic momentum opposite direction

Fig 8.32 From Principles of Electronic Materials and Devices, Third Edition, S.O. Kasap (© McGraw-Hill, 2005)

(a) A typical M vs. H hysterisis curve

(b) The corresponding B vs. H hysterisis curve. The shaded area inside

the hysterisis loop Is the energy loss per unit volume per cycle.

How to fabricate the magnetics?

metallic

ceramic

Melting

elements

powder

Reaction

Raw materials

forming

crushing

Sintering,

at highT

At RT

Random distribution

Net M = 0

Magnetization

With H (Hysteresis)

At RT

Net M is not zero.

(ferro, ferri)