1. Magnetic Properties of Materials
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

2. Other Parameters … 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. 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

6. 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.
Ideal diamagnetic materials are superconductors in the superconducting state (Meissner effect)
… negative in diamagnetic materials

7. 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

8. Paramagnetism 𝑀 (a) … Curie’s law
(b), (c) … Curie-Weiss law for paramagnetic materials
(d) … diamagnetic material 𝐻
… Curie
… Curie-Weiss

9. Molecular field theory*
Paramagnetism
Meaning of constants 𝐶 and 𝜃 in Curie’s law and the Curie-Weiss law
Magnetism of electrons in an atom (orbital electrons)
Molecular field theory*
(Weiss 1907)
𝑛 … number of magnetic moments (atoms)
* Belongs to the mean field theory

10. Additional effect to the orbital magnetism
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

11. Elements with 3d Electrons

12. Ferromagnetism The major characteristics of ferromagnetic materials
Ordering of magnetic moments below 𝑇 c
Saturation of magnetization
Transition ferromagnetic  paramagnetic at 𝑇 c
Temperature dependency of 𝑀 s

13. Magnetic Properties of Ferromagnetic Materials – Examples

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
Example:
iron single crystal
Crystal anisotropy of magnetic properties (magnetization)
The average of physical properties is measured

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 𝑇c – at the ordering of magnetic moments

19. Spontaneous Magnetostriction
ErCo2
RT: Fd-3m
LT: R-3m
 = 90°    90°

20. Spontaneous Magnetostriction
Separation of crystallographically non-equivalent diffraction lines

21. Coefficients 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. Ordering of magnetic moments below 𝑇 c ( 𝑇 N … Néel temperature)
Antiferromagnetism
Ordering of magnetic moments below 𝑇 c ( 𝑇 N … Néel temperature)
Example: MnO, UN (fcc, Fm3m, NaCl structure), MnF2
Antiparallel ordering of magnetic moments
Negative critical temperature:
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 𝑇N = 53 K −𝜃 = 247 K
CrN 𝑇N = K

26. Influence of Real Structure
on magnetic properties of antiferromagnetic materials
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 𝑇N = 53 K −𝜃 = 247 K

27. 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.

28. Susceptibility and Magnetization of Ferrimagnetic Materials
NiO.Fe2O3

29. 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

30. 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

31. Nobel prize in physics 2007
For discovery of the giant magneto-resistance effect
Peter Andreas Grünberg
Albert Louis François Fert

32. Change of the Electrical Resistance in an External Magnetic Field
Definition of GMR:

33. Change of Electrical Resistance in an External Magnetic Field
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”
on magnetic properties of multilayers Co Cu .
50x

36. Reading Head in a Hard Disk
Pros:
Very small dimensions
[(Co 11Å/ Cu 22 Å) x 50] =
= 1650 Å = 165 nm = m

37. Storage capacity

38. Storage capacity Reading heads with GMR effect
Magneto-resistive reading heads
Inductive reading heads