Magnetic Properties of Materials
F  V0 H
dH
dx
𝐹 … force in 𝑥 direction
𝑉 … sample volume
𝜒…
magnetic susceptibility
𝐻 … magnetic field
𝑑𝐻/𝑑𝑥 … gradient of the magnetic
field
The magnetic susceptibility 𝜒
characterizes the magnetic
properties of materials
1
Other Parameters
F  V0 H
dH
dx
  1 



B  0 H  0 M


M  H



B  1    0 H  H
 
  B A
 

  0 H  A  M  0
  m
M
V
… 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
2
Magnetic Properties of Materials
… plus
antiferromagnetic
and ferrimagnetic
3
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
4
Diamagnetism
Change 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
5
Diamagnetism
Diamagnetic materials create an induced magnetic field
(magnetization 𝑀) in a direction opposite to the external magnetic
field, therefore the magnetic induction 𝐵 is small in the material.



 
B  0 H  M



H  M  B  0
Ideal diamagnetic materials are superconductors in the
superconducting state (Meissner effect)

M
   0
H
  1
… negative in diamagnetic
materials
6
Paramagnetism
Without an external magnetic field (𝐻 = 0), there is no magnetization
of the material (𝑀 = 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.
𝐻
H  0  M  0
H  0  M  0
7
Paramagnetism

M
   0
H
𝑀
(a) …
𝐻

C
T
… Curie

C
T 
… Curie-Weiss
Curie’s law
(b), (c) … Curie-Weiss law for
paramagnetic materials
(d) …
diamagnetic material
8
Paramagnetism
Meaning of constants 𝐶 and 𝜃 in Curie’s law and the Curie-Weiss law
Magnetism of electrons in an
atom (orbital electrons)
n m2  0 H
M
3k BT
2
n

 C
M
orbit
 para

 m 0 
H
3k BT
T
n m2  0
C
3k B
𝑛 … number of magnetic moments
(atoms)
Molecular field theory*
(Weiss 1907)
H total  H ext  H mol
H mol  M
 total 
C
M
M


H total H ext  M T
H ext C
T  C
C
C
M



H ext T  C T  
M
 ext
  C
9
* Belongs to the mean field theory
Spin Paramagnetism
Additional 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
10
Elements with 3d Electrons
11
Ferromagnetism
The major characteristics of
ferromagnetic materials
• Ordering of magnetic moments below 𝑇c
• Saturation of magnetization
• Transition ferromagnetic 
paramagnetic at 𝑇c
• Temperature dependency of 𝑀s
12
Magnetic Properties of Ferromagnetic
Materials – Examples
770°C
1131°C
358°C
15.8°C
13
Influence of Real Structure
(Residual Stress)
on magnetic properties of ferromagnetic
materials
Nickel (fcc)
Iron (bcc)
14
Influence of Real Structure
(Crystallite Orientation)
on magnetic properties of ferromagnetic
materials
Example:
iron single crystal
Crystal anisotropy of magnetic properties (magnetization)
The average of physical properties is measured
15
Permanent Magnets
Wide hysteresis curve
is needed
16
Materials for Permanent Magnets
17
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 𝑇c – at the ordering of magnetic
moments
18
Spontaneous Magnetostriction
b
ErCo2
RT: Fd-3m
LT: R-3m
 = 90°    90°
a
o
c
19
Spontaneous Magnetostriction
Separation of crystallographically non-equivalent diffraction lines
20
Magnetostriction
Coefficients of magnetostriction in Er(Co,Ge)2 and Er(Co,Si)2
21
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
22
Antiferromagnetism
Ordering of magnetic moments below 𝑇c (𝑇N … Néel temperature)
Example: MnO, UN (fcc,
Fm3m, NaCl structure),
MnF2
Antiparallel ordering of
magnetic moments
Negative critical temperature:

C
C

T     T  
Susceptibility in paramagnetic state
23
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
24
Magnetic Properties of Antiferromagnetic
Materials – Examples
UN 𝑇N = 53 K −𝜃 = 247 K
CrN 𝑇N = 273-286 K
25
Influence of Real Structure
on magnetic properties of antiferromagnetic
materials
UN
𝑇N = 53 K
 (10-8 m3/mol)
12
−𝜃 = 247 K
o
10
Ts = 200 C
8
400 C
o
6
4
UN s.c.
2
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
0
0
50
100 150 200 250 300
T (K)
26
Ferrimagnetism
Spontaneous 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.
b
o
a
c
27
Susceptibility and Magnetization of
Ferrimagnetic Materials
NiO.Fe2O3
28
GMR Effect
Giant Magnetoresistance in Multilayers
Diamagnetic material: Cu, Ag, Au
Ferromagnetic material: Fe, Co, Ni
dia
dia
ferro
ferro
I
I
dia
dia
ferro
ferro
H=0
H>0
29
Physical Principle of GMR
Scattering 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
30
Nobel prize in physics 2007
For discovery of the giant magneto-resistance effect
Peter Andreas
Grünberg
Albert Louis François Fert
31
Change of the Electrical Resistance
in an External Magnetic Field
Definition of GMR:
R



 H    H  0
 H  0
32
G M R (% )
Change of Electrical Resistance in an
External Magnetic Field
25
25
20
20
15
15
10
10
5
5
0
-100
0
-50
0
B (mT )
50
100
-100
System: Co/Cu
-50
0
B (mT )
50
100
33
Important Parameters of Magnetic
Multilayers
• Selection of materials
(diamagnetic, ferromagnetic)
• Thickness of layers
• Roughness and morphology of
the interfaces
10 nm
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)
34
Influence of Thickness of “Spacers”
on magnetic properties of multilayers
Co
Cu
.
.
.
.
.
Co
Cu
50x
35
Reading Head in a Hard Disk
Pros:
Very small dimensions
[(Co 11Å/ Cu 22 Å) x 50] =
= 1650 Å = 165 nm = 0.165 m
36
Storage capacity
Areal Density
100000
GMR Read Head
MB/in
2
10000
MR Read Head
1000
100
Inductive Read Head
10
1980
1985
1990
1995
2000
2005
Date of General Availability
37
Storage capacity
1T
2
Capacity (bytes/inch )
10T
100G
10G
Reading heads
with GMR effect
1G
Magneto-resistive
reading heads
100M
Inductive reading heads
10M
1980
1990
2000
Year
2010
2020
38