1

Magnetic Properties of Materials

dx

dHHVF 0

… force in direction

… sample volume

… magnetic susceptibility

… magnetic field

… gradient of the magnetic field

The magnetic susceptibility characterizes the magnetic properties of materials

2

Other Parameters

VM

MAH

AB

HHB

HM

MHB

dx

dHHVF

m

0

1

1

0

0

00

0 … force acting on a material

… permeability

(similar to permittivity: = 1 + P/[0E])

… magnetic induction

… magnetization

… magnetic flux (B… magnetic flux density)

… magnetization and magnetic moment

3

Magnetic Properties of Materials

… plus antiferromagnetic and ferrimagnetic

4

Interaction with an External Magnetic Field

Material Interaction

Diamagnetic Is repelled by the applied magnetic field

Paramagnetic Are attracted by the applied magnetic field with different forces

Ferromagnetic

Antiferromagnetic

Ferrimagnetic

5

DiamagnetismChange of the inner or atomic “electrical” current within an external magnetic field:

Change in angular velocity of strongly bound electrons

Rotation (circular movement) of free (metallic) electrons

6

Diamagnetism

Diamagnetic materials create an induced magnetic field (magnetization ) in a direction opposite to the external magnetic field, therefore the magnetic induction is small in the material.

0

0

BMH

MHB

Ideal diamagnetic materials are superconductors in the superconducting state (Meissner effect)

1

0

H

M

… negative in diamagnetic materials

7

Paramagnetism

Without an external magnetic field ( = 0), there is no magnetization of the material ( = 0), because the magnetic moments of single atoms (electrons) are oriented randomly.

In an external magnetic field (H > 0), the magnetic moments of single atoms (electrons) are oriented in the direction of the external magnetic field M > 0.

Temperature vibrations disturb the orientation of magnetic moments susceptibility depends on temperature.

00 MH 00 MH

𝐻

8

Paramagnetism

𝐻

𝑀 0H

M

(a) … Curie’s law

(b), (c) … Curie-Weiss law for paramagnetic materials

(d) … diamagnetic material

T

CT

C … Curie

… Curie-Weiss

9

Paramagnetism

Meaning of constants and in Curie’s law and the Curie-Weiss law

Magnetism of electrons in an atom (orbital electrons)

B

m

B

m

B

m

k

nC

T

C

Tk

n

H

M

Tk

HnM

3

3

3

02

02

orbitpara

02

… number of magnetic moments (atoms)

Molecular field theory* (Weiss 1907)

C

T

C

CT

C

H

M

CT

CHM

T

C

MH

M

H

M

MH

HHH

extext

ext

exttotaltotal

mol

molexttotal

* Belongs to the mean field theory

10

Spin ParamagnetismAdditional effect to the orbital magnetism

Elements with 3d electrons (occupation of orbitals is described by Hund’s rules):

Fe: 3s2, 3p6, 3d6 Spin magnetic

Co: 3s2, 3p6, 3d7 Spin magnetic

Ni: 3s2, 3p6, 3d8 Spin magnetic

Cu: 3s2, 3p6, 3d10 Not spin magnetic

Zn: 3s2, 3p6, 3d10 Not spin magnetic

11

Elements with 3d Electrons

Ferromagnetism

The major characteristics of ferromagnetic materials

• Ordering of magnetic moments below

• Saturation of magnetization

• Transition ferromagnetic paramagnetic at

• Temperature dependency of 12

13

Magnetic Properties of Ferromagnetic Materials – Examples

770°C1131°C358°C

15.8°C

14

Influence of Real Structure(Residual Stress)

on magnetic properties of ferromagnetic materials

Nickel (fcc) Iron (bcc)

15

Influence of Real Structure (Crystallite Orientation)on magnetic properties of ferromagnetic

materials

Crystal anisotropy of magnetic properties (magnetization)

The average of physical properties is measured

Example: iron single crystal

16

Permanent Magnets

Wide hysteresis curve is needed

17

Materials for Permanent Magnets

18

Magnetoelastic Effects

Magnetostriction

Change in length (in the lattice parameters) of magnetic crystals within a magnetic field

Spontaneous magnetostriction

Change in length (lattice parameters) of magnetic crystals in the own magnetic field

Observed in some materials below – at the ordering of magnetic moments

19

Spontaneous Magnetostriction

o

a

b

c

ErCo2

RT: Fd-3m

LT: R-3m

= 90° 90°

20

Spontaneous MagnetostrictionSeparation of crystallographically non-equivalent diffraction lines

21

MagnetostrictionCoefficients of magnetostriction in Er(Co,Ge)2 and Er(Co,Si)2

22

Er(Co1-xSix)2

Increase of lattice parameters (volume of unit cell) at low temperatures

Ordering of magnetic moments magnetic interactions between single atoms Change of the crystal structure

23

AntiferromagnetismOrdering of magnetic moments below ( … Néel temperature)

Example: MnO, UN (fcc, Fm3m, NaCl structure), MnF2

Antiparallel ordering of magnetic moments

Negative critical temperature:

T

C

T

C

Susceptibility in paramagnetic state

24

Experimental Methods to Investigate the Orientation of

Magnetic Moments

Neutron diffraction

Elastic scattering of neutrons on atomic nuclei Information about the crystal structure (similar to x-ray diffraction)

Interaction between the magnetic moments of the neutrons and the magnetic moments of atoms information about the magnetic structure

25

Magnetic Properties of Antiferromagnetic Materials – Examples

UN = 53 K = 247 KCrN = 273-286 K

26

Influence of Real Structureon magnetic properties of antiferromagnetic

materials

T (K)

0 50 100 150 200 250 300

(1

0-8 m

3 /mo

l)

0

2

4

6

8

10

12Ts = 200 oC

400 oC

UN s.c.

Thin layers of UN

Different temperature of coating different residual stress, crystallite sizes and density of defects

Formation of an apparent ferromagnetic component at low temperatures unbalanced magnetic moments

UN = 53 K = 247 K

27

FerrimagnetismSpontaneous ordering of magnetic moments and hysteresis below the Curie temperature as in ferromagnetic materials

A ferrimagnetic compound is typically a ceramic material (ferrite – FeO.Fe2O3, NiO.Fe2O3, CuO.Fe2O3, …) with spinel structure.

o

a

b

c

28

Susceptibility and Magnetization of Ferrimagnetic Materials

NiO.Fe2O3

29

GMR EffectGiant Magnetoresistance in Multilayers

dia

ferro

dia

ferro

H = 0

dia

ferro

dia

ferro

H > 0

Diamagnetic material: Cu, Ag, Au

Ferromagnetic material: Fe, Co, Ni

I I

30

Physical Principle of GMRScattering depends on the relative orientations of the electron spins and the magnetic moments of atoms.Parallel: weakest scattering Antiparallel: strongest scattering

Antiferromagnetic coupling of two ferromagnetic layers above a diamagnetic layer

Nobel prize in physics 2007

31

Peter Andreas Grünberg

Albert Louis François Fert

For discovery of the giant magneto-resistance effect

32

Change of the Electrical Resistance in an External Magnetic Field

0

0

H

HHR

Definition of GMR:

33

Change of Electrical Resistance in an External Magnetic Field

-100 -50 0 50 100

0

5

10

15

20

25

B (mT)

-100 -50 0 50 1000

5

10

15

20

25

GM

R (

%)

B (mT)

System: Co/Cu

34

Important Parameters of Magnetic Multilayers

• Selection of materials (diamagnetic, ferromagnetic)

• Thickness of layers• Roughness and morphology of

the interfaces

Methods for investigation• Measurement of the resistance

within a variable magnetic field• XRD, neutron diffraction• TEM

Applications• Magnetic field sensors

(reading heads for hard disks)• Solenoid valves (Spin valves)

10 nm

35

Influence of Thickness of “Spacers”

CoCu . . . . .CoCu

50x

on magnetic properties of multilayers

36

Reading Head in a Hard Disk

Pros:

Very small dimensions

[(Co 11Å/ Cu 22 Å) x 50] =

= 1650 Å = 165 nm = 0.165 m

37

Storage capacity

Areal Density

10

100

1000

10000

100000

1980 1985 1990 1995 2000 2005

Date of General Availability

MB

/in2

Inductive Read Head

MR Read Head

GMR Read Head

Storage capacity

38

1980 1990 2000 2010 202010M

100M

1G

10G

100G

1T

10T

Cap

acity

(by

tes/

inch

2 )

Year

Inductive reading heads

Magneto-resistive reading heads

Reading heads with GMR effect